Finite Group DatabasebetaFinite Group Databasebeta| order | 22550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C2×#26014767 |
| derived, Hall | C11×C41 ⋊ C2×C25 |
| Hall | C2×C11×C41 ⋊ C25 |
| Hall | C2×C41 ⋊ C11⋊C25 |
| Sylow | C41 ⋊ C2×C11⋊C25 |
| Hall | C2×C11 ⋊ C41⋊C25 |
| Sylow | C11 ⋊ C2×C41⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #14555918 |
| commutator, hypocenter | C11×C41 | C2×C25 |
| Frattini | C5 | C2×#14555918 |
| Fitting, socle, prime radical | C2×C5×C11×C41 | C5 |
| cosocle | C5×C11×C41 | C2×C5 |
| LCS | G ▷ C11×C41 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22550 |
950 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22550, 6);