19-blocks with cyclic defect group in the ATLAS groups:
Block information:
- k(B),l(B) invariants.
- Principal block of local subgroup, where relevant.
- Diagonal of Cartan matrix when the decomposition matrix is known
- Degrees of irreducible characters, divided by gcd.
k(B) = 9, l(B) = 3
.. .. [ ]
- 2F4(8)
19-block 6,
[ 1, 56, 512, 567, 567, 567, 567, 567, 567 ]
[ 2, 2, 7 ]
- 3.L3(7)
19-block 1,
[ 1, 56, 288, 288, 288, 288, 288, 288, 343 ]
- 3.L3(7).3
19-block 1,
[ 1, 56, 288, 288, 288, 288, 288, 288, 343 ]
- 3.L3(7).3
19-block 2,
[ 1, 56, 288, 288, 288, 288, 288, 288, 343 ]
- 3.L3(7).3
19-block 3,
[ 1, 56, 288, 288, 288, 288, 288, 288, 343 ]
- L3(7)
19-block 1,
[ 1, 56, 288, 288, 288, 288, 288, 288, 343 ]
- L3(7).3
19-block 1,
[ 1, 56, 288, 288, 288, 288, 288, 288, 343 ]
- L3(7).3
19-block 2,
[ 1, 56, 288, 288, 288, 288, 288, 288, 343 ]
- L3(7).3
19-block 3,
[ 1, 56, 288, 288, 288, 288, 288, 288, 343 ]
[ 2, 7, 7 ]
- 3.U3(8)
19-block 1,
[ 1, 56, 512, 567, 567, 567, 567, 567, 567 ]
- 3.U3(8).3_2
19-block 1,
[ 1, 56, 512, 567, 567, 567, 567, 567, 567 ]
- 3.U3(8).3_2
19-block 2,
[ 1, 56, 512, 567, 567, 567, 567, 567, 567 ]
- 3.U3(8).3_2
19-block 3,
[ 1, 56, 512, 567, 567, 567, 567, 567, 567 ]
- U3(8)
19-block 1,
[ 1, 56, 512, 567, 567, 567, 567, 567, 567 ]
- U3(8).3_2
19-block 1,
[ 1, 56, 512, 567, 567, 567, 567, 567, 567 ]
- U3(8).3_2
19-block 2,
[ 1, 56, 512, 567, 567, 567, 567, 567, 567 ]
- U3(8).3_2
19-block 3,
[ 1, 56, 512, 567, 567, 567, 567, 567, 567 ]
[ 7, 7, 7 ]
- 3.L3(7)
19-block 19,
[ 1, 1, 1, 3, 3, 3, 3, 3, 3 ]
- 3.L3(7)
19-block 20,
[ 1, 1, 1, 3, 3, 3, 3, 3, 3 ]
- 3.L3(7).2
19-block 21,
[ 1, 1, 1, 3, 3, 3, 3, 3, 3 ]
- 3.U3(8)
19-block 27,
[ 1, 1, 1, 3, 3, 3, 3, 3, 3 ]
- 3.U3(8)
19-block 28,
[ 1, 1, 1, 3, 3, 3, 3, 3, 3 ]
- 3.U3(8).2
19-block 25,
[ 1, 1, 1, 3, 3, 3, 3, 3, 3 ]
k(B) = 9, l(B) = 6
.. .. [ ]
- 2F4(8)
19-block 1,
[ 1, 170741088, 357739200, 357739200, 545261600, 67629477825, 67629477825,
67629477825, 68719476736 ]
- ONM2
19-block 1,
[ 1, 1, 56, 56, 343, 343, 576, 576, 576 ]
[ 2, 2, 2, 2, 2, 4 ]
- 3.ON
19-block 27,
[ 11, 11, 2728, 3906, 4608, 4608, 4608, 5632, 5632 ]
- 3.ON
19-block 28,
[ 11, 11, 2728, 3906, 4608, 4608, 4608, 5632, 5632 ]
- 3.ON.2
19-block 32,
[ 11, 11, 2728, 3906, 4608, 4608, 4608, 5632, 5632 ]
[ 2, 2, 2, 2, 4, 4 ]
- 3.L3(7).2
19-block 1,
[ 1, 1, 56, 56, 343, 343, 576, 576, 576 ]
- 3.ON
19-block 1,
[ 1, 85064, 116963, 175616, 175616, 175770, 207360, 207360, 207360 ]
- 3.ON.2
19-block 1,
[ 1, 85064, 116963, 175616, 175616, 175770, 207360, 207360, 207360 ]
- 3.ON.2
19-block 2,
[ 1, 85064, 116963, 175616, 175616, 175770, 207360, 207360, 207360 ]
- J1
19-block 1,
[ 1, 56, 56, 77, 77, 77, 120, 120, 120 ]
- J1
19-block 1,
[ 1, 56, 56, 77, 77, 77, 120, 120, 120 ]
- L3(7).2
19-block 1,
[ 1, 1, 56, 56, 343, 343, 576, 576, 576 ]
- ON
19-block 1,
[ 1, 85064, 116963, 175616, 175616, 175770, 207360, 207360, 207360 ]
- ON
19-block 1,
[ 1, 85064, 116963, 175616, 175616, 175770, 207360, 207360, 207360 ]
- ON.2
19-block 1,
[ 1, 85064, 116963, 175616, 175616, 175770, 207360, 207360, 207360 ]
- ON.2
19-block 2,
[ 1, 85064, 116963, 175616, 175616, 175770, 207360, 207360, 207360 ]
[ 2, 2, 4, 4, 4, 4 ]
- 3.U3(8).2
19-block 1,
[ 1, 1, 56, 56, 512, 512, 1134, 1134, 1134 ]
- U3(8).2
19-block 1,
[ 1, 1, 56, 56, 512, 512, 1134, 1134, 1134 ]
[ 2, 4, 4, 4, 4, 4 ]
- R(27)
19-block 1,
[ 1, 1443, 1443, 2184, 2184, 19683, 26936, 26936, 26936 ]
[ 4, 4, 4, 4, 4, 4 ]
- 19:6
19-block 1,
[ 1, 1, 1, 1, 1, 1, 6, 6, 6 ]
k(B) = 11, l(B) = 2
.. .. [ ]
- L2(113)
19-block 1,
[ 1, 112, 112, 112, 112, 112, 112, 112, 112, 112, 113 ]
- L2(37)
19-block 1,
[ 1, 36, 36, 36, 36, 36, 36, 36, 36, 36, 37 ]
k(B) = 11, l(B) = 9
.. .. [ ]
- 2.B
19-block 149,
[ 47, 17899245, 10449529740, 82241557632, 82241557632, 765064872000,
875914271232, 1867392432360, 4189738949253, 4189738949253, 10285909803008 ]
- 2E6(2).3
19-block 1,
[ 1, 48620, 4331600, 137225088, 145411200, 145411200, 2217779200,
12745441280, 58615481925, 58615481925, 68719476736 ]
- 2E6(2).3
19-block 2,
[ 1, 48620, 4331600, 137225088, 145411200, 145411200, 2217779200,
12745441280, 58615481925, 58615481925, 68719476736 ]
- 2E6(2).3
19-block 3,
[ 1, 48620, 4331600, 137225088, 145411200, 145411200, 2217779200,
12745441280, 58615481925, 58615481925, 68719476736 ]
- 2E6(2).3.2
19-block 2,
[ 1, 48620, 4331600, 137225088, 145411200, 145411200, 2217779200,
12745441280, 58615481925, 58615481925, 68719476736 ]
- 2^2.2E6(2)
19-block 118,
[ 357, 36465, 10633194, 176432256, 217817600, 265228425, 265228425,
297729432, 297729432, 385945560, 536870912 ]
- 2^2.2E6(2)
19-block 184,
[ 357, 36465, 10633194, 176432256, 217817600, 265228425, 265228425,
297729432, 297729432, 385945560, 536870912 ]
- 2^2.2E6(2)
19-block 1,
[ 1, 48620, 4331600, 137225088, 145411200, 145411200, 2217779200,
12745441280, 58615481925, 58615481925, 68719476736 ]
- 2^2.2E6(2)
19-block 250,
[ 357, 36465, 10633194, 176432256, 217817600, 265228425, 265228425,
297729432, 297729432, 385945560, 536870912 ]
- 2^2.2E6(2).2
19-block 286,
[ 357, 36465, 10633194, 176432256, 217817600, 265228425, 265228425,
297729432, 297729432, 385945560, 536870912 ]
- 2^2.2E6(2).3
19-block 1,
[ 1, 48620, 4331600, 137225088, 145411200, 145411200, 2217779200,
12745441280, 58615481925, 58615481925, 68719476736 ]
- 2^2.2E6(2).3
19-block 238,
[ 357, 36465, 10633194, 176432256, 217817600, 265228425, 265228425,
297729432, 297729432, 385945560, 536870912 ]
- 2^2.2E6(2).3
19-block 2,
[ 1, 48620, 4331600, 137225088, 145411200, 145411200, 2217779200,
12745441280, 58615481925, 58615481925, 68719476736 ]
- 2^2.2E6(2).3
19-block 3,
[ 1, 48620, 4331600, 137225088, 145411200, 145411200, 2217779200,
12745441280, 58615481925, 58615481925, 68719476736 ]
- 2^2.2E6(2).3.2
19-block 2,
[ 1, 48620, 4331600, 137225088, 145411200, 145411200, 2217779200,
12745441280, 58615481925, 58615481925, 68719476736 ]
- J3M3
19-block 1,
[ 1, 9, 9, 18, 18, 18, 18, 20, 20, 20, 20 ]
[ 2, 2, 2, 2, 2, 2, 2, 2, 3 ]
- 2.2E6(2)
19-block 118,
[ 357, 36465, 10633194, 176432256, 217817600, 265228425, 265228425,
297729432, 297729432, 385945560, 536870912 ]
- 2.L2(19)
19-block 1,
[ 1, 9, 9, 18, 18, 18, 18, 20, 20, 20, 20 ]
- 2.L2(19)
19-block 3,
[ 5, 5, 9, 9, 9, 9, 9, 10, 10, 10, 10 ]
- 3.J3
19-block 1,
[ 1, 85, 85, 324, 816, 1215, 1215, 1920, 1920, 1920, 2754 ]
- HN
19-block 1,
[ 1, 8910, 656250, 656250, 2661120, 2784375, 2985984, 3200000, 4561920,
5103000, 5103000 ]
- HN
19-block 1,
[ 1, 8910, 656250, 656250, 2661120, 2784375, 2985984, 3200000, 4561920,
5103000, 5103000 ]
- J3
19-block 1,
[ 1, 85, 85, 324, 816, 1215, 1215, 1920, 1920, 1920, 2754 ]
- J3
19-block 1,
[ 1, 85, 85, 324, 816, 1215, 1215, 1920, 1920, 1920, 2754 ]
- L2(19)
19-block 1,
[ 1, 9, 9, 18, 18, 18, 18, 20, 20, 20, 20 ]
- M
19-block 4,
[ 112723, 88374008632, 20994117890625, 143644700131937550,
1518492242208593750, 1518492242208593750, 21072664474170885576,
41446909902018576384, 758590357247129760507, 809253910512343711744,
1506986809419880546875 ]
- M
19-block 4,
[ 112723, 88374008632, 20994117890625, 143644700131937550,
1518492242208593750, 1518492242208593750, 21072664474170885576,
41446909902018576384, 758590357247129760507, 809253910512343711744,
1506986809419880546875 ]
[ 2, 2, 2, 2, 2, 2, 2, 3, 3 ]
- 3.J3
19-block 12,
[ 2, 2, 17, 17, 36, 135, 135, 170, 170, 306, 340 ]
- 3.J3
19-block 13,
[ 2, 2, 17, 17, 36, 135, 135, 170, 170, 306, 340 ]
- 3.J3.2
19-block 13,
[ 2, 2, 17, 17, 36, 135, 135, 170, 170, 306, 340 ]
[ 2, 2, 2, 2, 2, 3, 3, 3, 3 ]
- 2.2E6(2)
19-block 1,
[ 1, 48620, 4331600, 137225088, 145411200, 145411200, 2217779200,
12745441280, 58615481925, 58615481925, 68719476736 ]
- 2E6(2)
19-block 1,
[ 1, 48620, 4331600, 137225088, 145411200, 145411200, 2217779200,
12745441280, 58615481925, 58615481925, 68719476736 ]
[ 2, 2, 2, 3, 3, 3, 3, 3, 3 ]
- 3.U3(8).3_1
19-block 1,
[ 1, 1, 1, 56, 56, 56, 512, 512, 512, 1701, 1701 ]
- U3(8).3_1
19-block 1,
[ 1, 1, 1, 56, 56, 56, 512, 512, 512, 1701, 1701 ]
- U3(8).3_3
19-block 1,
[ 1, 1, 1, 56, 56, 56, 512, 512, 512, 1701, 1701 ]
[ 3, 3, 3, 3, 3, 3, 3, 3, 3 ]
- 3.U3(8).3_1
19-block 29,
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9 ]
- 3.U3(8).3_1
19-block 30,
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9 ]
- 3.U3(8).6
19-block 23,
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9 ]
k(B) = 19, l(B) = 1
.. .. [ ]
- L2(113)
19-block 2,
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
[ 19 ]
- 3.L3(7).3
19-block 47,
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
- 3.L3(7).3
19-block 48,
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
- 3.U3(8).3_2
19-block 71,
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
- 3.U3(8).3_2
19-block 72,
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
k(B) = 19, l(B) = 18
.. .. [ ]
- 2.B
19-block 1,
[ 1, 4371, 356054375, 80426400000, 635966233056, 8379477898506,
8379477898506, 19246163186250, 123485536419840, 718889622405120,
1042755084800000, 1679281227336960, 3469068040246875, 9211433539600384,
9573585768140625, 9573585768140625, 11854109736960000, 13940902029600000,
14014628339712000 ]
- 2.B
19-block 2,
[ 4185, 49538, 411250, 1192008125, 114107686875, 178145092125, 178145092125,
355001692500, 928109000000, 928109000000, 83849979761730, 213903009596250,
334715881500000, 363106960734375, 400497110417408, 515396075520000,
540187648000000, 540187648000000, 567232388136960 ]
- 2E6(2).3.2
19-block 1,
[ 1, 1, 48620, 48620, 4331600, 4331600, 137225088, 137225088, 145411200,
145411200, 145411200, 145411200, 2217779200, 2217779200, 12745441280,
12745441280, 68719476736, 68719476736, 117230963850 ]
- 2^2.2E6(2).2
19-block 174,
[ 357, 357, 36465, 36465, 10633194, 10633194, 176432256, 176432256,
217817600, 217817600, 265228425, 265228425, 265228425, 265228425,
385945560, 385945560, 536870912, 536870912, 595458864 ]
- 2^2.2E6(2).2
19-block 1,
[ 1, 1, 48620, 48620, 4331600, 4331600, 137225088, 137225088, 145411200,
145411200, 145411200, 145411200, 2217779200, 2217779200, 12745441280,
12745441280, 68719476736, 68719476736, 117230963850 ]
- 2^2.2E6(2).3.2
19-block 1,
[ 1, 1, 48620, 48620, 4331600, 4331600, 137225088, 137225088, 145411200,
145411200, 145411200, 145411200, 2217779200, 2217779200, 12745441280,
12745441280, 68719476736, 68719476736, 117230963850 ]
- 2^2.2E6(2).3.2
19-block 234,
[ 357, 357, 36465, 36465, 10633194, 10633194, 176432256, 176432256,
217817600, 217817600, 265228425, 265228425, 265228425, 265228425,
385945560, 385945560, 536870912, 536870912, 595458864 ]
- B
19-block 1,
[ 1, 4371, 356054375, 80426400000, 635966233056, 8379477898506,
8379477898506, 19246163186250, 123485536419840, 718889622405120,
1042755084800000, 1679281227336960, 3469068040246875, 9211433539600384,
9573585768140625, 9573585768140625, 11854109736960000, 13940902029600000,
14014628339712000 ]
- B
19-block 1,
[ 1, 4371, 356054375, 80426400000, 635966233056, 8379477898506,
8379477898506, 19246163186250, 123485536419840, 718889622405120,
1042755084800000, 1679281227336960, 3469068040246875, 9211433539600384,
9573585768140625, 9573585768140625, 11854109736960000, 13940902029600000,
14014628339712000 ]
- B
19-block 2,
[ 4185, 49538, 411250, 1192008125, 114107686875, 178145092125, 178145092125,
355001692500, 928109000000, 928109000000, 83849979761730, 213903009596250,
334715881500000, 363106960734375, 400497110417408, 515396075520000,
540187648000000, 540187648000000, 567232388136960 ]
- B
19-block 2,
[ 4185, 49538, 411250, 1192008125, 114107686875, 178145092125, 178145092125,
355001692500, 928109000000, 928109000000, 83849979761730, 213903009596250,
334715881500000, 363106960734375, 400497110417408, 515396075520000,
540187648000000, 540187648000000, 567232388136960 ]
[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]
- 19:18
19-block 1,
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 18 ]
- 2.2E6(2).2
19-block 174,
[ 357, 357, 36465, 36465, 10633194, 10633194, 176432256, 176432256,
217817600, 217817600, 265228425, 265228425, 265228425, 265228425,
385945560, 385945560, 536870912, 536870912, 595458864 ]
- 2.2E6(2).2
19-block 1,
[ 1, 1, 48620, 48620, 4331600, 4331600, 137225088, 137225088, 145411200,
145411200, 145411200, 145411200, 2217779200, 2217779200, 12745441280,
12745441280, 68719476736, 68719476736, 117230963850 ]
- 2.L2(19).2
19-block 1,
[ 1, 1, 18, 18, 18, 18, 18, 18, 18, 18, 18, 20, 20, 20, 20, 20, 20, 20, 20 ]
- 2.L2(19).2
19-block 4,
[ 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10 ]
- 2E6(2).2
19-block 1,
[ 1, 1, 48620, 48620, 4331600, 4331600, 137225088, 137225088, 145411200,
145411200, 145411200, 145411200, 2217779200, 2217779200, 12745441280,
12745441280, 68719476736, 68719476736, 117230963850 ]
- 3.J3.2
19-block 1,
[ 1, 1, 170, 324, 324, 816, 816, 1215, 1215, 1215, 1215, 1920, 1920, 1920,
1920, 1920, 1920, 2754, 2754 ]
- 3.U3(8).6
19-block 1,
[ 1, 1, 1, 1, 1, 1, 56, 56, 56, 56, 56, 56, 512, 512, 512, 512, 512, 512,
3402 ]
- HN.2
19-block 1,
[ 1, 1, 8910, 8910, 1312500, 2661120, 2661120, 2784375, 2784375, 2985984,
2985984, 3200000, 3200000, 4561920, 4561920, 5103000, 5103000, 5103000,
5103000 ]
- J3.2
19-block 1,
[ 1, 1, 170, 324, 324, 816, 816, 1215, 1215, 1215, 1215, 1920, 1920, 1920,
1920, 1920, 1920, 2754, 2754 ]
- L2(19).2
19-block 1,
[ 1, 1, 18, 18, 18, 18, 18, 18, 18, 18, 18, 20, 20, 20, 20, 20, 20, 20, 20 ]
- M
19-block 1,
[ 1, 125510727015275, 2374124840062976, 3503434660075044981,
3503434660075044981, 28585990950721640625, 172399434201593354756,
172399434201593354756, 643356925889917747200, 776097192277137500000,
10145274012943412428800, 114212876389603002704448, 115192831837135016250000,
4926670174323484069683200, 9416031858681585751556096,
14930164283563048960000000, 58437394633227526183321600,
64326163427522624205703125, 103354104243912727763091456 ]
- M
19-block 1,
[ 1, 125510727015275, 2374124840062976, 3503434660075044981,
3503434660075044981, 28585990950721640625, 172399434201593354756,
172399434201593354756, 643356925889917747200, 776097192277137500000,
10145274012943412428800, 114212876389603002704448, 115192831837135016250000,
4926670174323484069683200, 9416031858681585751556096,
14930164283563048960000000, 58437394633227526183321600,
64326163427522624205703125, 103354104243912727763091456 ]
- M
19-block 2,
[ 3337, 14281514, 3225293995077, 50618319074698375, 522297386207788555,
2210429668141406250, 122490006146291875000, 335523964617101588328,
698467065154117187500, 3734347066265022158952, 11104393747011956015625,
11690961460670425101597, 11690961460670425101597, 503982057964565799370752,
2102684501576635104886784, 2196144373184795498250240,
3016378267349713752845268, 3396455376594621818203125,
3446004428155217835156250 ]
- M
19-block 2,
[ 3337, 14281514, 3225293995077, 50618319074698375, 522297386207788555,
2210429668141406250, 122490006146291875000, 335523964617101588328,
698467065154117187500, 3734347066265022158952, 11104393747011956015625,
11690961460670425101597, 11690961460670425101597, 503982057964565799370752,
2102684501576635104886784, 2196144373184795498250240,
3016378267349713752845268, 3396455376594621818203125,
3446004428155217835156250 ]
- M
19-block 3,
[ 21296876, 18538750076, 222879856734249, 1044868466775133, 39660520552077425,
8754193822112578125, 21803647757861753437500, 91068387388302451493925,
261575621299360905468750, 433528694560598978525184,
626877403613887304040448, 626877403613887304040448,
689763222744895005949242, 689763222744895005949242,
8874260875527017936065100, 74612213529720383654779356,
136107644194473772613203125, 172248852397651745653437500,
241866941438795926688759808 ]
- M
19-block 3,
[ 21296876, 18538750076, 222879856734249, 1044868466775133, 39660520552077425,
8754193822112578125, 21803647757861753437500, 91068387388302451493925,
261575621299360905468750, 433528694560598978525184,
626877403613887304040448, 626877403613887304040448,
689763222744895005949242, 689763222744895005949242,
8874260875527017936065100, 74612213529720383654779356,
136107644194473772613203125, 172248852397651745653437500,
241866941438795926688759808 ]
- R(27).3
19-block 1,
[ 1, 1, 1, 1443, 1443, 1443, 1443, 1443, 1443, 2184, 2184, 2184, 2184, 2184,
2184, 19683, 19683, 19683, 80808 ]
- Th
19-block 1,
[ 1, 248, 27000, 27000, 85995, 85995, 767637, 767637, 4096000, 4096000,
4881384, 4936750, 6696000, 6696000, 21326760, 21326760, 76271625, 77376000,
190373976 ]
- Th
19-block 1,
[ 1, 248, 27000, 27000, 85995, 85995, 767637, 767637, 4096000, 4096000,
4881384, 4936750, 6696000, 6696000, 21326760, 21326760, 76271625, 77376000,
190373976 ]
- U3(8).6
19-block 1,
[ 1, 1, 1, 1, 1, 1, 56, 56, 56, 56, 56, 56, 512, 512, 512, 512, 512, 512,
3402 ]
Last Update: January 26, 2004,using IndexOfCyclicBlocks.gap, created by M.S\
chaps