Finite Group DatabasebetaFinite Group Databasebeta| order | 3996 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | A4×#66526 |
| Fitting, socle, derived, Hall | C22×C37 ⋊ C3×C9 |
| Sylow | C37 ⋊ C9×A4 |
| Sylow | C22 ⋊ C3×#66526 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C22×C37 | C3×C9 |
| prime radical | A4×C37⋊C3 | C3 |
| cosocle | C22×C37⋊C3 | C32 |
| LCS | G ▷ C22×C37 | |
| UCS | C1 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 148 |
52 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#66526⋊C2, S4×#66526, #72241662 |
| maximal normal subgroup of | A4×#66526⋊C2, S4×#66526, #72241662 |
Past the SmallGroups library coverage — no SmallGroups id.