Finite Group DatabasebetaFinite Group Databasebeta| order | 22743 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7 · Schur multiplier (H2) = C3 |
| direct product | C3×C7×C361⋊C3 |
| unambiguous semidirect product | C361⋊(C32×C7) |
| unambiguous semidirect product | (C3×C361)⋊(C3×C7) |
| Fitting | C3×C7×C361 ⋊ C3 |
| derived, Sylow | C361 ⋊ C32×C7 |
| Hall | C7×C361 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | C361⋊C3 |
| commutator, cosocle, hypocenter | C361 | C32×C7 |
| Frattini | C19 | C3×C7×C19⋊C3 |
| Fitting | C3×C7×C361 | C3 |
| socle | C3×C7×C19 | C19⋊C3 |
| LCS | G ▷ C361 | |
| UCS | C1 ◁ C3×C7 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7581 |
2583 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22743, 11);