Finite Group DatabasebetaFinite Group Databasebeta| order | 23595 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| Fitting, derived, Hall | C13×C121 ⋊ C3×C5 |
| Hall | C13×C121⋊C5 ⋊ C3 |
| Hall | C13⋊C3×C121 ⋊ C5 |
| Sylow | C121 ⋊ C5×C13⋊C3 |
| Sylow | C13 ⋊ C3×C121⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C13×C121 | C3×C5 |
| Frattini | C11 | C13⋊C3×C11⋊C5 |
| socle | C11×C13 | C3×C11⋊C5 |
| LCS | G ▷ C13×C121 | |
| UCS | C1 | |
24 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, 4);