Finite Group DatabasebetaFinite Group Databasebeta| order | 23595 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×#10597243 |
| unambiguous semidirect product | C13⋊(C3×#10597243) |
| Fitting, socle, derived, Hall | C112×C13 ⋊ C3×C5 |
| Hall | C13×#10597243 ⋊ C3 |
| Hall | C112×C13⋊C3 ⋊ C5 |
| Sylow | C112 ⋊ C5×C13⋊C3 |
| Sylow | C13 ⋊ C3×#10597243 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C13 | C3×C5 |
| LCS | G ▷ C112×C13 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1573 |
203 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23595, 9);