Finite Group DatabasebetaFinite Group Databasebeta| order | 48672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | D3×#72214122 |
| Fitting, socle, derived | C3×C132 ⋊ C2×C3×C42 |
| Hall | C3×#92788 ⋊ C2×C42 |
| Sylow | C132 ⋊ C3×C42×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C132 | C2×C3×C42 |
| prime radical | D3×#11759815⋊C2 | C22 |
| cosocle | C3×D132 | C23×C3 |
| LCS | G ▷ C3×C132 | |
| UCS | C1 | |
1029 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
177 conjugacy classes — view the full character table.
| holomorph of | C3×#261 |
Past the SmallGroups library coverage — no SmallGroups id.