Finite Group DatabasebetaFinite Group Databasebeta| order | 23751 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×#11717942 |
| derived, Hall | C7×C13 ⋊ C9×C29 |
| Hall | C7×C13×C29 ⋊ C9 |
| Hall | C13×C29 ⋊ C7⋊C9 |
| Hall | C7×C29 ⋊ C13⋊C9 |
| Sylow | C13 ⋊ C29×C7⋊C9 |
| Sylow | C7 ⋊ C29×C13⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C29 | #63271 |
| commutator, hypocenter | C7×C13 | C9×C29 |
| Frattini | C3 | C29×#63271 |
| Fitting, socle, prime radical | C3×C7×C13×C29 | C3 |
| cosocle | C3×C7×C13 | C3×C29 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C3×C29 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23751 |
2871 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23751, 6);