Finite Group DatabasebetaFinite Group Databasebeta| order | 10368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×D3×S42 |
| Fitting, socle | C24×C32 ⋊ C2×D32 |
| derived | C3×A42 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×S42 |
| commutator, cosocle, hypocenter | C3×A42 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C24×C32 | C2×D32 |
| LCS | G ▷ C3×A42 | |
| UCS | C1 ◁ C3 | |
6500 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 6500 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 14 points:
(1,2,3)(4,5,6)(7,10,8,9)(11,13,14,12);(8,9,10)(13,14);(5,6)225 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((1,2,3)(4,5,6)(7,10,8,9)(11,13,14,12), (8,9,10)(13,14), (5,6));