Finite Group DatabasebetaFinite Group Databasebeta| order | 10368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C25 |
| direct product | D32×A4×S4 |
| Fitting, socle | C24×C32 ⋊ C22×C3×D3 |
| derived | C22×C32×A4 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C22×C32×A4 | C23×C3 |
| Fitting, socle | C24×C32 | C22×C3×D3 |
| LCS | G ▷ C22×C32×A4 | |
| UCS | C1 | |
9845 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 9845 conjugacy classes of subgroups — too many to draw. Only its 144 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:
(2,4,3)(5,7,6)(10,11)(12,13);(1,4)(2,3)(7,8)(9,10,11);(13,14)180 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((2,4,3)(5,7,6)(10,11)(12,13), (1,4)(2,3)(7,8)(9,10,11), (13,14));