Finite Group DatabasebetaFinite Group Databasebeta| order | 2200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | D5×C11⋊AGL(1,𝔽5) |
| Fitting, socle, derived, Hall | C52×C11 ⋊ C2×C4 |
| Sylow | C52 ⋊ C2×Dic11 |
| Sylow | C11 ⋊ D5×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C11 | C2×C4 |
| prime radical | D52×C11 | C2 |
| cosocle | C5×D5×C11 | C22 |
| LCS | G ▷ C52×C11 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 220 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #72276319, D5×AGL(1,𝔽5)×D11, AGL(1,𝔽5)×C11⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | #72276319, D5×AGL(1,𝔽5)×D11, AGL(1,𝔽5)×C11⋊AGL(1,𝔽5), … |
Past the SmallGroups library coverage — no SmallGroups id.