Order = 13685760 = 210.35.5.11.
Mult = 1.
Out = 2.

Porting notes

Porting incomplete.

Standard generators

Standard generators of U5(2) are a, b where a is in class 2A, b has order 5 and ab has order 11.

Standard generators of U5(2):2 are c, d where c has order 2 (necessarily in class 2C), d has order 4 (necessarily in class 4D), cd has order 11 and cdcdd has order 4.

Presentations

Group Presentation Link
U5(2) 〈 a, b | a2 = b5 = (ab)11 = [a,b]3 = [a,b2]3 = [a,bab]3 = [a,bab2]3 = 1 〉 Details
U5(2):2 〈 c, d | c2 = d4 = (cd)11 = (cd2)6 = (cdcd2)4 = [c,d]9 = (cd−1(cdcdcd−1)2cd2)2 = [d2, cdcdc]3 = 1 〉 Details

Representations

Representations of U5(2)

Representations of U5(2):2

Maximal subgroups

Maximal subgroups of U5(2)

Subgroup Order Index Programs/reps
21+6.31+2.2A4 Program: Generators
3 × U4(2) Program: Generators mapping onto standard generators
Program: Generators mapping onto standard generators
24+4:(3 × A5) Program: Generators
34:S5 Program: Generators
S3 × 31+2:2A4
L2(11) Program: Standard generators

Maximal subgroups of U5(2):2

Subgroup Order Index Programs/reps
U5(2) Program: Standard generators
Program: Generators
21+6.31+2.2S4 Program: Generators
(3 × U4(2)):2 Program: Generators
24+4:(3 × A5):2 Program: Generators
34:(S5 × 2) Program: Generators
S3 × 31+2:2S4
L2(11):2 Program: Generators

Conjugacy classes

Conjugacy classes of U5(2)

Conjugacy class Centraliser order Power up Class rep(s)
1A 13 685 760 abababbabababbabababbabababbabababbabababbabababbabababb
2A 82 944 abababbabababbabababbabababb
2B 4 608 (aabababbababababbab)3
3A 77 760 Omitted owing to length.
3B 77 760 Omitted owing to length.
3C 3 888 aabababbababababbabaabababbababababbab
3D 3 888 abbabababbababbabbabababbababbabbabababbababbabbabababbababb
3E 1 944 abababbababababbababababbababababbab
3F 324 abbabbababbabbabbababb
4A 1 152 (babababbabababbab)3
4B 384 abababbabababb
4C 96 (abababbababb)3
5A 15 (abb)3
6A 1 728 (babababbabababbabbabababbabababbab)5
6B 1 728 babababbabababbabbabababbabababbab
6C 1 296 (ababbbabababbabababbab)15
6D 1 296 (ababbbabababbabababbab)3
6E 432 abbabababbababbabbabababbababb
6F 432 ababbababb
6G 288 (abababbababbabababbababb)5
6H 288 abababbababbabababbababb
6I 216 abababbababababbab
6J 144 (aabababbababababbab)5
6K 144 aabababbababababbab
6L 108 abbabbababb
6M 108 (abbabbababb)5
6N 36 abababbabababbabababbbabababbabababbab
8A 16 abababb
9A 54 ababbbabababbabababbabababbbabababbabababbab
9B 54 Omitted owing to length.
9C 27 abababbabababbababababbabababbab
9D 27 abababbabababbab
11A 11 ab
11B 11 abab
12A 144 babababbabababbab
12B 144 (babababbabababbab)5
12C 72 (abbabababbababb)5
12D 72 abbabababbababb
12E 36 abababbab
12F 24 abababbababb
12G 24 (abababbababb)5
12H 24 ababb
12I 24 (ababb)5
15A 15 abb
15B 15 abbabb
18A 18 (ababbbabababbabababbab)5
18B 18 ababbbabababbabababbab

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Conjugacy classes of U5(2):2

Conjugacy class Centraliser order Power up Class rep(s)
1A 27 371 520 (cddcdcddcdddcdcddcddcdddcdcdd)8
2A 165 888 (cddcdcddcdddcdcddcddcdddcdcdd)4
2B 9 216 (dcdddcdcdd)3
3A 77 760 (dcdcdddcdcddcddcdddcdcdd)4
3C 3 888 (dcdddcdcdd)2
3E 3 888 (cdd)2
3F 648 (cddcdcdddcdddcdcdd)2
4A 2 304 (cddcdcddcdddcdcddcddcdddcdcdd)2
4B 768 (cdcdddcdcddcddcdddcdcdd)4
4C 192 (dcdcdddcdcddcddcdddcdcdd)3
5A 30 (dcdcddcdddcdcdd)2
6A 1 728 (cddcdcdd)2
6C 1 296 (cddcdddcdcdd)3
6E 432 (cdcdcddcdddcdcdddcdcdd)2
6G 288 (dcdcdddcdcddcddcdddcdcdd)2
6I 432 (cddcdcdddcdcddcdddcdcdd)4
6J 144 dcdddcdcdd
6L 108 cddcdcdddcdddcdcdd
6N 72 (cdddcdcddcddcdddcdcdd)2
8A 32 (cdcdddcdcddcddcdddcdcdd)2
9A 54 (cddcdddcdcdd)2
9C 27 dcdcdd
11A 11 cd
12A 144 cddcdcdd
12C 72 cdcdcddcdddcdcdddcdcdd
12E 72 (cddcdcdddcdcddcdddcdcdd)2
12F 24 dcdcdddcdcddcddcdddcdcdd
12H 24 dcdcddcddcdddcdcdd
15A 15 cddcddcdcdddcdcddcdddcdcdd
18A 18 cddcdddcdcdd
2C 1 440 (cdd)3
4D 96 (cdddcdcddcddcdddcdcdd)3
6O 36 cdd
6P 36 cdddcdcdd
8B 192 (cddcdcdddcdcddcdddcdcdd)3
8C 192 (cddcdcdddcdcddcdddcdcdd)15
8D 32 cddcdcddcdddcdcddcddcdddcdcdd
10A 10 dcdcddcdddcdcdd
12J 12 cdddcdcddcddcdddcdcdd
16A 16 cdcdddcdcddcddcdddcdcdd
16B 16 (cdcdddcdcddcddcdddcdcdd)5
24A 24 cddcdcdddcdcddcdddcdcdd
24B 24 (cddcdcdddcdcddcdddcdcdd)5

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