Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×#85440 |
| Fitting | C25×C8 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C4⋊S4 |
| commutator, cosocle | C4×A4 | C25 |
| Frattini | C4 | C24×S4 |
| Fitting | C25×C8 | D3 |
| socle | C25 | C2×D12 |
| hypercenter | C23×C8 | S4 |
| hypocenter | A4 | C22×#135 |
| LCS | G ▷ C4×A4 ▷ C2×A4 ▷ A4 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8 | |
10931 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#85440 |
| maximal normal subgroup of | A4×#85440 |
Past the SmallGroups library coverage — no SmallGroups id.