Subgroup Information for GL2_13
Created in GAP4 by M. Schaps
- H
= C1=
SM_1 of order 1. Class: 1 Length: 1 Order: 1
G = (C13XC13):H =
SM_2 of order 169
k(B) = 169, l(B) = 1
- H
= C2=
SM_1 of order 2. Class: 2 Length: 1 Order: 2
G = (C13XC13):H =
SM_4 of order 338
k(B) = 86, l(B) = 2
- H
= C2=
SM_1 of order 2. Class: 3 Length: 182 Order: 2
G = (C13XC13):H =
SM_3 of order 338
k(B) = 104, l(B) = 2
- H
= C3=
SM_1 of order 3. Class: 4 Length: 1 Order: 3
G = (C13XC13):H =
SM_4 of order 507
k(B) = 59, l(B) = 3
- H
= C3=
SM_1 of order 3. Class: 5 Length: 91 Order: 3
G = (C13XC13):H =
SM_5 of order 507
k(B) = 59, l(B) = 3
- H
= C3=
SM_1 of order 3. Class: 6 Length: 182 Order: 3
G = (C13XC13):H =
SM_3 of order 507
k(B) = 91, l(B) = 3
- H
= C4=
SM_1 of order 4. Class: 7 Length: 1 Order: 4
G = (C13XC13):H =
SM_10 of order 676
k(B) = 46, l(B) = 4
Non-trivial central extensions by C2:
C8 =
SM_1
of order 8
, k(B2) = 46, l(B2) = 4;
SM_19
of order 1352
- H
= C2XC2=
SM_2 of order 4. Class: 8 Length: 91 Order: 4
G = (C13XC13):H =
SM_13 of order 676
k(B) = 64, l(B) = 4
Maximal subgroups: H1 =C2
H2 =C2
H3 =C2
Non-trivial central extensions by C2:
C4XC2 =
SM_2
of order 8
, k(B2) = 64, l(B2) = 4;
SM_23
of order 1352
D8 =
SM_3
of order 8
, k(B2) = 61, l(B2) = 1;
SM_25
of order 1352
Q8 =
SM_4
of order 8
, k(B2) = 61, l(B2) = 1;
SM_26
of order 1352
- H
= C4=
SM_1 of order 4. Class: 9 Length: 91 Order: 4
G = (C13XC13):H =
SM_11 of order 676
k(B) = 46, l(B) = 4
Non-trivial central extensions by C2:
C8 =
SM_1
of order 8
, k(B2) = 46, l(B2) = 4;
SM_20
of order 1352
- H
= C4=
SM_1 of order 4. Class: 10 Length: 182 Order: 4
G = (C13XC13):H =
SM_12 of order 676
k(B) = 55, l(B) = 4
Non-trivial central extensions by C2:
C8 =
SM_1
of order 8
, k(B2) = 55, l(B2) = 4;
SM_21
of order 1352
- H
= C4=
SM_1 of order 4. Class: 11 Length: 182 Order: 4
G = (C13XC13):H =
SM_9 of order 676
k(B) = 91, l(B) = 4
Non-trivial central extensions by C2:
C8 =
SM_1
of order 8
, k(B2) = 91, l(B2) = 4;
SM_18
of order 1352
- H
= C6=
SM_2 of order 6. Class: 12 Length: 1 Order: 6
G = (C13XC13):H =
SM_9 of order 1014
k(B) = 34, l(B) = 6
Maximal subgroups: H1 =C3
H2 =C2
- H
= C6=
SM_2 of order 6. Class: 13 Length: 91 Order: 6
G = (C13XC13):H =
SM_10 of order 1014
k(B) = 34, l(B) = 6
Maximal subgroups: H1 =C3
H2 =C2
- H
= C6=
SM_2 of order 6. Class: 14 Length: 182 Order: 6
G = (C13XC13):H =
SM_11 of order 1014
k(B) = 40, l(B) = 6
Maximal subgroups: H1 =C3
H2 =C2
- H
= C6=
SM_2 of order 6. Class: 15 Length: 182 Order: 6
G = (C13XC13):H =
SM_14 of order 1014
k(B) = 56, l(B) = 6
Maximal subgroups: H1 =C3
H2 =C2
- H
= C6=
SM_2 of order 6. Class: 16 Length: 182 Order: 6
G = (C13XC13):H =
SM_12 of order 1014
k(B) = 40, l(B) = 6
Maximal subgroups: H1 =C3
H2 =C2
- H
= C6=
SM_2 of order 6. Class: 17 Length: 182 Order: 6
G = (C13XC13):H =
SM_13 of order 1014
k(B) = 50, l(B) = 6
Maximal subgroups: H1 =C3
H2 =C2
- H
= C6=
SM_2 of order 6. Class: 18 Length: 182 Order: 6
G = (C13XC13):H =
SM_8 of order 1014
k(B) = 104, l(B) = 6
Maximal subgroups: H1 =C3
H2 =C2
- H
= S3=
SM_1 of order 6. Class: 19 Length: 364 Order: 6
G = (C13XC13):H =
SM_7 of order 1014
k(B) = 49, l(B) = 3
Maximal subgroups: H1 =C3
H2 =C2
H3 =C2
H4 =C2
- H
= C7=
SM_1 of order 7. Class: 20 Length: 78 Order: 7
G = (C13XC13):H =
SM_2 of order 1183
k(B) = 31, l(B) = 7
- H
= C8=
SM_1 of order 8. Class: 21 Length: 78 Order: 8
G = (C13XC13):H =
SM_40 of order 1352
k(B) = 29, l(B) = 8
Non-trivial central extensions by C2:
C16 =
SM_1
of order 16
, k(B2) = 29, l(B2) = 8
- H
= Q8=
SM_4 of order 8. Class: 22 Length: 91 Order: 8
G = (C13XC13):H =
SM_44 of order 1352
k(B) = 26, l(B) = 5
Maximal subgroups: H1 =C4
H2 =C4
H3 =C4
Non-trivial central extensions by C2:
(C4:C4) =
SM_4
of order 16
, k(B2) = 26, l(B2) = 5
- H
= C4XC2=
SM_2 of order 8. Class: 23 Length: 91 Order: 8
G = (C13XC13):H =
SM_41 of order 1352
k(B) = 38, l(B) = 8
Maximal subgroups: H1 =C4
H2 =C2XC2
H3 =C4
Non-trivial central extensions by C2:
C4XC4 =
SM_2
of order 16
, k(B2) = 38, l(B2) = 8
(C2XC2):C4 =
SM_3
of order 16
, k(B2) = 32, l(B2) = 2
(C4:C4) =
SM_4
of order 16
, k(B2) = 32, l(B2) = 2
C2XC8 =
SM_5
of order 16
, k(B2) = 38, l(B2) = 8
C8:C2 =
SM_6
of order 16
, k(B2) = 32, l(B2) = 2
- H
= C4XC2=
SM_2 of order 8. Class: 24 Length: 182 Order: 8
G = (C13XC13):H =
SM_42 of order 1352
k(B) = 56, l(B) = 8
Maximal subgroups: H1 =C4
H2 =C4
H3 =C2XC2
Non-trivial central extensions by C2:
C4XC4 =
SM_2
of order 16
, k(B2) = 56, l(B2) = 8
(C2XC2):C4 =
SM_3
of order 16
, k(B2) = 50, l(B2) = 2
(C4:C4) =
SM_4
of order 16
, k(B2) = 50, l(B2) = 2
C2XC8 =
SM_5
of order 16
, k(B2) = 56, l(B2) = 8
C8:C2 =
SM_6
of order 16
, k(B2) = 50, l(B2) = 2
- H
= D8=
SM_3 of order 8. Class: 25 Length: 273 Order: 8
G = (C13XC13):H =
SM_43 of order 1352
k(B) = 44, l(B) = 5
Maximal subgroups: H1 =C4
H2 =C2XC2
H3 =C2XC2
Non-trivial central extensions by C2:
(C2XC2):C4 =
SM_3
of order 16
, k(B2) = 44, l(B2) = 5
(C4:C4) =
SM_4
of order 16
, k(B2) = 44, l(B2) = 5
D16 =
SM_7
of order 16
, k(B2) = 41, l(B2) = 2
C8:C2 =
SM_8
of order 16
, k(B2) = 41, l(B2) = 2
GQ16 =
SM_9
of order 16
, k(B2) = 41, l(B2) = 2
- H
= C3XC3=
SM_2 of order 9. Class: 26 Length: 91 Order: 9
G = (C13XC13):H =
SM_9 of order 1521
k(B) = 49, l(B) = 9
Maximal subgroups: H1 =C3
H2 =C3
H3 =C3
H4 =C3
Non-trivial central extensions by C3:
C9XC3 =
SM_2
of order 27
, k(B2) = 49, l(B2) = 9
(C3XC3):C3 =
SM_3
of order 27
, k(B2) = 41, l(B2) = 1
C9.C3 =
SM_4
of order 27
, k(B2) = 41, l(B2) = 1
- H
= C12=
SM_2 of order 12. Class: 27 Length: 1 Order: 12
G = (C13XC13):H of order 2028
k(B) = 26, l(B) = 12
Maximal subgroups: H1 =C6
H2 =C4
Non-trivial central extensions by C2:
C24 =
SM_2
of order 24
, k(B2) = 26, l(B2) = 12
- H
= C2XC2XC3=
SM_5 of order 12. Class: 28 Length: 91 Order: 12
G = (C13XC13):H of order 2028
k(B) = 32, l(B) = 12
Maximal subgroups: H1 =C6
H2 =C6
H3 =C6
H4 =C2XC2
Non-trivial central extensions by C2:
C2XC4XC3 =
SM_9
of order 24
, k(B2) = 32, l(B2) = 12
D8XC3 =
SM_10
of order 24
, k(B2) = 23, l(B2) = 3
Q8XC3 =
SM_11
of order 24
, k(B2) = 23, l(B2) = 3
- H
= C2XC2XC3=
SM_5 of order 12. Class: 29 Length: 91 Order: 12
G = (C13XC13):H of order 2028
k(B) = 32, l(B) = 12
Maximal subgroups: H1 =C6
H2 =C6
H3 =C6
H4 =C2XC2
Non-trivial central extensions by C2:
C2XC4XC3 =
SM_9
of order 24
, k(B2) = 32, l(B2) = 12
D8XC3 =
SM_10
of order 24
, k(B2) = 23, l(B2) = 3
Q8XC3 =
SM_11
of order 24
, k(B2) = 23, l(B2) = 3
- H
= C12=
SM_2 of order 12. Class: 30 Length: 91 Order: 12
G = (C13XC13):H of order 2028
k(B) = 26, l(B) = 12
Maximal subgroups: H1 =C6
H2 =C4
Non-trivial central extensions by C2:
C24 =
SM_2
of order 24
, k(B2) = 26, l(B2) = 12
- H
= C12=
SM_2 of order 12. Class: 31 Length: 91 Order: 12
G = (C13XC13):H of order 2028
k(B) = 26, l(B) = 12
Maximal subgroups: H1 =C6
H2 =C4
Non-trivial central extensions by C2:
C24 =
SM_2
of order 24
, k(B2) = 26, l(B2) = 12
- H
= C12=
SM_2 of order 12. Class: 32 Length: 91 Order: 12
G = (C13XC13):H of order 2028
k(B) = 26, l(B) = 12
Maximal subgroups: H1 =C6
H2 =C4
Non-trivial central extensions by C2:
C24 =
SM_2
of order 24
, k(B2) = 26, l(B2) = 12
- H
= C12=
SM_2 of order 12. Class: 33 Length: 182 Order: 12
G = (C13XC13):H of order 2028
k(B) = 41, l(B) = 12
Maximal subgroups: H1 =C6
H2 =C4
Non-trivial central extensions by C2:
C24 =
SM_2
of order 24
, k(B2) = 41, l(B2) = 12
- H
= C2XC2XC3=
SM_5 of order 12. Class: 34 Length: 182 Order: 12
G = (C13XC13):H of order 2028
k(B) = 64, l(B) = 12
Maximal subgroups: H1 =C6
H2 =C6
H3 =C6
H4 =C2XC2
Non-trivial central extensions by C2:
C2XC4XC3 =
SM_9
of order 24
, k(B2) = 64, l(B2) = 12
D8XC3 =
SM_10
of order 24
, k(B2) = 55, l(B2) = 3
Q8XC3 =
SM_11
of order 24
, k(B2) = 55, l(B2) = 3
- H
= C12=
SM_2 of order 12. Class: 35 Length: 182 Order: 12
G = (C13XC13):H of order 2028
k(B) = 49, l(B) = 12
Maximal subgroups: H1 =C6
H2 =C4
Non-trivial central extensions by C2:
C24 =
SM_2
of order 24
, k(B2) = 49, l(B2) = 12
- H
= C12=
SM_2 of order 12. Class: 36 Length: 182 Order: 12
G = (C13XC13):H of order 2028
k(B) = 29, l(B) = 12
Maximal subgroups: H1 =C6
H2 =C4
Non-trivial central extensions by C2:
C24 =
SM_2
of order 24
, k(B2) = 29, l(B2) = 12
- H
= C12=
SM_2 of order 12. Class: 37 Length: 182 Order: 12
G = (C13XC13):H of order 2028
k(B) = 169, l(B) = 12
Maximal subgroups: H1 =C6
H2 =C4
Non-trivial central extensions by C2:
C24 =
SM_2
of order 24
, k(B2) = 169, l(B2) = 12
- H
= C12=
SM_2 of order 12. Class: 38 Length: 182 Order: 12
G = (C13XC13):H of order 2028
k(B) = 34, l(B) = 12
Maximal subgroups: H1 =C6
H2 =C4
Non-trivial central extensions by C2:
C24 =
SM_2
of order 24
, k(B2) = 34, l(B2) = 12
- H
= GQ12=
SM_1 of order 12. Class: 39 Length: 182 Order: 12
G = (C13XC13):H of order 2028
k(B) = 20, l(B) = 6
Maximal subgroups: H1 =C6
H2 =C4
H3 =C4
H4 =C4
Non-trivial central extensions by C2:
C3:C8 =
SM_1
of order 24
, k(B2) = 20, l(B2) = 6
- H
= C12=
SM_2 of order 12. Class: 40 Length: 182 Order: 12
G = (C13XC13):H of order 2028
k(B) = 41, l(B) = 12
Maximal subgroups: H1 =C6
H2 =C4
Non-trivial central extensions by C2:
C24 =
SM_2
of order 24
, k(B2) = 41, l(B2) = 12
- H
= C12=
SM_2 of order 12. Class: 41 Length: 182 Order: 12
G = (C13XC13):H of order 2028
k(B) = 34, l(B) = 12
Maximal subgroups: H1 =C6
H2 =C4
Non-trivial central extensions by C2:
C24 =
SM_2
of order 24
, k(B2) = 34, l(B2) = 12
- H
= C12=
SM_2 of order 12. Class: 42 Length: 182 Order: 12
G = (C13XC13):H of order 2028
k(B) = 29, l(B) = 12
Maximal subgroups: H1 =C6
H2 =C4
Non-trivial central extensions by C2:
C24 =
SM_2
of order 24
, k(B2) = 29, l(B2) = 12
- H
= D12=
SM_4 of order 12. Class: 43 Length: 182 Order: 12
G = (C13XC13):H of order 2028
k(B) = 38, l(B) = 6
Maximal subgroups: H1 =S3
H2 =S3
H3 =C6
H4 =C2XC2
H5 =C2XC2
H6 =C2XC2
Non-trivial central extensions by C2:
C3:Q8 =
SM_4
of order 24
, k(B2) = 35, l(B2) = 3
S3XC4 =
SM_5
of order 24
, k(B2) = 38, l(B2) = 6
D24 =
SM_6
of order 24
, k(B2) = 35, l(B2) = 3
GQ12XC2 =
SM_7
of order 24
, k(B2) = 38, l(B2) = 6
D8PS3 =
SM_8
of order 24
, k(B2) = 35, l(B2) = 3
- H
= C12=
SM_2 of order 12. Class: 44 Length: 182 Order: 12
G = (C13XC13):H of order 2028
k(B) = 61, l(B) = 12
Maximal subgroups: H1 =C6
H2 =C4
Non-trivial central extensions by C2:
C24 =
SM_2
of order 24
, k(B2) = 61, l(B2) = 12
- H
= C12=
SM_2 of order 12. Class: 45 Length: 182 Order: 12
G = (C13XC13):H of order 2028
k(B) = 37, l(B) = 12
Maximal subgroups: H1 =C6
H2 =C4
Non-trivial central extensions by C2:
C24 =
SM_2
of order 24
, k(B2) = 37, l(B2) = 12
- H
= C14=
SM_2 of order 14. Class: 47 Length: 78 Order: 14
G = (C13XC13):H of order 2366
k(B) = 26, l(B) = 14
Maximal subgroups: H1 =C7
H2 =C2
- H
= D14=
SM_1 of order 14. Class: 48 Length: 156 Order: 14
G = (C13XC13):H of order 2366
k(B) = 35, l(B) = 5
Maximal subgroups: H1 =C7
H2 =C2
H3 =C2
H4 =C2
H5 =C2
H6 =C2
H7 =C2
H8 =C2
- H
= C4XC4=
SM_2 of order 16. Class: 49 Length: 91 Order: 16
G = (C13XC13):H of order 2704
k(B) = 49, l(B) = 16
Maximal subgroups: H1 =C4XC2
H2 =C4XC2
H3 =C4XC2
Non-trivial central extensions by C2:
(C2XC4):C4 =
SM_2
of order 32
, k(B2) = 37, l(B2) = 4
C4XC8 =
SM_3
of order 32
, k(B2) = 49, l(B2) = 16
C8:C4 =
SM_4
of order 32
, k(B2) = 37, l(B2) = 4
- H
= D8YC4=
SM_13 of order 16. Class: 50 Length: 91 Order: 16
G = (C13XC13):H of order 2704
k(B) = 34, l(B) = 10
Maximal subgroups: H1 =D8
H2 =D8
H3 =D8
H4 =C4XC2
H5 =C4XC2
H6 =C4XC2
H7 =Q8
Non-trivial central extensions by C2:
(C4XC2):C4 =
SM_24
of order 32
, k(B2) = 34, l(B2) = 10
D8XC4 =
SM_25
of order 32
, k(B2) = 34, l(B2) = 10
Q8XC4 =
SM_26
of order 32
, k(B2) = 34, l(B2) = 10
D8PD8 =
SM_28
of order 32
, k(B2) = 28, l(B2) = 4
((C2XC2):C4)PQ8 =
SM_29
of order 32
, k(B2) = 28, l(B2) = 4
(C4XC2XC2):C2 =
SM_30
of order 32
, k(B2) = 28, l(B2) = 4
(C4XC4):C2 =
SM_31
of order 32
, k(B2) = 28, l(B2) = 4
(C4XC4).C2 =
SM_32
of order 32
, k(B2) = 28, l(B2) = 4
(C4XC4):C2 =
SM_33
of order 32
, k(B2) = 28, l(B2) = 4
- H
= C8:C2=
SM_6 of order 16. Class: 51 Length: 273 Order: 16
G = (C13XC13):H of order 2704
k(B) = 25, l(B) = 10
Maximal subgroups: H1 =C4XC2
H2 =C8
H3 =C8
Non-trivial central extensions by C2:
C8:C4 =
SM_4
of order 32
, k(B2) = 25, l(B2) = 10
(C2XC2):C8 =
SM_5
of order 32
, k(B2) = 25, l(B2) = 10
C4:C8 =
SM_12
of order 32
, k(B2) = 25, l(B2) = 10
- H
= C2XC3XC3=
SM_5 of order 18. Class: 52 Length: 91 Order: 18
G = (C13XC13):H of order 3042
k(B) = 38, l(B) = 18
Maximal subgroups: H1 =C3XC3
H2 =C6
H3 =C6
H4 =C6
H5 =C6
Non-trivial central extensions by C3:
C2XC3XC9 =
SM_9
of order 54
, k(B2) = 38, l(B2) = 18
((C3XC3):C3)XC2 =
SM_10
of order 54
, k(B2) = 22, l(B2) = 2
(C9:C3)XC2 =
SM_11
of order 54
, k(B2) = 22, l(B2) = 2
- H
= C2XC3XC3=
SM_5 of order 18. Class: 53 Length: 182 Order: 18
G = (C13XC13):H of order 3042
k(B) = 56, l(B) = 18
Maximal subgroups: H1 =C3XC3
H2 =C6
H3 =C6
H4 =C6
H5 =C6
Non-trivial central extensions by C3:
C2XC3XC9 =
SM_9
of order 54
, k(B2) = 56, l(B2) = 18
((C3XC3):C3)XC2 =
SM_10
of order 54
, k(B2) = 40, l(B2) = 2
(C9:C3)XC2 =
SM_11
of order 54
, k(B2) = 40, l(B2) = 2
- H
= S3XC3=
SM_3 of order 18. Class: 54 Length: 364 Order: 18
G = (C13XC13):H of order 3042
k(B) = 35, l(B) = 9
Maximal subgroups: H1 =C3XC3
H2 =S3
H3 =C6
H4 =C6
H5 =C6
Non-trivial central extensions by C3:
S3XC9 =
SM_4
of order 54
, k(B2) = 35, l(B2) = 9
- H
= C21=
SM_2 of order 21. Class: 55 Length: 78 Order: 21
G = (C13XC13):H of order 3549
k(B) = 29, l(B) = 21
Maximal subgroups: H1 =C7
H2 =C3
- H
= C24=
SM_2 of order 24. Class: 56 Length: 78 Order: 24
G = (C13XC13):H of order 4056
k(B) = 31, l(B) = 24
Maximal subgroups: H1 =C12
H2 =C8
Non-trivial central extensions by C2:
C48 =
SM_2
of order 48
, k(B2) = 31, l(B2) = 24
- H
= C2XC4XC3=
SM_9 of order 24. Class: 57 Length: 91 Order: 24
G = (C13XC13):H of order 4056
k(B) = 34, l(B) = 24
Maximal subgroups: H1 =C12
H2 =C12
H3 =C2XC2XC3
H4 =C4XC2
Non-trivial central extensions by C2:
C4XC4XC3 =
SM_20
of order 48
, k(B2) = 34, l(B2) = 24
((C2XC2):C4)XC3 =
SM_21
of order 48
, k(B2) = 16, l(B2) = 6
GQ16XC3 =
SM_22
of order 48
, k(B2) = 16, l(B2) = 6
C2XC8XC3 =
SM_23
of order 48
, k(B2) = 34, l(B2) = 24
(C8:C2)XC3 =
SM_24
of order 48
, k(B2) = 16, l(B2) = 6
- H
= C3:Q8=
SM_4 of order 24. Class: 58 Length: 91 Order: 24
G = (C13XC13):H of order 4056
k(B) = 16, l(B) = 9
Maximal subgroups: H1 =GQ12
H2 =GQ12
H3 =C12
H4 =Q8
H5 =Q8
H6 =Q8
Non-trivial central extensions by C2:
C3:(C4:C4) =
SM_12
of order 48
, k(B2) = 16, l(B2) = 9
C3:(C4:C4) =
SM_13
of order 48
, k(B2) = 16, l(B2) = 9
- H
= Q8XC3=
SM_11 of order 24. Class: 59 Length: 91 Order: 24
G = (C13XC13):H of order 4056
k(B) = 22, l(B) = 15
Maximal subgroups: H1 =C12
H2 =C12
H3 =C12
H4 =Q8
Non-trivial central extensions by C2:
GQ16XC3 =
SM_22
of order 48
, k(B2) = 22, l(B2) = 15
- H
= C2XC4XC3=
SM_9 of order 24. Class: 60 Length: 91 Order: 24
G = (C13XC13):H of order 4056
k(B) = 34, l(B) = 24
Maximal subgroups: H1 =C12
H2 =C2XC2XC3
H3 =C12
H4 =C4XC2
Non-trivial central extensions by C2:
C4XC4XC3 =
SM_20
of order 48
, k(B2) = 34, l(B2) = 24
((C2XC2):C4)XC3 =
SM_21
of order 48
, k(B2) = 16, l(B2) = 6
GQ16XC3 =
SM_22
of order 48
, k(B2) = 16, l(B2) = 6
C2XC8XC3 =
SM_23
of order 48
, k(B2) = 34, l(B2) = 24
(C8:C2)XC3 =
SM_24
of order 48
, k(B2) = 16, l(B2) = 6
- H
= D24=
SM_6 of order 24. Class: 61 Length: 91 Order: 24
G = (C13XC13):H of order 4056
k(B) = 34, l(B) = 9
Maximal subgroups: H1 =D12
H2 =D12
H3 =C12
H4 =D8
H5 =D8
H6 =D8
Non-trivial central extensions by C2:
C3:SD16 =
SM_6
of order 48
, k(B2) = 31, l(B2) = 6
D48 =
SM_7
of order 48
, k(B2) = 31, l(B2) = 6
GQ48 =
SM_8
of order 48
, k(B2) = 31, l(B2) = 6
C3:(C4:C4) =
SM_13
of order 48
, k(B2) = 34, l(B2) = 9
C3:((C4XC2):C2)) =
SM_14
of order 48
, k(B2) = 34, l(B2) = 9
- H
= Q8:C3=
SM_3 of order 24. Class: 62 Length: 91 Order: 24
G = (C13XC13):H of order 4056
k(B) = 14, l(B) = 7
Maximal subgroups: H1 =Q8
H2 =C6
H3 =C6
H4 =C6
H5 =C6
Non-trivial central extensions by C2:
- H
= C3:C8=
SM_1 of order 24. Class: 63 Length: 182 Order: 24
G = (C13XC13):H of order 4056
k(B) = 19, l(B) = 12
Maximal subgroups: H1 =C12
H2 =C8
H3 =C8
H4 =C8
Non-trivial central extensions by C2:
C3:C16 =
SM_1
of order 48
, k(B2) = 19, l(B2) = 12
- H
= C2XC4XC3=
SM_9 of order 24. Class: 64 Length: 182 Order: 24
G = (C13XC13):H of order 4056
k(B) = 56, l(B) = 24
Maximal subgroups: H1 =C12
H2 =C12
H3 =C2XC2XC3
H4 =C4XC2
Non-trivial central extensions by C2:
C4XC4XC3 =
SM_20
of order 48
, k(B2) = 56, l(B2) = 24
((C2XC2):C4)XC3 =
SM_21
of order 48
, k(B2) = 38, l(B2) = 6
GQ16XC3 =
SM_22
of order 48
, k(B2) = 38, l(B2) = 6
C2XC8XC3 =
SM_23
of order 48
, k(B2) = 56, l(B2) = 24
(C8:C2)XC3 =
SM_24
of order 48
, k(B2) = 38, l(B2) = 6
- H
= C2XC4XC3=
SM_9 of order 24. Class: 65 Length: 182 Order: 24
G = (C13XC13):H of order 4056
k(B) = 40, l(B) = 24
Maximal subgroups: H1 =C12
H2 =C12
H3 =C2XC2XC3
H4 =C4XC2
Non-trivial central extensions by C2:
C4XC4XC3 =
SM_20
of order 48
, k(B2) = 40, l(B2) = 24
((C2XC2):C4)XC3 =
SM_21
of order 48
, k(B2) = 22, l(B2) = 6
GQ16XC3 =
SM_22
of order 48
, k(B2) = 22, l(B2) = 6
C2XC8XC3 =
SM_23
of order 48
, k(B2) = 40, l(B2) = 24
(C8:C2)XC3 =
SM_24
of order 48
, k(B2) = 22, l(B2) = 6
- H
= C2XC4XC3=
SM_9 of order 24. Class: 66 Length: 182 Order: 24
G = (C13XC13):H of order 4056
k(B) = 40, l(B) = 24
Maximal subgroups: H1 =C12
H2 =C12
H3 =C2XC2XC3
H4 =C4XC2
Non-trivial central extensions by C2:
C4XC4XC3 =
SM_20
of order 48
, k(B2) = 40, l(B2) = 24
((C2XC2):C4)XC3 =
SM_21
of order 48
, k(B2) = 22, l(B2) = 6
GQ16XC3 =
SM_22
of order 48
, k(B2) = 22, l(B2) = 6
C2XC8XC3 =
SM_23
of order 48
, k(B2) = 40, l(B2) = 24
(C8:C2)XC3 =
SM_24
of order 48
, k(B2) = 22, l(B2) = 6
- H
= S3XC4=
SM_5 of order 24. Class: 67 Length: 182 Order: 24
G = (C13XC13):H of order 4056
k(B) = 28, l(B) = 12
Maximal subgroups: H1 =D12
H2 =GQ12
H3 =C12
H4 =C4XC2
H5 =C4XC2
H6 =C4XC2
Non-trivial central extensions by C2:
S3XC8 =
SM_4
of order 48
, k(B2) = 28, l(B2) = 12
C3S(C8SC2) =
SM_5
of order 48
, k(B2) = 22, l(B2) = 6
GQ12XC4 =
SM_11
of order 48
, k(B2) = 28, l(B2) = 12
C3:(C4:C4) =
SM_12
of order 48
, k(B2) = 22, l(B2) = 6
C3:((C4XC2):C2)) =
SM_14
of order 48
, k(B2) = 22, l(B2) = 6
- H
= C2XC4XC3=
SM_9 of order 24. Class: 68 Length: 182 Order: 24
G = (C13XC13):H of order 4056
k(B) = 50, l(B) = 24
Maximal subgroups: H1 =C12
H2 =C12
H3 =C2XC2XC3
H4 =C4XC2
Non-trivial central extensions by C2:
C4XC4XC3 =
SM_20
of order 48
, k(B2) = 50, l(B2) = 24
((C2XC2):C4)XC3 =
SM_21
of order 48
, k(B2) = 32, l(B2) = 6
GQ16XC3 =
SM_22
of order 48
, k(B2) = 32, l(B2) = 6
C2XC8XC3 =
SM_23
of order 48
, k(B2) = 50, l(B2) = 24
(C8:C2)XC3 =
SM_24
of order 48
, k(B2) = 32, l(B2) = 6
- H
= D8PS3=
SM_8 of order 24. Class: 69 Length: 182 Order: 24
G = (C13XC13):H of order 4056
k(B) = 28, l(B) = 9
Maximal subgroups: H1 =D12
H2 =GQ12
H3 =C2XC2XC3
H4 =D8
H5 =D8
H6 =D8
Non-trivial central extensions by C2:
C3:(C4:C4) =
SM_12
of order 48
, k(B2) = 28, l(B2) = 9
C3:((C4XC2):C2)) =
SM_14
of order 48
, k(B2) = 28, l(B2) = 9
C3:D16 =
SM_15
of order 48
, k(B2) = 22, l(B2) = 3
C3:SD16 =
SM_16
of order 48
, k(B2) = 22, l(B2) = 3
C3:(GQ16) =
SM_17
of order 48
, k(B2) = 22, l(B2) = 3
C3:GQ16 =
SM_18
of order 48
, k(B2) = 22, l(B2) = 3
C3:((C2XC2):C4) =
SM_19
of order 48
, k(B2) = 28, l(B2) = 9
- H
= C2XC4XC3=
SM_9 of order 24. Class: 70 Length: 182 Order: 24
G = (C13XC13):H of order 4056
k(B) = 104, l(B) = 24
Maximal subgroups: H1 =C12
H2 =C12
H3 =C2XC2XC3
H4 =C4XC2
Non-trivial central extensions by C2:
C4XC4XC3 =
SM_20
of order 48
, k(B2) = 104, l(B2) = 24
((C2XC2):C4)XC3 =
SM_21
of order 48
, k(B2) = 86, l(B2) = 6
GQ16XC3 =
SM_22
of order 48
, k(B2) = 86, l(B2) = 6
C2XC8XC3 =
SM_23
of order 48
, k(B2) = 104, l(B2) = 24
(C8:C2)XC3 =
SM_24
of order 48
, k(B2) = 86, l(B2) = 6
- H
= Q8:C3=
SM_3 of order 24. Class: 71 Length: 182 Order: 24
G = (C13XC13):H of order 4056
k(B) = 30, l(B) = 7
Maximal subgroups: H1 =Q8
H2 =C6
H3 =C6
H4 =C6
H5 =C6
Non-trivial central extensions by C2:
- H
= D8XC3=
SM_10 of order 24. Class: 72 Length: 273 Order: 24
G = (C13XC13):H of order 4056
k(B) = 28, l(B) = 15
Maximal subgroups: H1 =C12
H2 =C2XC2XC3
H3 =C2XC2XC3
H4 =D8
Non-trivial central extensions by C2:
((C2XC2):C4)XC3 =
SM_21
of order 48
, k(B2) = 28, l(B2) = 15
GQ16XC3 =
SM_22
of order 48
, k(B2) = 28, l(B2) = 15
D16XC3 =
SM_25
of order 48
, k(B2) = 19, l(B2) = 6
SD16XC3 =
SM_26
of order 48
, k(B2) = 19, l(B2) = 6
GQ16XC3 =
SM_27
of order 48
, k(B2) = 19, l(B2) = 6
- H
= D28=
SM_3 of order 28. Class: 76 Length: 78 Order: 28
G = (C13XC13):H of order 4732
k(B) = 34, l(B) = 10
Maximal subgroups: H1 =D14
H2 =D14
H3 =C14
H4 =C2XC2
H5 =C2XC2
H6 =C2XC2
H7 =C2XC2
H8 =C2XC2
H9 =C2XC2
H10 =C2XC2
Non-trivial central extensions by C2:
C7:Q8 =
SM_3
of order 56
, k(B2) = 31, l(B2) = 7
D14XC4 =
SM_4
of order 56
, k(B2) = 34, l(B2) = 10
C7:D8 =
SM_5
of order 56
, k(B2) = 31, l(B2) = 7
GQ28XC2 =
SM_6
of order 56
, k(B2) = 34, l(B2) = 10
C7:D8 =
SM_7
of order 56
, k(B2) = 31, l(B2) = 7
- H
= C28=
SM_2 of order 28. Class: 77 Length: 78 Order: 28
G = (C13XC13):H of order 4732
k(B) = 34, l(B) = 28
Maximal subgroups: H1 =C14
H2 =C4
Non-trivial central extensions by C2:
C56 =
SM_2
of order 56
, k(B2) = 34, l(B2) = 28
- H
= GQ28=
SM_1 of order 28. Class: 78 Length: 78 Order: 28
G = (C13XC13):H of order 4732
k(B) = 16, l(B) = 10
Maximal subgroups: H1 =C14
H2 =C4
H3 =C4
H4 =C4
H5 =C4
H6 =C4
H7 =C4
H8 =C4
Non-trivial central extensions by C2:
C7:C8 =
SM_1
of order 56
, k(B2) = 16, l(B2) = 10
- H
= (C4XC4):C2=
SM_11 of order 32. Class: 79 Length: 273 Order: 32
G = (C13XC13):H of order 5408
k(B) = 35, l(B) = 14
Maximal subgroups: H1 =C8:C2
H2 =D8YC4
H3 =C4XC4
Non-trivial central extensions by C2:
(C8XC4):C2 =
SM_6
of order 64
, k(B2) = 35, l(B2) = 14
(C8XC4).C2 =
SM_7
of order 64
, k(B2) = 35, l(B2) = 14
(D8XC2):C4 =
SM_8
of order 64
, k(B2) = 26, l(B2) = 5
(Q8XC2):C4 =
SM_9
of order 64
, k(B2) = 26, l(B2) = 5
(D8XC2).C4 =
SM_10
of order 64
, k(B2) = 26, l(B2) = 5
(C4:C4).C4 =
SM_11
of order 64
, k(B2) = 26, l(B2) = 5
(C4XC4):C4 =
SM_20
of order 64
, k(B2) = 35, l(B2) = 14
- H
= C2XC2XC3XC3=
SM_14 of order 36. Class: 80 Length: 91 Order: 36
G = (C13XC13):H of order 6084
k(B) = 64, l(B) = 36
Maximal subgroups: H1 =C2XC3XC3
H2 =C2XC3XC3
H3 =C2XC3XC3
H4 =C2XC2XC3
H5 =C2XC2XC3
H6 =C2XC2XC3
H7 =C2XC2XC3
Non-trivial central extensions by C2:
C2XC4XC3XC3 =
SM_36
of order 72
, k(B2) = 64, l(B2) = 36
D8XC3XC3 =
SM_37
of order 72
, k(B2) = 37, l(B2) = 9
Q8XC3XC3 =
SM_38
of order 72
, k(B2) = 37, l(B2) = 9
Non-trivial central extensions by C3:
SM_29
of order 108
, k(B2) = 64, l(B2) = 36
SM_30
of order 108
, k(B2) = 32, l(B2) = 4
SM_31
of order 108
, k(B2) = 32, l(B2) = 4
- H
= C4XC3XC3=
SM_8 of order 36. Class: 81 Length: 91 Order: 36
G = (C13XC13):H of order 6084
k(B) = 46, l(B) = 36
Maximal subgroups: H1 =C2XC3XC3
H2 =C12
H3 =C12
H4 =C12
H5 =C12
Non-trivial central extensions by C2:
C8XC3XC3 =
SM_14
of order 72
, k(B2) = 46, l(B2) = 36
Non-trivial central extensions by C3:
SM_12
of order 108
, k(B2) = 46, l(B2) = 36
SM_13
of order 108
, k(B2) = 14, l(B2) = 4
SM_14
of order 108
, k(B2) = 14, l(B2) = 4
- H
= C4XC3XC3=
SM_8 of order 36. Class: 82 Length: 91 Order: 36
G = (C13XC13):H of order 6084
k(B) = 46, l(B) = 36
Maximal subgroups: H1 =C2XC3XC3
H2 =C12
H3 =C12
H4 =C12
H5 =C12
Non-trivial central extensions by C2:
C8XC3XC3 =
SM_14
of order 72
, k(B2) = 46, l(B2) = 36
Non-trivial central extensions by C3:
SM_12
of order 108
, k(B2) = 46, l(B2) = 36
SM_13
of order 108
, k(B2) = 14, l(B2) = 4
SM_14
of order 108
, k(B2) = 14, l(B2) = 4
- H
= GQ12XC3=
SM_6 of order 36. Class: 83 Length: 182 Order: 36
G = (C13XC13):H of order 6084
k(B) = 28, l(B) = 18
Maximal subgroups: H1 =C2XC3XC3
H2 =GQ12
H3 =C12
H4 =C12
H5 =C12
Non-trivial central extensions by C2:
(C3:C8)XC3 =
SM_12
of order 72
, k(B2) = 28, l(B2) = 18
Non-trivial central extensions by C3:
SM_7
of order 108
, k(B2) = 28, l(B2) = 18
- H
= S3XC6=
SM_12 of order 36. Class: 84 Length: 182 Order: 36
G = (C13XC13):H of order 6084
k(B) = 34, l(B) = 18
Maximal subgroups: H1 =S3XC3
H2 =S3XC3
H3 =C2XC3XC3
H4 =D12
H5 =C2XC2XC3
H6 =C2XC2XC3
H7 =C2XC2XC3
Non-trivial central extensions by C2:
(C3:Q8)XC3 =
SM_26
of order 72
, k(B2) = 25, l(B2) = 9
S3XC3XC4 =
SM_27
of order 72
, k(B2) = 34, l(B2) = 18
(C3:D8)XC3 =
SM_28
of order 72
, k(B2) = 25, l(B2) = 9
GQ12XC3XC2 =
SM_29
of order 72
, k(B2) = 34, l(B2) = 18
(C3:D8)XC3 =
SM_30
of order 72
, k(B2) = 25, l(B2) = 9
Non-trivial central extensions by C3:
SM_24
of order 108
, k(B2) = 34, l(B2) = 18
- H
= C4XC3XC3=
SM_8 of order 36. Class: 85 Length: 182 Order: 36
G = (C13XC13):H of order 6084
k(B) = 55, l(B) = 36
Maximal subgroups: H1 =C2XC3XC3
H2 =C12
H3 =C12
H4 =C12
H5 =C12
Non-trivial central extensions by C2:
C8XC3XC3 =
SM_14
of order 72
, k(B2) = 55, l(B2) = 36
Non-trivial central extensions by C3:
SM_12
of order 108
, k(B2) = 55, l(B2) = 36
SM_13
of order 108
, k(B2) = 23, l(B2) = 4
SM_14
of order 108
, k(B2) = 23, l(B2) = 4
- H
= C4XC3XC3=
SM_8 of order 36. Class: 86 Length: 182 Order: 36
G = (C13XC13):H of order 6084
k(B) = 91, l(B) = 36
Maximal subgroups: H1 =C2XC3XC3
H2 =C12
H3 =C12
H4 =C12
H5 =C12
Non-trivial central extensions by C2:
C8XC3XC3 =
SM_14
of order 72
, k(B2) = 91, l(B2) = 36
Non-trivial central extensions by C3:
SM_12
of order 108
, k(B2) = 91, l(B2) = 36
SM_13
of order 108
, k(B2) = 59, l(B2) = 4
SM_14
of order 108
, k(B2) = 59, l(B2) = 4
- H
= C42=
SM_6 of order 42. Class: 91 Length: 78 Order: 42
G = (C13XC13):H of order 7098
k(B) = 46, l(B) = 42
Maximal subgroups: H1 =C21
H2 =C14
H3 =C6
- H
= D14XC3=
SM_4 of order 42. Class: 92 Length: 156 Order: 42
G = (C13XC13):H of order 7098
k(B) = 25, l(B) = 15
Maximal subgroups: H1 =C21
H2 =D14
H3 =C6
H4 =C6
H5 =C6
H6 =C6
H7 =C6
H8 =C6
H9 =C6
- H
= C4XC4XC3=
SM_20 of order 48. Class: 93 Length: 91 Order: 48
G = (C13XC13):H of order 8112
k(B) = 59, l(B) = 48
Maximal subgroups: H1 =C2XC4XC3
H2 =C2XC4XC3
H3 =C2XC4XC3
H4 =C4XC4
Non-trivial central extensions by C2:
C3X((C4XC2):C4) =
SM_45
of order 96
, k(B2) = 23, l(B2) = 12
C4XC8XC3 =
SM_46
of order 96
, k(B2) = 59, l(B2) = 48
C3X(C8:C4) =
SM_47
of order 96
, k(B2) = 23, l(B2) = 12
- H
= (D8YC4)XC3=
SM_47 of order 48. Class: 94 Length: 91 Order: 48
G = (C13XC13):H of order 8112
k(B) = 38, l(B) = 30
Maximal subgroups: H1 =D8XC3
H2 =D8XC3
H3 =D8XC3
H4 =C2XC4XC3
H5 =C2XC4XC3
H6 =C2XC4XC3
H7 =Q8XC3
H8 =D8YC4
Non-trivial central extensions by C2:
C3X((C4XC2):C4) =
SM_164
of order 96
, k(B2) = 38, l(B2) = 30
C3XD8XC4 =
SM_165
of order 96
, k(B2) = 38, l(B2) = 30
Q8XC12 =
SM_166
of order 96
, k(B2) = 38, l(B2) = 30
C3X((C2XC2XC4):C2) =
SM_168
of order 96
, k(B2) = 20, l(B2) = 12
C3X(C2XC2):Q8 =
SM_169
of order 96
, k(B2) = 20, l(B2) = 12
C3X(C4XC2XC2):C2 =
SM_170
of order 96
, k(B2) = 20, l(B2) = 12
C3X((C4XC4):C2) =
SM_171
of order 96
, k(B2) = 20, l(B2) = 12
C3X((C4:C4).C2) =
SM_172
of order 96
, k(B2) = 20, l(B2) = 12
C3X((C4XC4):C2) =
SM_173
of order 96
, k(B2) = 20, l(B2) = 12
- H
= (Q8YC4):C3=
SM_33 of order 48. Class: 95 Length: 91 Order: 48
G = (C13XC13):H of order 8112
k(B) = 22, l(B) = 14
Maximal subgroups: H1 =Q8:C3
H2 =D8YC4
H3 =C12
H4 =C12
H5 =C12
H6 =C12
Non-trivial central extensions by C2:
(Q8:C3)XC4 =
SM_69
of order 96
, k(B2) = 22, l(B2) = 14
- H
= C3:(D8YC4)=
SM_37 of order 48. Class: 96 Length: 91 Order: 48
G = (C13XC13):H of order 8112
k(B) = 32, l(B) = 18
Maximal subgroups: H1 =D8PS3
H2 =D8PS3
H3 =S3XC4
H4 =S3XC4
H5 =D24
H6 =C3:Q8
H7 =C2XC4XC3
H8 =D8YC4
H9 =D8YC4
H10 =D8YC4
Non-trivial central extensions by C2:
(C3:Q8)XC4 =
SM_75
of order 96
, k(B2) = 32, l(B2) = 18
C3:((C4:C4).C2) =
SM_77
of order 96
, k(B2) = 26, l(B2) = 12
C3:((C4XC2):C4) =
SM_79
of order 96
, k(B2) = 32, l(B2) = 18
D24XC4 =
SM_80
of order 96
, k(B2) = 32, l(B2) = 18
C3:((C4XC4):C2) =
SM_82
of order 96
, k(B2) = 26, l(B2) = 12
C3:((C4XC4):C2) =
SM_83
of order 96
, k(B2) = 26, l(B2) = 12
C3:((C4XC4):C2) =
SM_86
of order 96
, k(B2) = 20, l(B2) = 6
C3:((C4XC2XC2):C2) =
SM_90
of order 96
, k(B2) = 20, l(B2) = 6
C3:((C2XC2XC4):C2) =
SM_91
of order 96
, k(B2) = 20, l(B2) = 6
C3:((C4XC4):C2) =
SM_92
of order 96
, k(B2) = 20, l(B2) = 6
C3X((C4:C4).C2) =
SM_96
of order 96
, k(B2) = 20, l(B2) = 6
C3:((C4XC2XC2):C2) =
SM_101
of order 96
, k(B2) = 20, l(B2) = 6
C3:((C2XC2):Q8) =
SM_103
of order 96
, k(B2) = 20, l(B2) = 6
C3:((C4XC4):C2) =
SM_105
of order 96
, k(B2) = 20, l(B2) = 6
C3:((C2XC2):Q8) =
SM_131
of order 96
, k(B2) = 26, l(B2) = 12
C3:((C4XC2):C4) =
SM_133
of order 96
, k(B2) = 32, l(B2) = 18
(C3:D8)XC4 =
SM_135
of order 96
, k(B2) = 32, l(B2) = 18
C3:((C4XC2XC2):C2) =
SM_136
of order 96
, k(B2) = 26, l(B2) = 12
C3:((C2XC2XC4):C2) =
SM_137
of order 96
, k(B2) = 26, l(B2) = 12
- H
= C4XC4XC3=
SM_20 of order 48. Class: 97 Length: 91 Order: 48
G = (C13XC13):H of order 8112
k(B) = 59, l(B) = 48
Maximal subgroups: H1 =C2XC4XC3
H2 =C2XC4XC3
H3 =C2XC4XC3
H4 =C4XC4
Non-trivial central extensions by C2:
C3X((C4XC2):C4) =
SM_45
of order 96
, k(B2) = 23, l(B2) = 12
C4XC8XC3 =
SM_46
of order 96
, k(B2) = 59, l(B2) = 48
C3X(C8:C4) =
SM_47
of order 96
, k(B2) = 23, l(B2) = 12
- H
= C3:(C8:C2)=
SM_10 of order 48. Class: 98 Length: 91 Order: 48
G = (C13XC13):H of order 8112
k(B) = 23, l(B) = 18
Maximal subgroups: H1 =C3:C8
H2 =C3:C8
H3 =C2XC4XC3
H4 =C8:C2
H5 =C8:C2
H6 =C8:C2
Non-trivial central extensions by C2:
C3:(C8:C4) =
SM_10
of order 96
, k(B2) = 23, l(B2) = 18
C3:(C4:C8) =
SM_11
of order 96
, k(B2) = 23, l(B2) = 18
C3:((C2XC2):C8) =
SM_37
of order 96
, k(B2) = 23, l(B2) = 18
- H
= (Q8YC4):C3=
SM_33 of order 48. Class: 99 Length: 182 Order: 48
G = (C13XC13):H of order 8112
k(B) = 30, l(B) = 14
Maximal subgroups: H1 =Q8:C3
H2 =D8YC4
H3 =C12
H4 =C12
H5 =C12
H6 =C12
Non-trivial central extensions by C2:
(Q8:C3)XC4 =
SM_69
of order 96
, k(B2) = 30, l(B2) = 14
- H
= C4XC4XC3=
SM_20 of order 48. Class: 100 Length: 182 Order: 48
G = (C13XC13):H of order 8112
k(B) = 91, l(B) = 48
Maximal subgroups: H1 =C2XC4XC3
H2 =C2XC4XC3
H3 =C2XC4XC3
H4 =C4XC4
Non-trivial central extensions by C2:
C3X((C4XC2):C4) =
SM_45
of order 96
, k(B2) = 55, l(B2) = 12
C4XC8XC3 =
SM_46
of order 96
, k(B2) = 91, l(B2) = 48
C3X(C8:C4) =
SM_47
of order 96
, k(B2) = 55, l(B2) = 12
- H
= (C8:C2)XC3=
SM_24 of order 48. Class: 101 Length: 273 Order: 48
G = (C13XC13):H of order 8112
k(B) = 35, l(B) = 30
Maximal subgroups: H1 =C2XC4XC3
H2 =C24
H3 =C24
H4 =C8:C2
Non-trivial central extensions by C2:
C3X(C8:C4) =
SM_47
of order 96
, k(B2) = 35, l(B2) = 30
C3X((C2XC2):C8) =
SM_48
of order 96
, k(B2) = 35, l(B2) = 30
C3X(C4:C8) =
SM_55
of order 96
, k(B2) = 35, l(B2) = 30
- H
= D14XC4=
SM_4 of order 56. Class: 109 Length: 78 Order: 56
G = (C13XC13):H of order 9464
k(B) = 32, l(B) = 20
Maximal subgroups: H1 =GQ28
H2 =C28
H3 =D28
H4 =C4XC2
H5 =C4XC2
H6 =C4XC2
H7 =C4XC2
H8 =C4XC2
H9 =C4XC2
H10 =C4XC2
Non-trivial central extensions by C2:
SM_3
of order 112
, k(B2) = 32, l(B2) = 20
SM_4
of order 112
, k(B2) = 26, l(B2) = 14
SM_10
of order 112
, k(B2) = 32, l(B2) = 20
SM_11
of order 112
, k(B2) = 26, l(B2) = 14
SM_13
of order 112
, k(B2) = 26, l(B2) = 14
- H
= C56=
SM_2 of order 56. Class: 110 Length: 78 Order: 56
G = (C13XC13):H of order 9464
k(B) = 59, l(B) = 56
Maximal subgroups: H1 =C28
H2 =C8
Non-trivial central extensions by C2:
SM_2
of order 112
, k(B2) = 59, l(B2) = 56
- H
= C7:C8=
SM_1 of order 56. Class: 111 Length: 78 Order: 56
G = (C13XC13):H of order 9464
k(B) = 23, l(B) = 20
Maximal subgroups: H1 =C28
H2 =C8
H3 =C8
H4 =C8
H5 =C8
H6 =C8
H7 =C8
H8 =C8
Non-trivial central extensions by C2:
SM_1
of order 112
, k(B2) = 23, l(B2) = 20
- H
= (C3:Q8)XC3=
SM_26 of order 72. Class: 112 Length: 91 Order: 72
G = (C13XC13):H of order 12168
k(B) = 32, l(B) = 27
Maximal subgroups: H1 =GQ12XC3
H2 =GQ12XC3
H3 =C4XC3XC3
H4 =Q8XC3
H5 =Q8XC3
H6 =Q8XC3
H7 =C3:Q8
Non-trivial central extensions by C2:
SM_77
of order 144
, k(B2) = 32, l(B2) = 27
SM_78
of order 144
, k(B2) = 32, l(B2) = 27
Non-trivial central extensions by C3:
SM_44
of order 216
, k(B2) = 32, l(B2) = 27
- H
= SL23XC3=
SM_25 of order 72. Class: 113 Length: 91 Order: 72
G = (C13XC13):H of order 12168
k(B) = 34, l(B) = 21
Maximal subgroups: H1 =Q8:C3
H2 =Q8:C3
H3 =Q8:C3
H4 =Q8XC3
H5 =C2XC3XC3
H6 =C2XC3XC3
H7 =C2XC3XC3
H8 =C2XC3XC3
Non-trivial central extensions by C2:
Non-trivial central extensions by C3:
SM_38
of order 216
, k(B2) = 34, l(B2) = 21
SM_39
of order 216
, k(B2) = 18, l(B2) = 5
SM_40
of order 216
, k(B2) = 34, l(B2) = 21
SM_41
of order 216
, k(B2) = 18, l(B2) = 5
SM_42
of order 216
, k(B2) = 18, l(B2) = 5
- H
= C2XC4XC3XC3=
SM_36 of order 72. Class: 114 Length: 91 Order: 72
G = (C13XC13):H of order 12168
k(B) = 86, l(B) = 72
Maximal subgroups: H1 =C4XC3XC3
H2 =C4XC3XC3
H3 =C2XC2XC3XC3
H4 =C2XC4XC3
H5 =C2XC4XC3
H6 =C2XC4XC3
H7 =C2XC4XC3
Non-trivial central extensions by C2:
SM_101
of order 144
, k(B2) = 86, l(B2) = 72
SM_102
of order 144
, k(B2) = 32, l(B2) = 18
SM_103
of order 144
, k(B2) = 32, l(B2) = 18
SM_104
of order 144
, k(B2) = 86, l(B2) = 72
SM_105
of order 144
, k(B2) = 32, l(B2) = 18
Non-trivial central extensions by C3:
SM_73
of order 216
, k(B2) = 86, l(B2) = 72
SM_74
of order 216
, k(B2) = 22, l(B2) = 8
SM_75
of order 216
, k(B2) = 22, l(B2) = 8
- H
= (C3:D8)XC3=
SM_28 of order 72. Class: 115 Length: 91 Order: 72
G = (C13XC13):H of order 12168
k(B) = 38, l(B) = 27
Maximal subgroups: H1 =S3XC6
H2 =S3XC6
H3 =C4XC3XC3
H4 =D8XC3
H5 =D8XC3
H6 =D8XC3
H7 =D24
Non-trivial central extensions by C2:
SM_71
of order 144
, k(B2) = 29, l(B2) = 18
SM_72
of order 144
, k(B2) = 29, l(B2) = 18
SM_73
of order 144
, k(B2) = 29, l(B2) = 18
SM_78
of order 144
, k(B2) = 38, l(B2) = 27
SM_79
of order 144
, k(B2) = 38, l(B2) = 27
Non-trivial central extensions by C3:
SM_48
of order 216
, k(B2) = 38, l(B2) = 27
- H
= S3XC3XC4=
SM_27 of order 72. Class: 116 Length: 182 Order: 72
G = (C13XC13):H of order 12168
k(B) = 44, l(B) = 36
Maximal subgroups: H1 =S3XC6
H2 =GQ12XC3
H3 =C4XC3XC3
H4 =S3XC4
H5 =C2XC4XC3
H6 =C2XC4XC3
H7 =C2XC4XC3
Non-trivial central extensions by C2:
SM_69
of order 144
, k(B2) = 44, l(B2) = 36
SM_70
of order 144
, k(B2) = 26, l(B2) = 18
SM_76
of order 144
, k(B2) = 44, l(B2) = 36
SM_77
of order 144
, k(B2) = 26, l(B2) = 18
SM_79
of order 144
, k(B2) = 26, l(B2) = 18
Non-trivial central extensions by C3:
SM_47
of order 216
, k(B2) = 44, l(B2) = 36
- H
= (C3:D8)XC3=
SM_30 of order 72. Class: 117 Length: 182 Order: 72
G = (C13XC13):H of order 12168
k(B) = 44, l(B) = 27
Maximal subgroups: H1 =S3XC6
H2 =GQ12XC3
H3 =C2XC2XC3XC3
H4 =D8XC3
H5 =D8XC3
H6 =D8XC3
H7 =D8PS3
Non-trivial central extensions by C2:
SM_77
of order 144
, k(B2) = 44, l(B2) = 27
SM_79
of order 144
, k(B2) = 44, l(B2) = 27
SM_80
of order 144
, k(B2) = 26, l(B2) = 9
SM_81
of order 144
, k(B2) = 26, l(B2) = 9
SM_82
of order 144
, k(B2) = 26, l(B2) = 9
SM_83
of order 144
, k(B2) = 26, l(B2) = 9
SM_84
of order 144
, k(B2) = 44, l(B2) = 27
Non-trivial central extensions by C3:
SM_58
of order 216
, k(B2) = 44, l(B2) = 27
- H
= (C3:C8)XC3=
SM_12 of order 72. Class: 118 Length: 182 Order: 72
G = (C13XC13):H of order 12168
k(B) = 41, l(B) = 36
Maximal subgroups: H1 =C4XC3XC3
H2 =C3:C8
H3 =C24
H4 =C24
H5 =C24
Non-trivial central extensions by C2:
SM_28
of order 144
, k(B2) = 41, l(B2) = 36
Non-trivial central extensions by C3:
SM_13
of order 216
, k(B2) = 41, l(B2) = 36
- H
= C2XC4XC3XC3=
SM_36 of order 72. Class: 119 Length: 182 Order: 72
G = (C13XC13):H of order 12168
k(B) = 104, l(B) = 72
Maximal subgroups: H1 =C4XC3XC3
H2 =C4XC3XC3
H3 =C2XC2XC3XC3
H4 =C2XC4XC3
H5 =C2XC4XC3
H6 =C2XC4XC3
H7 =C2XC4XC3
Non-trivial central extensions by C2:
SM_101
of order 144
, k(B2) = 104, l(B2) = 72
SM_102
of order 144
, k(B2) = 50, l(B2) = 18
SM_103
of order 144
, k(B2) = 50, l(B2) = 18
SM_104
of order 144
, k(B2) = 104, l(B2) = 72
SM_105
of order 144
, k(B2) = 50, l(B2) = 18
Non-trivial central extensions by C3:
SM_73
of order 216
, k(B2) = 104, l(B2) = 72
SM_74
of order 216
, k(B2) = 40, l(B2) = 8
SM_75
of order 216
, k(B2) = 40, l(B2) = 8
- H
= GQ28XC3=
SM_4 of order 84. Class: 132 Length: 78 Order: 84
G = (C13XC13):H of order 14196
k(B) = 32, l(B) = 30
Maximal subgroups: H1 =C42
H2 =GQ28
H3 =C12
H4 =C12
H5 =C12
H6 =C12
H7 =C12
H8 =C12
H9 =C12
Non-trivial central extensions by C2:
SM_4
of order 168
, k(B2) = 32, l(B2) = 30
- H
= C84=
SM_6 of order 84. Class: 133 Length: 78 Order: 84
G = (C13XC13):H of order 14196
k(B) = 86, l(B) = 84
Maximal subgroups: H1 =C42
H2 =C28
H3 =C12
Non-trivial central extensions by C2:
SM_6
of order 168
, k(B2) = 86, l(B2) = 84
- H
= D14XC6=
SM_12 of order 84. Class: 134 Length: 78 Order: 84
G = (C13XC13):H of order 14196
k(B) = 38, l(B) = 30
Maximal subgroups: H1 =D14XC3
H2 =D14XC3
H3 =C42
H4 =D28
H5 =C2XC2XC3
H6 =C2XC2XC3
H7 =C2XC2XC3
H8 =C2XC2XC3
H9 =C2XC2XC3
H10 =C2XC2XC3
H11 =C2XC2XC3
Non-trivial central extensions by C2:
SM_24
of order 168
, k(B2) = 29, l(B2) = 21
SM_25
of order 168
, k(B2) = 38, l(B2) = 30
SM_26
of order 168
, k(B2) = 29, l(B2) = 21
SM_27
of order 168
, k(B2) = 38, l(B2) = 30
SM_28
of order 168
, k(B2) = 29, l(B2) = 21
- H
= ((C2XC2XC4):C3).C2=
SM_67 of order 96. Class: 135 Length: 91 Order: 96
G = (C13XC13):H of order 16224
k(B) = 29, l(B) = 16
Maximal subgroups: H1 =(Q8YC4):C3
H2 =(C4XC4):C2
H3 =(C4XC4):C2
H4 =(C4XC4):C2
H5 =C3:C8
H6 =C3:C8
H7 =C3:C8
H8 =C3:C8
Non-trivial central extensions by C2:
SM_183
of order 192
, k(B2) = 29, l(B2) = 16
- H
= C3:((C4XC4):C2)=
SM_12 of order 96. Class: 136 Length: 91 Order: 96
G = (C13XC13):H of order 16224
k(B) = 40, l(B) = 30
Maximal subgroups: H1 =C3:(C8:C2)
H2 =C4XC4XC3
H3 =C3:(D8YC4)
H4 =(C4XC4):C2
H5 =(C4XC4):C2
H6 =(C4XC4):C2
Non-trivial central extensions by C2:
SM_10
of order 192
, k(B2) = 19, l(B2) = 9
SM_11
of order 192
, k(B2) = 19, l(B2) = 9
SM_15
of order 192
, k(B2) = 40, l(B2) = 30
SM_18
of order 192
, k(B2) = 40, l(B2) = 30
SM_23
of order 192
, k(B2) = 19, l(B2) = 9
SM_24
of order 192
, k(B2) = 19, l(B2) = 9
SM_82
of order 192
, k(B2) = 40, l(B2) = 30
- H
= C3X((C4XC4):C2)=
SM_54 of order 96. Class: 137 Length: 273 Order: 96
G = (C13XC13):H of order 16224
k(B) = 49, l(B) = 42
Maximal subgroups: H1 =(C8:C2)XC3
H2 =(D8YC4)XC3
H3 =C4XC4XC3
H4 =(C4XC4):C2
Non-trivial central extensions by C2:
SM_131
of order 192
, k(B2) = 49, l(B2) = 42
SM_132
of order 192
, k(B2) = 49, l(B2) = 42
SM_133
of order 192
, k(B2) = 22, l(B2) = 15
SM_134
of order 192
, k(B2) = 22, l(B2) = 15
SM_135
of order 192
, k(B2) = 22, l(B2) = 15
SM_136
of order 192
, k(B2) = 22, l(B2) = 15
SM_145
of order 192
, k(B2) = 49, l(B2) = 42
- H
=
SM_4 of order 112. Class: 141 Length: 78 Order: 112
G = (C13XC13):H of order 18928
k(B) = 40, l(B) = 34
Maximal subgroups: H1 =C7:C8
H2 =C56
H3 =D14XC4
H4 =C8:C2
H5 =C8:C2
H6 =C8:C2
H7 =C8:C2
H8 =C8:C2
H9 =C8:C2
H10 =C8:C2
Non-trivial central extensions by C2:
SM_20
of order 224
, k(B2) = 40, l(B2) = 34
SM_21
of order 224
, k(B2) = 40, l(B2) = 34
SM_26
of order 224
, k(B2) = 40, l(B2) = 34
- H
=
SM_101 of order 144. Class: 143 Length: 91 Order: 144
G = (C13XC13):H of order 24336
k(B) = 169, l(B) = 144
Maximal subgroups: H1 =C2XC4XC3XC3
H2 =C2XC4XC3XC3
H3 =C2XC4XC3XC3
H4 =C4XC4XC3
H5 =C4XC4XC3
H6 =C4XC4XC3
H7 =C4XC4XC3
Non-trivial central extensions by C2:
SM_313
of order 288
, k(B2) = 61, l(B2) = 36
SM_314
of order 288
, k(B2) = 169, l(B2) = 144
SM_315
of order 288
, k(B2) = 61, l(B2) = 36
Non-trivial central extensions by C3:
SM_200
of order 432
, k(B2) = 169, l(B2) = 144
SM_201
of order 432
, k(B2) = 41, l(B2) = 16
SM_202
of order 432
, k(B2) = 41, l(B2) = 16
- H
=
SM_161 of order 144. Class: 144 Length: 91 Order: 144
G = (C13XC13):H of order 24336
k(B) = 64, l(B) = 54
Maximal subgroups: H1 =(C3:D8)XC3
H2 =(C3:D8)XC3
H3 =S3XC3XC4
H4 =S3XC3XC4
H5 =(C3:D8)XC3
H6 =C2XC4XC3XC3
H7 =(C3:Q8)XC3
H8 =C3:(D8YC4)
H9 =(D8YC4)XC3
H10 =(D8YC4)XC3
H11 =(D8YC4)XC3
Non-trivial central extensions by C2:
SM_639
of order 288
, k(B2) = 64, l(B2) = 54
SM_641
of order 288
, k(B2) = 46, l(B2) = 36
SM_643
of order 288
, k(B2) = 64, l(B2) = 54
SM_644
of order 288
, k(B2) = 64, l(B2) = 54
SM_646
of order 288
, k(B2) = 46, l(B2) = 36
SM_647
of order 288
, k(B2) = 46, l(B2) = 36
SM_650
of order 288
, k(B2) = 28, l(B2) = 18
SM_654
of order 288
, k(B2) = 28, l(B2) = 18
SM_655
of order 288
, k(B2) = 28, l(B2) = 18
SM_656
of order 288
, k(B2) = 28, l(B2) = 18
SM_660
of order 288
, k(B2) = 28, l(B2) = 18
SM_665
of order 288
, k(B2) = 28, l(B2) = 18
SM_667
of order 288
, k(B2) = 28, l(B2) = 18
SM_669
of order 288
, k(B2) = 28, l(B2) = 18
SM_695
of order 288
, k(B2) = 46, l(B2) = 36
SM_697
of order 288
, k(B2) = 64, l(B2) = 54
SM_699
of order 288
, k(B2) = 64, l(B2) = 54
SM_700
of order 288
, k(B2) = 46, l(B2) = 36
SM_701
of order 288
, k(B2) = 46, l(B2) = 36
Non-trivial central extensions by C3:
SM_347
of order 432
, k(B2) = 64, l(B2) = 54
- H
=
SM_75 of order 144. Class: 145 Length: 91 Order: 144
G = (C13XC13):H of order 24336
k(B) = 61, l(B) = 54
Maximal subgroups: H1 =(C3:C8)XC3
H2 =(C3:C8)XC3
H3 =C2XC4XC3XC3
H4 =(C8:C2)XC3
H5 =(C8:C2)XC3
H6 =(C8:C2)XC3
H7 =C3:(C8:C2)
Non-trivial central extensions by C2:
SM_237
of order 288
, k(B2) = 61, l(B2) = 54
SM_238
of order 288
, k(B2) = 61, l(B2) = 54
SM_264
of order 288
, k(B2) = 61, l(B2) = 54
Non-trivial central extensions by C3:
SM_127
of order 432
, k(B2) = 61, l(B2) = 54
- H
=
SM_157 of order 144. Class: 146 Length: 91 Order: 144
G = (C13XC13):H of order 24336
k(B) = 50, l(B) = 42
Maximal subgroups: H1 =SL23XC3
H2 =(Q8YC4):C3
H3 =(Q8YC4):C3
H4 =(Q8YC4):C3
H5 =(D8YC4)XC3
H6 =C4XC3XC3
H7 =C4XC3XC3
H8 =C4XC3XC3
H9 =C4XC3XC3
Non-trivial central extensions by C2:
SM_633
of order 288
, k(B2) = 50, l(B2) = 42
Non-trivial central extensions by C3:
SM_329
of order 432
, k(B2) = 50, l(B2) = 42
SM_330
of order 432
, k(B2) = 18, l(B2) = 10
SM_337
of order 432
, k(B2) = 50, l(B2) = 42
SM_338
of order 432
, k(B2) = 18, l(B2) = 10
SM_339
of order 432
, k(B2) = 18, l(B2) = 10
- H
=
SM_25 of order 168. Class: 175 Length: 78 Order: 168
G = (C13XC13):H of order 28392
k(B) = 64, l(B) = 60
Maximal subgroups: H1 =D14XC6
H2 =C84
H3 =GQ28XC3
H4 =D14XC4
H5 =C2XC4XC3
H6 =C2XC4XC3
H7 =C2XC4XC3
H8 =C2XC4XC3
H9 =C2XC4XC3
H10 =C2XC4XC3
H11 =C2XC4XC3
Non-trivial central extensions by C2:
SM_58
of order 336
, k(B2) = 64, l(B2) = 60
SM_59
of order 336
, k(B2) = 46, l(B2) = 42
SM_65
of order 336
, k(B2) = 64, l(B2) = 60
SM_66
of order 336
, k(B2) = 46, l(B2) = 42
SM_68
of order 336
, k(B2) = 46, l(B2) = 42
- H
=
SM_4 of order 168. Class: 176 Length: 78 Order: 168
G = (C13XC13):H of order 28392
k(B) = 61, l(B) = 60
Maximal subgroups: H1 =C84
H2 =C7:C8
H3 =C24
H4 =C24
H5 =C24
H6 =C24
H7 =C24
H8 =C24
H9 =C24
Non-trivial central extensions by C2:
SM_4
of order 336
, k(B2) = 61, l(B2) = 60
- H
=
SM_6 of order 168. Class: 177 Length: 78 Order: 168
G = (C13XC13):H of order 28392
k(B) = 169, l(B) = 168
Maximal subgroups: H1 =C84
H2 =C56
H3 =C24
Non-trivial central extensions by C2:
SM_6
of order 336
, k(B2) = 169, l(B2) = 168
- H
=
SM_239 of order 288. Class: 182 Length: 91 Order: 288
G = (C13XC13):H of order 48672
k(B) = 104, l(B) = 90
Maximal subgroups: H1
H2
H3
H4 =C3X((C4XC4):C2)
H5 =C3X((C4XC4):C2)
H6 =C3X((C4XC4):C2)
H7 =C3:((C4XC4):C2)
Non-trivial central extensions by C2:
SM_1077
of order 576
, k(B2) = 41, l(B2) = 27
SM_1078
of order 576
, k(B2) = 41, l(B2) = 27
SM_1082
of order 576
, k(B2) = 104, l(B2) = 90
SM_1085
of order 576
, k(B2) = 104, l(B2) = 90
SM_1090
of order 576
, k(B2) = 41, l(B2) = 27
SM_1091
of order 576
, k(B2) = 41, l(B2) = 27
SM_1149
of order 576
, k(B2) = 104, l(B2) = 90
Non-trivial central extensions by C3:
SM_335
of order 864
, k(B2) = 104, l(B2) = 90
- H
=
SM_400 of order 288. Class: 183 Length: 91 Order: 288
G = (C13XC13):H of order 48672
k(B) = 55, l(B) = 48
Maximal subgroups: H1
H2 =C3X((C4XC4):C2)
H3 =C3X((C4XC4):C2)
H4 =C3X((C4XC4):C2)
H5 =((C2XC2XC4):C3).C2
H6 =(C3:C8)XC3
H7 =(C3:C8)XC3
H8 =(C3:C8)XC3
H9 =(C3:C8)XC3
Non-trivial central extensions by C2:
SM_1984
of order 576
, k(B2) = 55, l(B2) = 48
Non-trivial central extensions by C3:
SM_683
of order 864
, k(B2) = 55, l(B2) = 48
- H
=
SM_59 of order 336. Class: 196 Length: 78 Order: 336
G = (C13XC13):H of order 56784
k(B) = 104, l(B) = 102
Maximal subgroups: H1
H2
H3
H4
H5 =(C8:C2)XC3
H6 =(C8:C2)XC3
H7 =(C8:C2)XC3
H8 =(C8:C2)XC3
H9 =(C8:C2)XC3
H10 =(C8:C2)XC3
H11 =(C8:C2)XC3
Non-trivial central extensions by C2:
SM_153
of order 672
, k(B2) = 104, l(B2) = 102
SM_154
of order 672
, k(B2) = 104, l(B2) = 102
SM_159
of order 672
, k(B2) = 104, l(B2) = 102
All computations performed in GAP4
[GAP 99] the GAP Group, Version 4.2, Aachen,St.Andrews ,1999.
http://www-gap.dcs.st-and.ac.uk/~gap
Last Updated June 16, '02 using BlockHtml.gap, created by M. Schaps