Finite Group DatabasebetaFinite Group Databasebeta| order | 25944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C2 |
| direct product | A4×AGL(1,𝔽47) |
| Fitting, socle, derived | C22×C47 ⋊ C2×C3×C23 |
| Hall | C22×AGL(1,𝔽47) ⋊ C3 |
| Hall | A4×D47 ⋊ C23 |
| Hall | C47⋊C23 ⋊ C2×A4 |
| Hall | C22×D47 ⋊ C3×C23 |
| Sylow | C47 ⋊ C2×A4×C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C47 | C2×C3×C23 |
| LCS | G ▷ C22×C47 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 188 |
188 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.