Finite Group DatabasebetaFinite Group Databasebeta| order | 4920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C2 |
| direct product | S4×C41⋊C5 |
| Fitting, socle | C22×C41 ⋊ C5×D3 |
| derived | A4×C41 ⋊ C2×C5 |
| Hall | S4×C41 ⋊ C5 |
| Sylow | C41 ⋊ C5×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | A4×C41 | C2×C5 |
| Fitting, socle | C22×C41 | C5×D3 |
| LCS | G ▷ A4×C41 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 164 |
65 conjugacy classes — view the full character table.
| maximal subgroup of | S4×D41⋊C5 |
| maximal normal subgroup of | S4×D41⋊C5 |
Past the SmallGroups library coverage — no SmallGroups id.