Finite Group DatabasebetaFinite Group Databasebeta| order | 4800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#67×#1043 |
| Fitting | C23×C3×C52 ⋊ C2×C4 |
| Hall | C3×C52 ⋊ C2×C4×D4 |
| Sylow | C52 ⋊ C2×C4×#67 |
| Sylow | C3 ⋊ C2×D4×#1043 |
3408 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×D4×#1043, C2×#638×#1043, #940×#1043, … |
| maximal normal subgroup of | C2×D3×D4×#1043, #940×#1043, C2×C3×#67×#1043, … |
| maximal quotient of | C2×#638×#1043, #940×#1043, C2×C3×#67×#1043, … |
Past the SmallGroups library coverage — no SmallGroups id.