Order = 20160 = 26.32.5.7.
Mult = 3 × 4 × 4.
Out = 2 × S3 = D12.

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Porting notes

Porting incomplete.

Standard generators

Standard generators of L3(4) = M21 are a, b where a has order 2, b has order 4, ab has order 7 and abb has order 5.

Standard generators of 3.L3(4) are preimages A, B where A has order 2 and B has order 4.

Standard generators of 2.L3(4) are preimages A, B where AB has order 7, ABB has order 5 and ABABABBB has order 5.

Standard generators of 4a.L3(4) are preimages A, B where B has order 4, AB has order 7 and ABB has order 5.

Standard generators of 4b.L3(4) are preimages A, B where B has order 4, AB has order 7 and ABB has order 5.

Standard generators of 6.L3(4) are preimages A, B where AB has order 2, B has order 4, AB has order 21, ABB has order 5 and ABABABBB has order 5.

Standard generators of 12a.L3(4) are preimages A, B where A has order 2, B has order 4, AB has order 21 and ABB has order 5.

Standard generators of 12b.L3(4) are preimages A, B where A has order 2, B has order 4, AB has order 21 and ABB has order 5.

Black box algorithms

Checking generators (semi-presentations)

Group Semi-presentation File
L3(4) 〈〈 a, b | some conditions 〉〉 Download

Presentations

Group Presentation Link
L3(4) 〈 a, b | a2 = b4 = (ab)7 = (ab2)5 = (abab2)7 = (ababab2ab−1)5 = 1 〉 Details

Representations

Representations of L3(4)

Representations of 3.L3(4)

Representations of 2.L3(4)

Representations of 4a.L3(4)

Representations of 4b.L3(4)

Representations of 6.L3(4)

Representations of 12a.L3(4)

Representations of 12b.L3(4)

Maximal subgroups

Maximal subgroups of L3(4)

Subgroup Order Index Programs/reps
24:A5 = M20 960 21 Program: Standard generators
24:A5 = M20 960 21 Program: Standard generators
A6 360 56 Program: Standard generators
A6 360 56 Program: Standard generators
A6 360 56 Program: Standard generators
L3(2) 168 120 Program: Generators
L3(2) 168 120 Program: Generators
L3(2) 168 120 Program: Generators
32:Q8 = M9 = U3(2) 72 280 Program: Generators