Finite Group DatabasebetaFinite Group Databasebeta| order | 3520 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | #106×AGL(1,𝔽11) |
| Fitting | C11×#106 ⋊ C2×C5 |
| Hall | D11×#106 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×#106 |
| Sylow | C11 ⋊ C2×C5×#106 |
260 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | #442×AGL(1,𝔽11), #365×AGL(1,𝔽11), #360×AGL(1,𝔽11), … |
| maximal normal subgroup of | #442×AGL(1,𝔽11), #365×AGL(1,𝔽11), #360×AGL(1,𝔽11), … |
| maximal quotient of | #365×AGL(1,𝔽11) |
Past the SmallGroups library coverage — no SmallGroups id.