Finite Group DatabasebetaFinite Group Databasebeta| order | 2640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×(D33⋊C4)⋊C5 |
| derived, Hall | C3×C11 ⋊ C22×C4×C5 |
| Hall | C2×D33⋊C4 ⋊ C5 |
| Hall | C3×C11⋊C5 ⋊ C22×C4 |
| Hall | C11⋊C5 ⋊ C2×C4×D3 |
| Sylow | C11 ⋊ C2×C4×C5×D3 |
| Sylow | C3 ⋊ C2×C4×AGL(1,𝔽11) |
216 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
132 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4×D3×AGL(1,𝔽11), C2×#72216761, #72217119, … |
| maximal normal subgroup of | C2×C4×D3×AGL(1,𝔽11), C2×#72216761, #72217119, … |
| maximal quotient of | #72216971, #72217226 |
Past the SmallGroups library coverage — no SmallGroups id.