Order = 62400 = 26.3.52.13.
Mult = 1.
Out = 4.

Porting notes

Porting incomplete. Standard generators have some notes that have not been copied over.

Standard generators

Standard generators of U3(4) are a, b where a has order 2, b has order 3 and ab has order 13.

Standard generators of U3(4) are , where a and b .

Standard generators of U3(4):2 are c, d where c has order 2 (necessarily in class 2B), d has order 3, cd has order 8, cdcdd has order 13 and cdcdcdcddcdcddcdd has order 10.

Standard generators of U3(4):4 are e, f where e is in class 2A, f is in class 4B/B', ef has order 12 and efefffeff has order 6.

Presentations

Group Presentation Link
U3(4) 〈 a, b | a2 = b3 = (ab)13 = [a, b]5 = [a, babab]3 = 1 〉 Details
U3(4):2 〈 c, d | c2 = d3 = (cd)8 = [c, d]13 = [c, dcdcdcd−1cdcd]2 = [c, d−1cdcd]5 = 1 〉 Details
U3(4):4 〈 e, f | e2 = f4 = (ef)12 = [e, f]5 = (ef2)10 = efefef2efef2ef−1ef2efefef−1ef2ef−1ef2 = 1 〉 Details

Representations

Representations of U3(4)

Representations of U3(4):2

Representations of U3(4):4

Maximal subgroups

Maximal subgroups of U3(4)

Subgroup Order Index Programs/reps
22+4:15 Program: Generators
5 × A5 Program: Generators
52:S3 Program: Generators
13:3 = F39 Program: Generators

Maximal subgroups of U3(4):2

Subgroup Order Index Programs/reps
U3(4) Program: Standard generators
22+4:(3 × D10) Program: Generators
D10 × A5 Program: Generators
52:D12 Program: Generators
13:6 = F78 Program: Generators

Maximal subgroups of U3(4):4

Subgroup Order Index Programs/reps
U3(4):2 Program: Standard generators
22+4:(3 × D10).2 Program: Generators
(D10 × A5).2 Program: Generators
52:(4 × S3) Program: Generators
13:12 = F156 Program: Generators