Finite Group DatabasebetaFinite Group Databasebeta| order | 22550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C11×C41 ⋊ C2×C25 |
| Hall | #26014765 ⋊ C2 |
| Hall | D451 ⋊ C25 |
| Sylow | C41 ⋊ D11⋊C25 |
| Sylow | C11 ⋊ D41⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | #17985250 |
| commutator, hypocenter | C11×C41 | C2×C25 |
| Fitting, socle, cosocle | C5×C11×C41 | C2×C5 |
| prime radical | C5×D451 | C5 |
| LCS | G ▷ C11×C41 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11275 |
Polycyclic presentation:
2,5,11,41,5|b^5=e,c^a=c^10,d^a=d^40,c^b=c^4,d^b=d^37275 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22550, 32);