Finite Group DatabasebetaFinite Group Databasebeta| order | 2200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | D5×Dic11⋊C5 |
| derived | C5×C11 ⋊ C2×C4×C5 |
| Hall | C5×C11⋊C5 ⋊ C2×C4 |
| Sylow | C11 ⋊ C4×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×AGL(1,𝔽11) |
| commutator, hypocenter | C5×C11 | C2×C4×C5 |
| Fitting, socle, cosocle | C2×C5×C11 | C22×C5 |
| prime radical | C2×D5×C11⋊C5 | C2 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C2 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 220 |
88 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.