Finite Group DatabasebetaFinite Group Databasebeta| order | 34440 |
| isoclinism | isoclinic class of PSL(2,𝔽41) |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C2 |
| projective special linear | PSL(2,𝔽41) |
| projective symplectic | PSp(2,𝔽41) |
| projective special unitary | PSU(2,𝔽41) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | G | C1 |
| LCS | G | |
| UCS | C1 | |
33 conjugacy classes of subgroups.
Permutation generators:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(2,22,15,32,34,8,7,37,33,38,16,25,20,4,12,19,30,17,14,40,3,29,26,13,24,31,39,23,18,27,5,10,6,36,35,9,11,28,21,41,42)23 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41), (2,22,15,32,34,8,7,37,33,38,16,25,20,4,12,19,30,17,14,40,3,29,26,13,24,31,39,23,18,27,5,10,6,36,35,9,11,28,21,41,42));