Finite Group DatabasebetaFinite Group Databasebeta| order | 2952 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×D3×#4223 |
| Fitting, socle, Hall | C32×C41 ⋊ C2×C4 |
| derived | C3×C41 ⋊ C2×C3×C4 |
| Sylow | C41 ⋊ C3×C4×D3 |
| Sylow | C32 ⋊ C2×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×#4223 |
| commutator, hypocenter | C3×C41 | C2×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C41 | C2×C4 |
| prime radical | C3×D3×D41 | C2 |
| cosocle | C3×D41 | C22×C3 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C3 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 246 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#4223, C3×D3×#66502, D3×C3⋊#66502, … |
| maximal normal subgroup of | D32×#4223, C3×D3×#66502, D3×C3⋊#66502, … |
Past the SmallGroups library coverage — no SmallGroups id.