Finite Group DatabasebetaFinite Group Databasebeta| order | 22550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C11 · Schur multiplier (H2) = C5 |
| direct product | C2×C5×C11×C41⋊C5 |
| unambiguous semidirect product | (C2×C41)⋊(C52×C11) |
| unambiguous semidirect product | (C2×C5×C41)⋊(C5×C11) |
| Fitting, socle | C2×C5×C11×C41 ⋊ C5 |
| derived, Sylow | C41 ⋊ C2×C52×C11 |
| Hall | C2×C11×C41 ⋊ C52 |
| Hall | C11×C41 ⋊ C2×C52 |
| Hall | C2×C41 ⋊ C52×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C11 | C41⋊C5 |
| commutator, cosocle, hypocenter | C41 | C2×C52×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C11×C41 | C5 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C2×C5×C11 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4510 |
1430 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22550, 80);