Order = 4157776806543360000 = 221.39.54.72.11.13.23.
Mult = 2.
Out = 1.

Porting notes

Fully copied from version 2. 30/7/06.

Standard generators

Standard generators of Co1 are a, b where a is in class 2B, b is in class 3C, ab has order 40 and ababb has order 6.

Standard generators of 2.Co1 = Co0 are preimages A, B where B has order 3 and ABABABABBABABBAB has order 33.

Black box algorithms

Finding generators

Group Algorithm File
Co1
Download

Checking generators (semi-presentations)

Group Semi-presentation File
Co1 〈〈 a, b | o(a) = 2, o(b) = 3, o(ab) = 40, o(abab2) = 6, o(z) = 42, o(ab2z21) = 11, o(uv) = 36, o(uvvuvuv) = 18; z = ab(ababb)2, u = (ab)20, v = bababababb 〉〉 Download

Representations

Representations of Co1

Representations of 2.Co1

Maximal subgroups

Maximal subgroups of Co1

Subgroup Order Index Programs/reps
Co2 42 305 421 312 000 98 280Program: Standard generators
3.Suz:2 2 690 072 985 600 1 545 600Program: Standard generators
211:M24 501 397 585 920 8 292 375Program: Generators
Co3 495 766 656 000 8 386 560Program: Generators
21+8.O8+(2) 89 181 388 800 46 621 575Program: Generators
U6(2):S3 55 180 984 320 75 348 000Program: Generators
(A4 × G2(4)):2 6 038 323 200 688 564 800
22+12:(A8 × S3) 1 981 808 640 2 097 970 875
24+12.(S3 × 3.S6) 849 346 560 4 895 265 375
32.U4(3).D8 235 146 240 17 681 664 000
36:2.M12 138 568 320 30 005 248 000
(A5 × J2):2 72 576 000 57 288 591 360
31+4:2.S4(3).2 25 194 240 165 028 864 000
(A6 × U3(3)).2 4 354 560 954 809 856 000
33+4:2.(S4 × S4) 2 519 424 1 650 288 640 000
A9 × S3 1 088 640 3 819 239 424 000
(A7 × L2(7)):2 846 720 4 910 450 688 000
(D10 × (A5 × A5).2).2 144 000 28 873 450 045 440
51+2:GL2(5) 60 000 69 296 280 109 056
53:(4 × A5).2 60 000 69 296 280 109 056
72:(3 × 2.S4) 3 528 1 178 508 165 120 000
52:2A5 3 000 1 385 925 602 181 120

Conjugacy classes

Conjugacy classes of Co1

Conjugacy class Centraliser order Power up Class rep(s)
1A4 157 776 806 543 360 000
2A89 181 388 800 4A 4B 4C 4D 6A 6C 6D 6E 6F 8A 8B 8C 8D 8E 8F 10A 10D 10E 12A 12B 12C 12D 12E 12G 12H 12I 12J 12K 14B 16A 16B 18A 18B 18C 20A 20C 24A 24B 24C 24D 24E 24F 28A 30A 30D 30E 36A 40A 60A
2B2 012 774 400 4E 6B 6H 10B 10C 12F 12L 14A 26A 28B 30B 30C 42A
2C389 283 840 4F 6G 6I 10F 12M 20B 22A
3A1 345 036 492 800 6A 6B 12A 12B 12C 12F 15A 15B 21A 24A 24B 24D 30A 30B 33A 39A 39B 42A 60A
3B58 786 560 6C 6E 6G 12E 12G 12I 12J 15D 21B 24C 24E 30D
3C12 597 120 6D 6F 9A 9B 9C 12D 12H 12K 15E 18A 18B 18C 24F 30E 36A
3D544 320 6H 6I 12L 12M 15C 21C 30C
4A371 589 120 8A 8B 12A 12D 12E 20A 24A 24C 24E 28A 36A 40A 60A
4B1 179 648 8C 8D 12B 12G 12K 16A 16B 24B
4C737 280 8E 12H 12I 20C 24F
4D294 912 8F 12C 12J 24D
4E48 384 12F 12L 28B
4F15 360 12M 20B
5A3 024 000 10A 10B 15A 15C 20A 30A 30C 35A 40A 60A
5B36 000 10C 10D 10F 15B 15D 20B 30B 30D
5C15 000 10E 15E 20C 30E
6A9 953 280 12A 12B 12C 24A 24B 24D 30A 60A
6B483 840 12F 30B 42A
6C155 520 30D
6D155 520 12H 24F 30E
6E20 736 12E 12G 12I 12J 24C 24E
6F15 552 12D 12K 18A 18B 18C 36A
6G3 456 Omitted owing to length.
6H1 440 12L 30C
6I576 12M
7A17 640 14A 21A 21B 28B 35A 42A
7B1 176 14B 21C 28A
8A92 160 24A 24C 40A
8B6 144 24E
8C6 144 16A 24B
8D2 048 16B
8E768 24F
8F768 24D
9A1 944 18A 36A
9B486 18B
9C486 18C
10A9 600 20A 30A 40A 60A
10B1 200 30C
10C1 200 30B
10D600 30D
10E600 20C 30E
10F160 20B
11A66 22A 33A
12A138 240 24A 60A
12B9 216 24B
12C4 608 24D
12D2 592 36A
12E1 728 24C 24E
12F864 ababababbababbabababbabababbabababbababbabababbabababb
12G576 ababbabababbababbabababbababbababababbababbabababb
12H288 24F
12I288 ababbabababbababbababababbababbabababb
12J288 abababbabababbabababbabababbababbabababb
12K288 Omitted owing to length.
12L72 abaababbabababbabababbabababbababbabababb
12M48 abababb
13A156 26A 39A 39B
14A168 28B 42A
14B56 28A
15A5 400 30A 60A
15B900 30B
15C180 30C
15D90 30D
15E30 30E
16A64 Omitted owing to length.
16B64 abababbababbababbabababbabababbabababbababbabababb
18A216 36A
18B54 ababababbabababbababbabababb
18C54 Omitted owing to length.
20A480 40A 60A
20B40 Omitted owing to length.
20C20 bababbabababbabababbabababbababbabababb
21A252 42A
21B63 aabbabababbabababbababbabababb
21C21 abababbababbabababb
22A22 ababbabababbabababbababbabababb
23A23 23B5
23B23 23A5
24A576 ababbababababbababbabababbababbabababbababababbababbabababb
24B192 Omitted owing to length.
24C144 Omitted owing to length.
24D96 ababababbababbabababb
24E48 ababbabababbababababbabababbababbabababb
24F24 abbabababbabababbababbabababb
26A52 abababbababbabababbabababbabababbabababbabababbababbabababb
28A28 Omitted owing to length.
28B28 abababbabababbababbabababb
30A120 60A
30B60 ababbababababbababbabababb
30C60 aababbabababbabababbabababbababbabababb
30D30 ababbabababbababababbababbabababb
30E30 ababababbababbabababbabbabababbabababbababbabababb
33A33 abbababbabababbabababbabababbababbabababb
35A35 ababbabababbabababbabababbababbabababbababababbababbabababb
36A36 Omitted owing to length.
39A39 39B7
39B39 39A7
40A40 ab
42A84 ababbabababb
60A60 abababbababbabababbababababbababbabababb
23A-B ababbabbababbabababbabababbabababbababbabababb
39A-B ababbababbabababbabababbabababbababbabababb

Download words for class representatives.