Finite Group DatabasebetaFinite Group Databasebeta| order | 22743 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#11924777 |
| derived | C7×C19 ⋊ C9×C19 |
| Hall | C7×C192 ⋊ C9 |
| Sylow | C192 ⋊ C7⋊C9 |
| Sylow | C7 ⋊ C19×#4294 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C19 | #87705 |
| commutator, hypocenter | C7×C19 | C9×C19 |
| Frattini | C3 | C19×#87705 |
| Fitting, socle, prime radical | C3×C7×C192 | C3 |
| cosocle | C3×C7×C19 | C3×C19 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C3×C19 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1197 |
2679 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22743, 17);