Subgroup Information for GL2_3
Created in GAP4 by M. Schaps
- H
= C1=
SM_1 of order 1. Class: 1 Length: 1 Order: 1
G = (C3XC3):H =
SM_2 of order 9 =
C3XC3
k(B) = 9, l(B) = 1
- H
= C2=
SM_1 of order 2. Class: 2 Length: 1 Order: 2
G = (C3XC3):H =
SM_4 of order 18 =
S3PS3
k(B) = 6, l(B) = 2
- H
= C2=
SM_1 of order 2. Class: 3 Length: 12 Order: 2
G = (C3XC3):H =
SM_3 of order 18 =
S3XC3
k(B) = 9, l(B) = 2
- H
= C4=
SM_1 of order 4. Class: 5 Length: 3 Order: 4
G = (C3XC3):H =
SM_9 of order 36 =
(C3XC3):C4
k(B) = 6, l(B) = 4
Non-trivial central extensions by C2:
C8 =
SM_1
of order 8
, k(B2) = 6, l(B2) = 4;
(C3XC3):C8 =
SM_19
of order 72
- H
= C2XC2=
SM_2 of order 4. Class: 6 Length: 6 Order: 4
G = (C3XC3):H =
SM_10 of order 36 =
S3XS3
k(B) = 9, 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) = 9, l(B2) = 4;
(C3XC3):(C4YC4) =
SM_21
of order 72
D8 =
SM_3
of order 8
, k(B2) = 6, l(B2) = 1;
(C3:D8)PS3 =
SM_23
of order 72
Q8 =
SM_4
of order 8
, k(B2) = 6, l(B2) = 1;
(C3XC3):Q8 =
SM_24
of order 72
- H
= Q8=
SM_4 of order 8. Class: 10 Length: 1 Order: 8
G = (C3XC3):H =
SM_41 of order 72 =
(C3XC3):Q8
k(B) = 6, 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) = 6, l(B2) = 5;
SM_120
of order 144
- H
= D8=
SM_3 of order 8. Class: 11 Length: 3 Order: 8
G = (C3XC3):H =
SM_40 of order 72 =
(C3XC3):D8
k(B) = 9, l(B) = 5
Maximal subgroups: H1 =C2XC2
H2 =C2XC2
H3 =C4
Non-trivial central extensions by C2:
(C2XC2):C4 =
SM_3
of order 16
, k(B2) = 9, l(B2) = 5;
SM_115
of order 144
(C4:C4) =
SM_4
of order 16
, k(B2) = 9, l(B2) = 5;
SM_116
of order 144
D16 =
SM_7
of order 16
, k(B2) = 6, l(B2) = 2;
SM_117
of order 144
C8:C2 =
SM_8
of order 16
, k(B2) = 6, l(B2) = 2;
SM_118
of order 144
GQ16 =
SM_9
of order 16
, k(B2) = 6, l(B2) = 2;
SM_119
of order 144
- H
= C8=
SM_1 of order 8. Class: 12 Length: 3 Order: 8
G = (C3XC3):H =
SM_39 of order 72 =
(C3XC3):C8
k(B) = 9, l(B) = 8
Non-trivial central extensions by C2:
C16 =
SM_1
of order 16
, k(B2) = 9, l(B2) = 8;
SM_114
of order 144
- H
= C8:C2=
SM_8 of order 16. Class: 14 Length: 3 Order: 16
G = (C3XC3):H =
SM_182 of order 144
k(B) = 9, l(B) = 7
Maximal subgroups: H1 =C8
H2 =D8
H3 =Q8
Non-trivial central extensions by C2:
(C8XC2):C2 =
SM_9
of order 32
, k(B2) = 9, l(B2) = 7;
SM_841
of order 288
(C8XC2).C2 =
SM_10
of order 32
, k(B2) = 9, l(B2) = 7;
SM_842
of order 288
C8:C4 =
SM_13
of order 32
, k(B2) = 9, l(B2) = 7;
SM_843
of order 288
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