Finite Group DatabasebetaFinite Group Databasebeta| order | 22743 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#21439055 |
| Fitting | C3×C7×C361 ⋊ C3 |
| derived, Hall | C7×C361 ⋊ C32 |
| Sylow | C361 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×C361⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #21439055 |
| commutator, cosocle, hypocenter | C7×C361 | C32 |
| Frattini | C19 | C3×#87704 |
| Fitting | C3×C7×C361 | C3 |
| socle | C3×C7×C19 | C19⋊C3 |
| LCS | G ▷ C7×C361 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7581 |
2535 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22743, 14);