Finite Group DatabasebetaFinite Group Databasebeta| order | 11232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D32×AGL(1,𝔽13) |
| Fitting, socle | C2×C32×C13 ⋊ C22×C3×C4 |
| derived | C32×C13 ⋊ C23×C3×C4 |
| Hall | C32×C13⋊C3 ⋊ C23×C4 |
| Sylow | C13 ⋊ C2×C3×C4×D32 |
2244 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | #3811×AGL(1,𝔽13) |
| maximal normal subgroup of | #3811×AGL(1,𝔽13) |
| maximal quotient of | #3811×AGL(1,𝔽13) |
Past the SmallGroups library coverage — no SmallGroups id.