Finite Group DatabasebetaFinite Group Databasebeta| order | 14400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#72231190 |
| Fitting, socle | C24×C52 ⋊ D32 |
| derived | C5×A42 ⋊ C22×C5 |
| Sylow | C52 ⋊ S42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #72231190 |
| commutator, cosocle, hypocenter | C5×A42 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C24×C52 | D32 |
| LCS | G ▷ C5×A42 | |
| UCS | C1 ◁ C5 | |
1286 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 1286 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,2,3,4,5)(6,7,9,10,8)(11,14,12,13)(15,17,18,16);(7,8)(9,10)(12,13,14)(17,18)265 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72260294 |
| maximal normal subgroup of | #72260294 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3,4,5)(6,7,9,10,8)(11,14,12,13)(15,17,18,16), (7,8)(9,10)(12,13,14)(17,18));