Finite Group DatabasebetaFinite Group Databasebeta| order | 2200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C5×D4×C11⋊C5 |
| Fitting | C5×D4×C11 ⋊ C5 |
| Hall | D4×C11 ⋊ C52 |
| Sylow | C11 ⋊ C52×D4 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 220 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D5×C11⋊C5, C5×D4×AGL(1,𝔽11), D4×C5⋊AGL(1,𝔽11), … |
| maximal normal subgroup of | D4×D5×C11⋊C5, C5×D4×AGL(1,𝔽11), D4×C5⋊AGL(1,𝔽11) |
Past the SmallGroups library coverage — no SmallGroups id.