Finite Group DatabasebetaFinite Group Databasebeta| order | 9408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D3×#13096688 |
| Fitting | C2×C3×C4×C72 ⋊ C23 |
| Hall | C3×C72 ⋊ C22×#41 |
| Sylow | C72 ⋊ C2×D3×#41 |
| Sylow | C3 ⋊ C2×#13096688 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D3×D72 |
| commutator, socle, cosocle | C2×C3×C72 | C25 |
| Frattini | C2 | C22×D3×D72 |
| Fitting | C2×C3×C4×C72 | C23 |
| hypercenter | C2×C4 | D3×D72 |
| hypocenter | C3×C72 | C22×#41 |
| LCS | G ▷ C2×C3×C72 ▷ C3×C72 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
4268 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
456 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.