Finite Group DatabasebetaFinite Group Databasebeta| order | 23751 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9 · Schur multiplier (H2) = C1 |
| derived, Hall | C13×C29 ⋊ C7×C9 |
| Hall | C29×C13⋊C9 ⋊ C7 |
| Hall | C13×C29⋊C7 ⋊ C9 |
| Sylow | C29 ⋊ C7×C13⋊C9 |
| Sylow | C13 ⋊ C9×C29⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C13⋊C3×C29⋊C7 |
| commutator, hypocenter | C13×C29 | C7×C9 |
| Fitting, socle, cosocle | C3×C13×C29 | C3×C7 |
| prime radical | C3×C13×C29⋊C7 | C3 |
| LCS | G ▷ C13×C29 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3393 |
231 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23751, 7);