Finite Group DatabasebetaFinite Group Databasebeta| order | 8800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×AGL(1,𝔽5)×AGL(1,𝔽11) |
| Fitting | C4×C5×C11 ⋊ C2×C4×C5 |
| derived | C5×C11 ⋊ C2×C42×C5 |
| Hall | C5×C11⋊C5 ⋊ C2×C42 |
| Sylow | C11 ⋊ C2×C4×C5×AGL(1,𝔽5) |
448 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 220 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)2×AGL(1,𝔽11), D4×AGL(1,𝔽5)×AGL(1,𝔽11) |
| maximal normal subgroup of | D4×AGL(1,𝔽5)×AGL(1,𝔽11) |
| maximal quotient of | AGL(1,𝔽5)2×AGL(1,𝔽11) |
Past the SmallGroups library coverage — no SmallGroups id.