Finite Group DatabasebetaFinite Group Databasebeta| order | 6072 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C2 |
| direct product | S4×C23⋊C11 |
| Fitting, socle | C22×C23 ⋊ D3×C11 |
| derived | A4×C23 ⋊ C2×C11 |
| Hall | C23×S4 ⋊ C11 |
| Sylow | C23 ⋊ C11×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | A4×C23 | C2×C11 |
| Fitting, socle | C22×C23 | D3×C11 |
| LCS | G ▷ A4×C23 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
65 conjugacy classes — view the full character table.
| maximal subgroup of | S4×AGL(1,𝔽23) |
| maximal normal subgroup of | S4×AGL(1,𝔽23) |
Past the SmallGroups library coverage — no SmallGroups id.