Finite Group DatabasebetaFinite Group Databasebeta| order | 2640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×D12×C11⋊C5 |
| Fitting | C2×C3×C4×C11 ⋊ C2×C5 |
| Hall | C2×C11×D12 ⋊ C5 |
| Hall | C3×C11⋊C5 ⋊ C2×D4 |
| Hall | C3×C11 ⋊ C2×C5×D4 |
| Sylow | C11 ⋊ C2×C5×D12 |
| Sylow | C3 ⋊ C2×D4×C11⋊C5 |
216 conjugacy classes of subgroups.
126 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×D4×C11⋊C5, C2×#72216746, C2×D12×AGL(1,𝔽11), … |
| maximal normal subgroup of | C2×D3×D4×C11⋊C5, C2×#72216746, C2×D12×AGL(1,𝔽11), … |
| maximal quotient of | C11⋊C5×#908, C11⋊C5×#882 |
Past the SmallGroups library coverage — no SmallGroups id.