Finite Group DatabasebetaFinite Group Databasebeta| order | 3520 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C24×C4 |
| direct product | #124×AGL(1,𝔽11) |
| Fitting | C11×#124 ⋊ C2×C5 |
| Hall | D11×#124 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×#124 |
| Sylow | C11 ⋊ C2×C5×#124 |
660 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | #535×AGL(1,𝔽11), #532×AGL(1,𝔽11), #496×AGL(1,𝔽11), … |
| maximal normal subgroup of | #535×AGL(1,𝔽11), #532×AGL(1,𝔽11), #496×AGL(1,𝔽11), … |
| maximal quotient of | #486×AGL(1,𝔽11) |
Past the SmallGroups library coverage — no SmallGroups id.