Finite Group DatabasebetaFinite Group Databasebeta| order | 10368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25×C3 |
| direct product | C3⋊D3×S42 |
| Fitting, socle | C24×C32 ⋊ C2×D32 |
| derived | C32×A42 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×A42 | C23 |
| Fitting, socle | C24×C32 | C2×D32 |
| LCS | G ▷ C32×A42 | |
| UCS | C1 | |
9522 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 9522 conjugacy classes of subgroups — too many to draw. Only its 129 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) = 144 |
A minimal faithful permutation representation — 3 generators on 14 points:
(1,4,2,3)(5,7,8,6)(12,13,14);(2,3,4)(10,11)(13,14);(7,8)(9,10,11)150 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((1,4,2,3)(5,7,8,6)(12,13,14), (2,3,4)(10,11)(13,14), (7,8)(9,10,11));