Finite Group DatabasebetaFinite Group Databasebeta| order | 14400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#72224613 |
| Fitting, socle | C2×C32×C52 ⋊ C2×C42 |
| derived, Hall | C32×C52 ⋊ C22×C42 |
| Sylow | C52 ⋊ C2×C4×#624 |
| Sylow | C32 ⋊ C22×AGL(1,𝔽5)2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72224613 |
| commutator, hypocenter | C32×C52 | C22×C42 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C52 | C2×C42 |
| prime radical | C2×D52×C3⋊D3 | C22 |
| cosocle | C32×D52 | C24 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 ◁ C2 | |
4618 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
228 conjugacy classes — view the full character table.
| maximal quotient of | #72231278 |
Past the SmallGroups library coverage — no SmallGroups id.