Finite Group DatabasebetaFinite Group Databasebeta| order | 2640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×((C2×D11)⋊C4)⋊C5 |
| Fitting | C2×C3×C4×C11 ⋊ C2×C5 |
| Hall | C3×(C2×D11)⋊C4 ⋊ C5 |
| Hall | (C2×D11)⋊C4 ⋊ C3×C5 |
| Hall | C3×C11⋊C5 ⋊ C22⋊C4 |
| Hall | C11⋊C5 ⋊ C3×C22⋊C4 |
| Hall | C3×C11 ⋊ C5×C22⋊C4 |
| Sylow | C11 ⋊ C3×C5×C22⋊C4 |
136 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
174 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C22⋊C4×AGL(1,𝔽11), D3×((C2×D11)⋊C4)⋊C5, #72217241, … |
| maximal normal subgroup of | C3×C22⋊C4×AGL(1,𝔽11), D3×((C2×D11)⋊C4)⋊C5, #72217241, … |
Past the SmallGroups library coverage — no SmallGroups id.