Order = 6065280 = 27.36.5.13.
Mult = 2.
Out = 2 × 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of L4(3) are a, b where a is in class 2A, b is in class 4B, ab has order 13 (necessarily in class 13A/B) and abb 8. Alternatively: a is in class 2A, b is in class 4B, ab has order 13 (necessarily in class 13A/B) and ababb has order 13.
Standard generators of 2.L4(3) are preimages A, B where AB has order 13 and ABABB has order 13.
Standard generators of L4(3).21 are c, d where c is in class 2C, d has order 5, cd has order 26 and cdcdd has order 5.
Standard generators of 2.L4(3).21 are preimages C, D where D has order 5.
Black box algorithms
Checking generators (semi-presentations)
| Group | Semi-presentation | File |
|---|---|---|
| L4(3) | 〈〈 a, b | some conditions 〉〉 | Download |