Finite Group DatabasebetaFinite Group Databasebeta| order | 23709 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C1129⋊C3 |
| unambiguous semidirect product | C1129⋊(C3×C7) |
| Fitting, socle, Hall | C7×C1129 ⋊ C3 |
| derived, Sylow | C1129 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C1129⋊C3 |
| commutator, cosocle, hypocenter | C1129 | C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C1129 | C3 |
| LCS | G ▷ C1129 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7903 |
2653 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23709, 2);