Finite Group DatabasebetaFinite Group Databasebeta| order | 22743 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| Fitting, derived, Hall | C7×C361 ⋊ C32 |
| Sylow | C361 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×C361⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C7×C361 | C32 |
| Frattini | C19 | ΓL(1,𝔽8)×C19⋊C3 |
| socle | C7×C19 | C3×C19⋊C3 |
| LCS | G ▷ C7×C361 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2527 |
615 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22743, 10);