Finite Group DatabasebetaFinite Group Databasebeta| order | 28800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
| direct product | C22×#72219548 |
| socle | C22×A52 ⋊ C2 |
| derived | A52 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C22 | #72219548 |
| commutator, cosocle, hypocenter | A52 | C23 |
| Frattini | C1 | G |
| socle | C22×A52 | C2 |
| LCS | G ▷ A52 | |
| UCS | C1 ◁ C22 | |
4447 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 4447 conjugacy classes of subgroups — too many to draw. Only its 31 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) = 100 |
A minimal faithful permutation representation — 3 generators on 14 points:
(3,4)(6,9,8)(10,14,12,13,11);(1,2)(6,8)(12,13);(3,4)(5,8,7,6)(11,14,12,13)104 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((3,4)(6,9,8)(10,14,12,13,11), (1,2)(6,8)(12,13), (3,4)(5,8,7,6)(11,14,12,13));