Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C22×#87477 |
| Fitting | C25×D4 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×S4 |
| commutator, cosocle | C2×A4 | C26 |
| Frattini | C2 | C25×S4 |
| Fitting | C25×D4 | D3 |
| socle | C25 | C23×D3 |
| hypercenter | C23×D4 | S4 |
| hypocenter | A4 | C22×H(5,𝔽2) |
| LCS | G ▷ C2×A4 ▷ A4 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
63131 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#87477 |
| maximal normal subgroup of | A4×#87477 |
Past the SmallGroups library coverage — no SmallGroups id.