Finite Group DatabasebetaFinite Group Databasebeta| order | 4800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#72224585 |
| Fitting | C23×C3×C52 ⋊ C2×C4 |
| Hall | C3×C52 ⋊ C2×C4×D4 |
| Sylow | C52 ⋊ C2×C4×#67 |
| Sylow | C3 ⋊ C2×#11717375 |
2176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#11717375, C2×#72231502, #72260127, … |
| maximal normal subgroup of | C2×D3×#11717375, #72260127, C2×C3×#72224585, … |
| maximal quotient of | #72231020, C2×#72231502, C2×C3×#72224585 |
Past the SmallGroups library coverage — no SmallGroups id.