Finite Group DatabasebetaFinite Group Databasebeta| order | 5280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | #239×AGL(1,𝔽11) |
| Fitting | C3×Q8×C11 ⋊ C22×C5 |
| Hall | D11×#239 ⋊ C5 |
| Hall | C3×C11⋊C5 ⋊ C2×#41 |
| Hall | C11⋊C5 ⋊ C2×#239 |
| Hall | C3×C11 ⋊ C2×C5×#41 |
| Sylow | C11 ⋊ C2×C5×#239 |
| Sylow | C3 ⋊ #41×AGL(1,𝔽11) |
656 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 201 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
165 conjugacy classes — view the full character table.
| maximal subgroup of | #914×AGL(1,𝔽11), D3×#41×AGL(1,𝔽11) |
| maximal normal subgroup of | #914×AGL(1,𝔽11), D3×#41×AGL(1,𝔽11) |
Past the SmallGroups library coverage — no SmallGroups id.