Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C2×S4×H(5,𝔽2) |
| Fitting | C23×H(5,𝔽2) ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×S4 |
| commutator, cosocle | C2×A4 | C26 |
| Frattini | C2 | C25×S4 |
| Fitting | C23×H(5,𝔽2) | D3 |
| socle | C24 | C24×D3 |
| hypercenter | C2×H(5,𝔽2) | S4 |
| hypocenter | A4 | C22×H(5,𝔽2) |
| LCS | G ▷ C2×A4 ▷ A4 | |
| UCS | C1 ◁ C22 ◁ C2×H(5,𝔽2) | |
58969 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | C2×S4×B(4,𝔽2), C2×#72220683 |
| maximal normal subgroup of | C2×S4×B(4,𝔽2) |
| maximal quotient of | C2×#72220683, C2×D42×S4 |
Past the SmallGroups library coverage — no SmallGroups id.