Order = 4154781481226426191177580544000000 = 241.313.56.72.11.13.17.19.23.31.47.
Mult = 2.
Out = 1.

Porting notes

Porting incomplete.

Standard generators

Standard generators of B are a, b where a is in class 2C, b is in class 3A, ab has order 55 and ababababbababbabb has order 23.

Black box algorithms

Finding generators

Group Algorithm File
B
Download

Checking generators (semi-presentations)

Group Semi-presentation File
B 〈〈 a, b | o(a) = 2, o(b) = 3, o(ab) = 55, o(ababababbababbabb) = 23, o(u) = 52, o(au26) = 35, o(v) = 38, o(v19ba) = 8; u = (ababb)2(ab)2(ababb)2, v = (ab)3(abbab)2ab(ababb)2abb 〉〉 Download

Representations

Representations of B

Maximal subgroups

Maximal subgroups of B

Subgroup Order Index Programs/reps
2.2E6(2):2 306 129 918 735 099 415 756 800 13 571 955 000Program: Generators
21+22.Co2 354 883 595 661 213 696 000 11 707 448 673 375Program: Generators
Fi23 4 089 470 473 293 004 800 1 015 970 529 280 000Program: Generators
29+16.S8(2) 1 589 728 887 019 929 600 2 613 515 747 968 125Program: Generators
Th 90 745 943 887 872 000 45 784 762 417 152 000Program: Generators
(22 × F4(2)):2 26 489 012 826 931 200 156 849 238 149 120 000Program: Generators
22+10+20.(M22:2 × S3) 22 858 846 741 463 040 181 758 140 654 146 875Program: Generators
[230].L5(2) 10 736 731 045 232 640 386 968 944 618 506 250Program: Generators
S3 × Fi22:2 774 741 019 852 800 5 362 800 438 804 480 000Program: Generators
[235].(S5 × L3(2)) 692 692 325 498 880 5 998 018 641 586 846 875
HN:2 546 061 824 000 000 7 608 628 361 513 926 656Program: Generators
O8+(3):S4 118 852 315 545 600 34 957 513 971 466 240 000
31+8.21+6.U4(2).2 130 606 940 160 31 811 337 714 034 278 400 000Program: Generators
(32:D8 × U4(3).2.2).2 1 881 169 920 2 208 615 732 717 237 043 200 000
5:4 × HS:2 1 774 080 000 2 341 935 809 673 986 624 716 800Program: Generators
S4 × 2F4(2) 862 617 600 4 816 481 232 502 590 013 440 000Program: Generators
[311].(S4 × 2S4) 204 073 344 20 359 256 136 981 938 176 000 000
S5 × M22:2 106 444 800 39 032 263 494 566 443 745 280 000
(S6 × L3(4):2).2 58 060 800 71 559 149 740 038 480 199 680 000
53.L3(5) 46 500 000 89 350 139 381 213 466 476 937 216
51+4.21+4.A5.4 24 000 000 173 115 895 051 101 091 299 065 856Program: Generators
(S6 × S6).4 2 073 600 2 003 656 192 721 077 445 591 040 000
52:4S4 × S5 288 000 14 426 324 587 591 757 608 255 488 000
L2(49).23 117 600 35 329 774 500 224 712 510 013 440 000
L2(31) 14 880 279 219 185 566 292 082 740 428 800 000
M11 7 920 524 593 621 366 973 003 936 563 200 000
L3(3) 5 616 739 811 517 312 397 826 064 384 000 000
L2(17):2 4 896 848 607 328 681 868 094 603 264 000 000
L2(11):2 1 320 3 147 561 728 201 838 023 619 379 200 000
47:23 1 081 3 843 461 129 719 173 164 826 624 000 000Program: Generators

Conjugacy classes

Conjugacy classes of B

Conjugacy class Centraliser order Power up Class rep(s)
1A4 154 781 481 226 426 191 177 580 544 000 000
2A306 129 918 735 099 415 756 800 6A 6B 6D 10A 14A 14B 18A 18B 22A 26B 30A 30B 34B 34C 38A 42A 42B 66A 70A
2B354 883 595 661 213 696 000 4A 4B 4C 4D 4F 4G 6C 6G 8A 8B 8C 8D 8E 8F 8H 8I 8L 10B 10D 12A 12B 12C 12D 12E 12G 12H 12I 12K 12L 12M 12O 14D 16A 16B 16C 16D 16E 16F 18C 20A 20B 20C 20D 20E 20F 20I 22B 24A 24B 24C 24D 24E 24F 24G 24K 24M 28A 28B 28C 28D 30D 30G 30H 32A 32B 32C 32D 36A 36B 40A 40B 40C 40D 44A 46A 46B 48A 48B 56A 56B 60A 60B
2C26 489 012 826 931 200 4I 6F 6K 10C 12T 14C 18F 20H 26A 30C 34A 42C 52A
2D11 689 182 992 793 600 4E 4H 4J 6E 6H 6I 6J 8G 8J 8K 8M 8N 10E 10F 12F 12J 12N 12P 12Q 12R 12S 14E 16G 16H 18D 18E 20G 20J 24H 24I 24J 24L 24N 28E 30E 30F 36C 40E 60C
3A387 370 509 926 400 6A 6B 6C 6E 6F 6H 12A 12C 12D 12E 12G 12H 12I 12J 12L 12P 15A 21A 24A 24B 24C 24D 24E 24G 24I 24J 30A 30B 30C 30D 30E 33A 39A 42A 42B 42C 48A 48B 60A 60B 66A
3B65 303 470 080 6D 6G 6I 6J 6K 9A 9B 12B 12F 12K 12M 12N 12O 12Q 12R 12S 12T 15B 18A 18B 18C 18D 18E 18F 24F 24H 24K 24L 24M 24N 27A 30F 30G 30H 36A 36B 36C 60C
4A372 051 542 016 000 12C 20A 20B 20C 28C 44A 60A
4B109 586 090 557 440 8B 8C 8E 12A 12B 12D 20D 24A 24B 24C 24D 28A 36A 40A 40B 40C
4C202 937 204 736 8A 8D 8F 8H 12G 12M 16A 16B 16C 16D 16E 16F 24E 24F 24G 24K 28B 32A 32B 32C 32D 48A 48B 56A 56B
4D190 253 629 440 12E 12H 12K 20E 28D 36B 60B
4E95 126 814 720 8G 8J 12F 12J 12N 20G 24H 24I 24J 28E 36C 40E 60C
4F24 159 191 040 8I 12I 12O 20I 24M
4G6 039 797 760 8L 12L 20F 40D
4H301 989 888 8K 8M 12P 12Q 12S 16G 16H 24L
4I143 769 600 12T 20H 52A
4J125 829 120 8N 12R 20J 24N
5A443 520 000 10A 10B 10C 10E 15A 20A 20C 20D 20E 20F 20H 30A 30B 30C 30D 30E 35A 40A 40B 40C 40D 55A 60A 60B 70A
5B6 000 000 10D 10F 15B 20B 20G 20I 20J 25A 30F 30G 30H 40E 60C
6A110 361 968 640 30B 42B 66A
6B6 270 566 400 30A 42A
6C318 504 960 12A 12C 12D 12E 12G 12H 12I 12L 24A 24B 24C 24D 24E 24G 30D 48A 48B 60A 60B
6D40 310 784 18A 18B
6E19 906 560 30E
6F17 418 240 30C 42C
6G14 929 920 12B 12K 12M 12O 18C 24F 24K 24M 30G 30H 36A 36B
6H10 616 832 12J 12P 24I 24J
6I9 953 280 12F 12Q 12R 24H 24L 24N 30F 60C
6J497 664 12N 12S 18D 18E 36C
6K373 248 12T 18F
7A564 480 14A 14B 14C 14D 14E 21A 28A 28B 28C 28D 28E 35A 42A 42B 42C 56A 56B 70A
8A396 361 728 24E 24F 56A 56B
8B11 796 480 24A 40A
8C11 796 480 24B 40B
8D6 291 456 16A 16B 16E 24G 48A 48B
8E5 898 240 24C 24D 40C
8F1 572 864 24K
8G1 474 560 24H 24I 40E
8H524 288 16C 16D 16F 32A 32B 32C 32D
8I196 608 24M
8J98 304 24J
8K98 304 16G 24L
8L81 920 40D
8M32 768 16H
8N12 288 24N
9A17 496 18E 27A 36C
9B11 664 18A 18B 18C 18D 18F 36A 36B
10A403 200 30A 30B 70A
10B76 800 20A 20C 20D 20E 20F 30D 40A 40B 40C 40D 60A 60B
10C28 800 20H 30C
10D24 000 20B 20I 30G 30H
10E19 200 30E
10F9 600 20G 20J 30F 40E 60C
11A1 320 22A 22B 33A 44A 55A 66A
12A3 981 312 Omitted owing to length.
12B746 496 36A
12C737 280 60A
12D663 552 24A 24B 24C 24D
12E276 480 60B
12F138 240 24H 60C
12G73 728 24E 24G 48A 48B
12H55 296 Omitted owing to length.
12I36 864 abababbababbabababbababbabababababbababbabbabbababb
12J27 648 24I 24J
12K20 736 36B
12L18 432 Omitted owing to length.
12M13 824 24F 24K
12N10 368 36C
12O9 216 24M
12P9 216 Omitted owing to length.
12Q9 216 24L
12R1 536 24N
12S1 152 ababbabababbababababbababbabb
12T864 ababababbababababbababbabababbababb
13A312 26A 26B 39A 52A
14A564 480 42A 70A
14B4 704 42B
14C4 704 42C
14D1 792 28A 28B 28C 28D 56A 56B
14E1 792 28E
15A3 600 30A 30B 30C 30D 30E 60A 60B
15B120 30F 30G 30H 60C
16A12 288 48A
16B12 288 48B
16C2 048 32A 32B
16D2 048 32C 32D
16E2 048 aababbabababababbababbabbabbababbabbababababbababb
16F1 024 ababbababababbababbabbabb
16G256 abababababbababbabbabbab
16H256 Omitted owing to length.
17A68 34A 34B 34C
18A1 296 abababababbababbabbabbababababababbababbabbabbababbabb
18B648 Omitted owing to length.
18C432 36A 36B
18D432 aabababababbababbabbabbababbabbababababbababbabb
18E216 36C
18F216 abababbababb
19A38 38A
20A38 400 60A
20B4 000 Omitted owing to length.
20C3 200 Omitted owing to length.
20D2 560 40A 40B 40C
20E960 60B
20F640 40D
20G480 40E 60C
20H400 abababbabababbababbabababbababb
20I160 ababababbababbababababbababbabbababababbababbabb
20J80
21A252 42A 42B 42C
22A132 66A
22B88 44A
23A46 23B5 46A 46B
23B46 23A5 46A 46B
24A2 304 abababbabababababbababbabbabbababababbababababbababb
24B2 304 Omitted owing to length.
24C2 304 Omitted owing to length.
24D2 304 Omitted owing to length.
24E2 304 ababbabababbabababbababb
24F1 728 ababbababbabababbabababbababb
24G768 48A 48B
24H576 Omitted owing to length.
24I576 abababbabababbababbababababbababbabb
24J192 abababbabababbababbabababbab
24K192 abababababbababbabababbab
24L192 abababbababababbababbabababbababababababbababbabbabb
24M96 abababbababababbababbabababbabababababbababbabbabb
24N96 bababababbababbabababababbababbabbabb
25A25 ababababbabababbab
26A104 52A
26B52 ababababbabababbababb
27A27 abababbababbababababbababbabb
28A448 aabababbababbabababababbababbabbabbababbabbababbab
28B448 56A 56B
28C224 abababbababbabababbababbababababbababb
28D224 Omitted owing to length.
28E112 abababbabababababbababbabb
30A3 600 Omitted owing to length.
30B360 aabababbabababbabababababbababbabbabbababbabbababb
30C360 Omitted owing to length.
30D240 60A 60B
30E240 abababbababbabababbababababbab
30F120 60C
30G60 30H7
30H60 30G7
31A31 31B3
31B31 31A3
32A128 32B3
32B128 32A3
32C128 32D5
32D128 32C5
33A66 66A
34A68 ababababbababbabababababbababbabbabb
34B68 34C3 abababbabababbab
34C68 34B3
35A70 70A
36A216 Omitted owing to length.
36B72 abababbababbabababababbababbabbabb
36C36 ababbabababbababbabababbab
38A38 ababababbababbababababbababbabb
39A39 ababababbababababbababbabb
40A320 Omitted owing to length.
40B320 abababbabababababbababbabbababababbababbabb
40C160 Omitted owing to length.
40D80 ababb
40E40 ababababbababababbababb
42A252 Omitted owing to length.
42B84 aabababababbababbabbabbababababababbababbabbabbababbabb
42C84 abababbababababababbababbabbabbababb
44A44 abababbabababababbababb
46A46 46B5 abababababbababbabbabb
46B46 46A5
47A47 47B5 abababbababababbababb
47B47 47A5
48A96 ababababbab
48B96 ababababbababbabbabbabababababbababbabbabbababb
52A52 ababbababbababababbababb
55A55 ab
56A112 56B5 ababbababababbababbabababbababb
56B112 56A5
60A120 abbababababbababbabbabababb
60B120 abababababbababbabbabbababbababababbababbabababababbababbabbabb
60C60 ababababbababababbab
66A66 abababbabababababbababbabbababababbababb
70A70 abababababbababbabababbababb
30G-H abababababbababbabbabababbab
31A-B ababababbababb
32A-B abababababbababb
32C-D ababababababbababbabbabbababb

Download words for class representatives.