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)
1A13 685 760 abababbabababbabababbabababbabababbabababbabababbabababb
2A82 944 abababbabababbabababbabababb
2B4 608 (aabababbababababbab)3
3A77 760 Omitted owing to length.
3B77 760 Omitted owing to length.
3C3 888 aabababbababababbabaabababbababababbab
3D3 888 abbabababbababbabbabababbababbabbabababbababbabbabababbababb
3E1 944 abababbababababbababababbababababbab
3F324 abbabbababbabbabbababb
4A1 152 (babababbabababbab)3
4B384 abababbabababb
4C96 (abababbababb)3
5A15 (abb)3
6A1 728 (babababbabababbabbabababbabababbab)5
6B1 728 babababbabababbabbabababbabababbab
6C1 296 (ababbbabababbabababbab)15
6D1 296 (ababbbabababbabababbab)3
6E432 abbabababbababbabbabababbababb
6F432 ababbababb
6G288 (abababbababbabababbababb)5
6H288 abababbababbabababbababb
6I216 abababbababababbab
6J144 (aabababbababababbab)5
6K144 aabababbababababbab
6L108 abbabbababb
6M108 (abbabbababb)5
6N36 abababbabababbabababbbabababbabababbab
8A16 abababb
9A54 ababbbabababbabababbabababbbabababbabababbab
9B54 Omitted owing to length.
9C27 abababbabababbababababbabababbab
9D27 abababbabababbab
11A11 ab
11B11 abab
12A144 babababbabababbab
12B144 (babababbabababbab)5
12C72 (abbabababbababb)5
12D72 abbabababbababb
12E36 abababbab
12F24 abababbababb
12G24 (abababbababb)5
12H24 ababb
12I24 (ababb)5
15A15 abb
15B15 abbabb
18A18 (ababbbabababbabababbab)5
18B18 ababbbabababbabababbab

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Conjugacy classes of U5(2):2

Conjugacy class Centraliser order Power up Class rep(s)
1A27 371 520 (cddcdcddcdddcdcddcddcdddcdcdd)8
2A165 888 (cddcdcddcdddcdcddcddcdddcdcdd)4
2B9 216 (dcdddcdcdd)3
3A77 760 (dcdcdddcdcddcddcdddcdcdd)4
3C3 888 (dcdddcdcdd)2
3E3 888 (cdd)2
3F648 (cddcdcdddcdddcdcdd)2
4A2 304 (cddcdcddcdddcdcddcddcdddcdcdd)2
4B768 (cdcdddcdcddcddcdddcdcdd)4
4C192 (dcdcdddcdcddcddcdddcdcdd)3
5A30 (dcdcddcdddcdcdd)2
6A1 728 (cddcdcdd)2
6C1 296 (cddcdddcdcdd)3
6E432 (cdcdcddcdddcdcdddcdcdd)2
6G288 (dcdcdddcdcddcddcdddcdcdd)2
6I432 (cddcdcdddcdcddcdddcdcdd)4
6J144 dcdddcdcdd
6L108 cddcdcdddcdddcdcdd
6N72 (cdddcdcddcddcdddcdcdd)2
8A32 (cdcdddcdcddcddcdddcdcdd)2
9A54 (cddcdddcdcdd)2
9C27 dcdcdd
11A11 cd
12A144 cddcdcdd
12C72 cdcdcddcdddcdcdddcdcdd
12E72 (cddcdcdddcdcddcdddcdcdd)2
12F24 dcdcdddcdcddcddcdddcdcdd
12H24 dcdcddcddcdddcdcdd
15A15 cddcddcdcdddcdcddcdddcdcdd
18A18 cddcdddcdcdd
2C1 440 (cdd)3
4D96 (cdddcdcddcddcdddcdcdd)3
6O36 cdd
6P36 cdddcdcdd
8B192 (cddcdcdddcdcddcdddcdcdd)3
8C192 (cddcdcdddcdcddcdddcdcdd)15
8D32 cddcdcddcdddcdcddcddcdddcdcdd
10A10 dcdcddcdddcdcdd
12J12 cdddcdcddcddcdddcdcdd
16A16 cdcdddcdcddcddcdddcdcdd
16B16 (cdcdddcdcddcddcdddcdcdd)5
24A24 cddcdcdddcdcddcdddcdcdd
24B24 (cddcdcdddcdcddcdddcdcdd)5

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