Order = 17971200 = 211.33.52.13.
Mult = 1.
Out = 2.

Porting notes

Porting incomplete.

Standard generators

Standard generators of 2F4(2)' = T are a, b where a is in class 2A, b has order 3 and ab has order 13.

Standard generators of 2F4(2)'.2 = 2F4(2) are c, d where c is in class 2A, d is in class 4F, cd has order 12 and cdcd2cd3 has order 4.

Presentations

Group Presentation Link
2F4(2)' 〈 a, b | a2 = b3 = (ab)13 = [a, b]5 = [a, bab]4 = ((ab)4ab−1)6 = 1 〉 Details
2F4(2)'.2 〈 c, d | c2 = d4 = (cd)12 = (cd2)8 = [c, d]5 = (cdcd2cd3)4 = (cdcd2cd2cd2)3cd−1(cd2)3 = [c, (dc)3(d−1c)2dcd−1cd−2] = [c, dcdcd−1cd2]2 = [c, d2cd]4 = (cd)4cd2cd(cd−1)4cd(cd2cd−1)2cdcd2cdcdcd−1cd−1cdcd2 = 1 〉 Details

Representations

Representations of 2F4(2)'

Representations of 2F4(2)'.2

Maximal subgroups

Maximal subgroups of 2F4(2)'

Subgroup Order Index Programs/reps
L3(3):2 Program: Generators
L3(3):2 Program: Generators
2.[28].5.4 Program: Generators
L2(25) Program: Generators
22.[28].S3 Program: Generators
A6.22 Program: Generators
A6.22 Program: Generators
52:4A4 Program: Generators

Maximal subgroups of 2F4(2)'.2

Subgroup Order Index Programs/reps
2F4(2)' Program: Standard generators
13:12 = F156
31+2:SD16
2.[29].5.4
L2(25).23
22.[29].S3
52:4S4

Conjugacy classes

Conjugacy classes of 2F4(2)'

Conjugacy class Centraliser order Power up Class rep(s)
1A17 971 200 Omitted owing to length.
2A10 240 Omitted owing to length.
2B1 536 abababbababababbababababbababababbab
3A108 abababbabababbabababbabababb
4A192 (abababb)3
4B128 Omitted owing to length.
4C64 abababbababababbab
5A50 aabababbababababbabaabababbababababbab
6A12 abababbabababb
8A32 Omitted owing to length.
8B32 Omitted owing to length.
8C16 abababbab
8D16 aabababbababababbabaabababbab
10A10 aabababbababababbab
12A12 abababb
12B12 (abababb)5
13A13 ab
13B13 abab
16A16 (abbaabababbababababbabaabababbab)5
16B16 (abbaabababbababababbabaabababbab)3
16C16 abbaabababbababababbabaabababbab
16D16 (abbaabababbababababbabaabababbab)15

Download words for class representatives.