Finite Group DatabasebetaFinite Group Databasebeta| order | 3520 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C5 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C42×AGL(1,𝔽11) |
| Fitting | C2×C42×C11 ⋊ C2×C5 |
| derived, Sylow | C11 ⋊ C22×C42×C5 |
| Hall | C2×C42×D11 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C22×C42 |
996 conjugacy classes of subgroups; only the 552 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 552 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#127×AGL(1,𝔽11), C2×#104×AGL(1,𝔽11), #532×AGL(1,𝔽11), … |
| maximal normal subgroup of | C2×#127×AGL(1,𝔽11), C2×#104×AGL(1,𝔽11), #532×AGL(1,𝔽11), … |
| maximal quotient of | C4×M16×AGL(1,𝔽11) |
Past the SmallGroups library coverage — no SmallGroups id.