Finite Group DatabasebetaFinite Group Databasebeta| order | 4608 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C27 |
| direct product | A4×#87477 |
| Fitting | C25×D4 ⋊ C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×A4×S4 |
| commutator, cosocle | C23×A4 | C24×C3 |
| Fitting | C25×D4 | C3×D3 |
| socle | C25 | C23×C3×D3 |
| hypercenter | C2×D4 | A4×S4 |
| hypocenter | C22×A4 | C3×H(5,𝔽2) |
| LCS | G ▷ C23×A4 ▷ C22×A4 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
24220 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
176 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.