Finite Group DatabasebetaFinite Group Databasebeta| order | 2952 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | D3×C3⋊#4223 |
| Fitting, socle, derived, Hall | C32×C41 ⋊ C2×C4 |
| Sylow | C41 ⋊ D3×Dic3 |
| Sylow | C32 ⋊ C2×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C41 | C2×C4 |
| prime radical | C3×D3×D41 | C2 |
| cosocle | C32×D41 | C22 |
| LCS | G ▷ C32×C41 | |
| UCS | C1 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 246 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#4223, D3×C3⋊(#4223⋊C5) |
| maximal normal subgroup of | D32×#4223, D3×C3⋊(#4223⋊C5) |
Past the SmallGroups library coverage — no SmallGroups id.