Finite Group DatabasebetaFinite Group Databasebeta| order | 22550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×(C41⋊C5)⋊D11 |
| unambiguous semidirect product | (C41⋊C5)⋊(C5×D11) |
| Fitting, socle | C5×C11×C41 ⋊ C2×C5 |
| derived, Hall | C11×C41 ⋊ C2×C52 |
| Hall | C5×C11×C41⋊C5 ⋊ C2 |
| Hall | C5×C41⋊C5 ⋊ D11 |
| Hall | D451 ⋊ C52 |
| Sylow | C41 ⋊ C52×D11 |
| Sylow | C11 ⋊ C5×D41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | (C41⋊C5)⋊D11 |
| commutator, cosocle, hypocenter | C11×C41 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C41 | C2×C5 |
| LCS | G ▷ C11×C41 | |
| UCS | C1 ◁ C5 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2255 |
395 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22550, 54);