Finite Group DatabasebetaFinite Group Databasebeta| order | 2200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C22⋊D5×C11⋊C5 |
| Fitting | C22×C5×C11 ⋊ C2×C5 |
| Hall | C5×C11⋊C5 ⋊ D4 |
| Sylow | C11 ⋊ C5×C22⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D5×C11⋊C5 |
| commutator, socle, cosocle | C2×C5×C11 | C22×C5 |
| Fitting | C22×C5×C11 | C2×C5 |
| hypercenter | C22 | D5×C11⋊C5 |
| hypocenter | C5×C11 | C5×D4 |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C2 ◁ C22 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 220 |
91 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D5×C11⋊C5, C22⋊D5×AGL(1,𝔽11), #72276394, … |
| maximal normal subgroup of | D4×D5×C11⋊C5, C22⋊D5×AGL(1,𝔽11), #72276394 |
Past the SmallGroups library coverage — no SmallGroups id.