Finite Group DatabasebetaFinite Group Databasebeta| order | 2560 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4 |
| direct product | AGL(1,𝔽5)×#1887 |
| Fitting | C5×#1887 ⋊ C4 |
| Sylow | C5 ⋊ C4×#1887 |
5264 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 4 generators on 17 points:
(5,6,9,8);(12,17)(14,16);(11,14,15,16);(1,2,3,4)(6,7,9,8)(10,11)(12,14)(13,15)(16,17)160 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((5,6,9,8), (12,17)(14,16), (11,14,15,16), (1,2,3,4)(6,7,9,8)(10,11)(12,14)(13,15)(16,17));