Order = 898128000 = 27.36.53.7.11.
Mult = 3.
Out = 2.


Porting notes

Porting incomplete.

Standard generators

Standard generators of McL are a, b where a is in class 2A, b is in class 5A, ab has order 11 and ababababbababbabb has order 7.

Standard generators of 3.McL are preimages A, B where A has order 2 and B has order 5.

Standard generators of McL:2 are c, d where c is in class 2B, d is in class 3B, cd has order 22 and cdcdcdcddcdcddcdd has order 24.


Black box algorithms

Finding generators

Group Algorithm File
McL
Download
McL:2
Download

Checking generators (semi-presentations)

Group Semi-presentation File
McL 〈〈 a, b | o(a) = 2, o(b) = 5, o(ab) = 11, o(ababababbababbabb) = 7, o(ab2) = 12 〉〉 Download
McL:2 〈〈 c, d | o(c) = 2, o(d) = 3, o(cd) = 22, o(cdcdcdcddcdcddcdd) = 24 〉〉 Download

Presentations

Group Presentation Link
McL a, b | a2 = b5 = (ab)11 = (ab2)12 = [a, b]5 = [a, b2]6 = (abab−2)7 = [a, b−2ab2ab−1ab(ab2)2abab−1] = [a, b2ab(ab2)2]2 = abab2ab−2abab−1ab2(ab−2ab)2(ab2ab−2ab2)2 = [a, b2ab2ab−1ab2]2 = [a, b2ab]4 = 1 〉 Details
McL:2 c, d | c2 = d3 = (cd)22 = (cdcdcd−1)6 = [c, (dcdcd−1c)2dcd−1cd−1] = [c, d−1cdcd]4 = (cd)6cd−1cd(cdcdcd−1)2(cdcd−1)2cdcdcd−1(cd)4(cd−1)6cdcdcd−1 = (cd)5cd−1(cd)3(cd−1cd−1cd)2cd(cdcd−1cd−1)2(cdcd−1)3cd−1cd(cdcdcd−1)2 = 1 〉 Details

Representations

Representations of McL

Representations of 3.McL

Representations of McL:2


Maximal subgroups

Maximal subgroups of McL

Subgroup Order Index Programs/reps
U4(3) 3 265 920 275Program: Generators
M22 443 520 2 025Program: Standard generators
M22 443 520 2 025Program: Standard generators
U3(5) 126 000 7 128Program: Standard generators
31+4:2.S5 58 320 15 400Program: Generators
34:M10 58 320 15 400Program: Generators
L3(4):21 40 320 22 275Program: Standard generators
2.A8 40 320 22 275Program: Generators
24:A7 40 320 22 275Program: Generators mapping onto standard generators
24:A7 40 320 22 275Program: Generators mapping onto standard generators
M11 7 920 113 400Program: Standard generators
51+2:3:8 3 000 299 376Program: Generators

Maximal subgroups of McL:2

Subgroup Order Index Programs/reps
McL Program: Standard generators
U4(3):2 Program: Generators
U3(5):2 Program: Generators
31+4:4.S5 Program: Generators
34:(M10 2) Program: Generators
L3(4):2:2. Program: Generators
2.S8 Program: Generators
Program: Generators
M11 2. Program: Generators
Program: Generators
51+2:3:8.2. Program: Generators
22+4:(S3 S3). Program: Generators

Conjugacy classes

Conjugacy classes of McL

Conjugacy class Centraliser order Power up Class rep(s)
1A898 128 000 Omitted owing to length.
2A40 320 4A 6A 6B 8A 10A 12A 14A 14B 30A 30B ababbbabbababbbabbababbbabbababbbabb
3A29 160 6A 9A 9B 12A 15A 15B 30A 30B abbabbabbabb
3B972 6B ababbbabbbabbababbbabbbabb
4A96 8A 12A ababbbabbababbbabb
5A750 10A 15A 15B 30A 30B (ababbbabbbababbbabbb)3
5B25 ababbbabbababbbabbbabb
6A360 12A 30A 30B abbabb
6B36 ababbbabbbabb
7A14 7B3 14A 14B ababbababb
7B14 7A3 14A 14B (ababbababb)3
8A8 ababbbabb
9A27 9B2 abababbabababb
9B27 9A2 abababb
10A30 30A 30B (ababbbabbb)3
11A11 11B2 ab
11B11 11A2 abab
12A12 abb
14A14 14B3 ababb
14B14 14A3 (ababb)3
15A30 15B7 30A 30B ababbbabbbababbbabbb
15B30 15A7 30A 30B (ababbbabbbababbbabbb)7
30A30 30B7 ababbbabbb
30B30 30A7 (ababbbabbb)7

Download words for class representatives.

Conjugacy classes of McL:2

Conjugacy class Centraliser order Power up Class rep(s)
1A1 796 256 000
2A80 640 4A 6A 6B 8A 10A 12A 14A 30A 4B 8B 8C 12B 12C 20A 20B 24A 24B
3A58 320 6A 9A 12A 15A 30A 12B 24A 24B
3B1 944 6B 6C 12C
4A192 8A 12A 8B 8C 24A 24B
5A1 500 10A 15A 30A 20A 20B
5B50 10B
6A720 12A 30A 12B 24A 24B
6B72 12C
7A14 14A
8A16 cdcdcddcdcdcddcdcdcddcdcddcdcdcddcdcdd
9A27 Omitted owing to length.
10A60 30A 20A 20B
11A22 11B2 22A 22B
11B22 11A2 22A 22B
12A24 24A 24B
14A14 cdcdcddcdcdcddcdcdd
15A30 30A
30A30 Omitted owing to length.
2B15 840 6C 10B 22A 22B
4B1 440 12B 12C 20A 20B
6C36 cdcdcdd
8B96 24A 24B
8C32 Omitted owing to length.
10B10 cdcdcddcdcdd
12B36 ccdcdcddcdcdcddcdcdcddcdcddcdcdcddcdcdd
12C36 Omitted owing to length.
20A20 20B11 cdcdcddcdcddcdcdd
20B20 20A11
22A22 22B7
22B22 22A7 cd
24A24 24B13 cdcdcddcdcdcddcdcdcddcdcdd
24B24 24A13

Download words for class representatives.