Finite Group DatabasebetaFinite Group Databasebeta| order | 3840 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×D3×#66297 |
| Fitting, socle | C25×C3 ⋊ C2×AGL(1,𝔽5) |
| derived | C3×C24⋊C5 ⋊ C22×C4 |
| Sylow | C3 ⋊ C22×#66297 |
1756 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 1756 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 30 |
A minimal faithful permutation representation — 3 generators on 13 points:
(3,8,6,10)(4,5,9,7)(11,12);(1,3,7,5,6)(2,4,10,8,9)(12,13);(1,2)(3,4)(5,8)(6,9)(7,10)66 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#11757163⋊C2 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((3,8,6,10)(4,5,9,7)(11,12), (1,3,7,5,6)(2,4,10,8,9)(12,13), (1,2)(3,4)(5,8)(6,9)(7,10));