Finite Group DatabasebetaFinite Group Databasebeta| order | 8064 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | ΓL(1,𝔽8)×AΣL(1,𝔽64) |
| Fitting, Hall | C7×#2846 ⋊ C32 |
| Sylow | #2846 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×AΣL(1,𝔽64) |
2644 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 2644 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 84 |
A minimal faithful permutation representation — 2 generators on 19 points:
(2,4)(7,11,8)(9,12,10)(13,14,15,17,16,18,19);(1,2)(3,4)(5,12,11,6)(7,10,8,9)(14,15,16)(17,19,18)140 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((2,4)(7,11,8)(9,12,10)(13,14,15,17,16,18,19), (1,2)(3,4)(5,12,11,6)(7,10,8,9)(14,15,16)(17,19,18));