Finite Group DatabasebetaFinite Group Databasebeta| order | 23565 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C1571⋊C5 |
| unambiguous semidirect product | C1571⋊(C3×C5) |
| unambiguous semidirect product | (C3×C1571)⋊C5 |
| Fitting, socle, Hall | C3×C1571 ⋊ C5 |
| derived, Sylow | C1571 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C1571⋊C5 |
| commutator, cosocle, hypocenter | C1571 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C1571 | C5 |
| LCS | G ▷ C1571 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4713 |
957 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23565, 1);