Finite Group DatabasebetaFinite Group Databasebeta| order | 2200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C2 |
| direct product | D5×C11×AGL(1,𝔽5) |
| Fitting, socle, Hall | C52×C11 ⋊ C2×C4 |
| derived, Sylow | C52 ⋊ C2×C4×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D5×AGL(1,𝔽5) |
| commutator, hypocenter | C52 | C2×C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C52×C11 | C2×C4 |
| prime radical | D52×C11 | C2 |
| cosocle | C5×D5 | C22×C11 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C11 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 220 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | C11×AGL(1,𝔽5)2, D5×AGL(1,𝔽5)×D11, AGL(1,𝔽5)×C11⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | C11×AGL(1,𝔽5)2, D5×AGL(1,𝔽5)×D11, AGL(1,𝔽5)×C11⋊AGL(1,𝔽5), … |
Past the SmallGroups library coverage — no SmallGroups id.