Finite Group DatabasebetaFinite Group Databasebeta| order | 25944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C2 |
| direct product | S4×C47⋊C23 |
| Fitting, socle | C22×C47 ⋊ D3×C23 |
| derived | A4×C47 ⋊ C2×C23 |
| Hall | S4×C47 ⋊ C23 |
| Sylow | C47 ⋊ C23×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | A4×C47 | C2×C23 |
| Fitting, socle | C22×C47 | D3×C23 |
| LCS | G ▷ A4×C47 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 188 |
125 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.