Finite Group DatabasebetaFinite Group Databasebeta| order | 5280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24 |
| direct product | (C2×D3)⋊C4×AGL(1,𝔽11) |
| Fitting | C2×C3×C4×C11 ⋊ C22×C5 |
| Hall | D11×(C2×D3)⋊C4 ⋊ C5 |
| Hall | C3×C11⋊C5 ⋊ C2×C22⋊C4 |
| Hall | C11⋊C5 ⋊ C2×(C2×D3)⋊C4 |
| Hall | C3×C11 ⋊ C2×C5×C22⋊C4 |
| Sylow | C11 ⋊ C2×C5×(C2×D3)⋊C4 |
| Sylow | C3 ⋊ C22⋊C4×AGL(1,𝔽11) |
528 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
198 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C22⋊C4×AGL(1,𝔽11), #882×AGL(1,𝔽11), #937×AGL(1,𝔽11) |
| maximal normal subgroup of | D3×C22⋊C4×AGL(1,𝔽11), #882×AGL(1,𝔽11), #937×AGL(1,𝔽11) |
Past the SmallGroups library coverage — no SmallGroups id.