Finite Group DatabasebetaFinite Group Databasebeta| order | 2560 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C27×C4 |
| direct product | AGL(1,𝔽5)×#2970 |
| Fitting | C5×#2970 ⋊ C4 |
| Sylow | C5 ⋊ C4×#2970 |
5544 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 5 generators on 21 points:
(1,2)(4,5)(14,15,16,19,17,18,20,21);(2,3,4,5);(6,8,9,12)(7,11,10,13)(15,18)(19,21);(7,10)(11,13);(6,7)(8,11)(9,10)(12,13)250 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2)(4,5)(14,15,16,19,17,18,20,21), (2,3,4,5), (6,8,9,12)(7,11,10,13)(15,18)(19,21), (7,10)(11,13), (6,7)(8,11)(9,10)(12,13));