Finite Group DatabasebetaFinite Group Databasebeta| order | 22366 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C211 · Schur multiplier (H2) = C1 |
| direct product | D53×C211 |
| unambiguous semidirect product | C53⋊(C2×C211) |
| Fitting, socle, Hall | C53×C211 ⋊ C2 |
| derived, Sylow | C53 ⋊ C2×C211 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C211 | D53 |
| commutator, cosocle, hypocenter | C53 | C2×C211 |
| Frattini | C1 | G |
| Fitting, socle | C53×C211 | C2 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C211 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11183 |
5908 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22366, 1);