Finite Group DatabasebetaFinite Group Databasebeta| order | 3520 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | SD32×AGL(1,𝔽11) |
| Fitting | C11×SD32 ⋊ C2×C5 |
| Hall | D11×SD32 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×SD32 |
| Sylow | C11 ⋊ C2×C5×SD32 |
180 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
121 conjugacy classes — view the full character table.
| maximal subgroup of | #509×AGL(1,𝔽11) |
| maximal normal subgroup of | #509×AGL(1,𝔽11) |
Past the SmallGroups library coverage — no SmallGroups id.