Order = 163849992929280 =
Mult = 1.
Out = 2.

Porting notes

Porting incomplete.

Standard generators

Standard generators of L7(2) are a, b where a is in class 2A, b has order 7 (necessarily in class 7E), ab has order 127 and ababababb has order 7.

Type I standard generators of L7(2):2 are c, d where c is in class 2A, d is in class 12H (centralizer order 144), cd has order 14 and cdcdd has order 12.

Type II standard generators of L7(2):2 are e, f where e is in class 2D, f is in class 8E/F (centralizer order 92160), ef has order ?? and efeff has order ??.

Black box algorithms

Checking generators (semi-presentations)

Group Semi-presentation File
L7(2) 〈〈 a, b | some conditions 〉〉 Download


Representations of L7(2)

Representations of L7(2):2

Maximal subgroups

Maximal subgroups of L7(2)

Subgroup Order Index Programs/reps
210:(S3 × L5(2))
210:(S3 × L5(2))
212:(L3(2) × A8)
212:(L3(2) × A8)
127:7 = F889.

Maximal subgroups of L7(2):2

Subgroup Order Index Programs/reps
24+4:(S3 × S3):2
S3 × L3(2):2
127:14 = F1778