Finite Group DatabasebetaFinite Group Databasebeta| order | 32715 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×C727⋊C9 |
| unambiguous semidirect product | C727⋊(C5×C9) |
| unambiguous semidirect product | (C5×C727)⋊C9 |
| derived, Sylow | C727 ⋊ C5×C9 |
| Hall | C5×C727 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C727⋊C3 |
| commutator, hypocenter | C727 | C5×C9 |
| Frattini | C3 | C5×C727⋊C3 |
| Fitting, socle, prime radical | C3×C5×C727 | C3 |
| cosocle | C3×C727 | C3×C5 |
| LCS | G ▷ C727 | |
| UCS | C1 ◁ C3×C5 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32715 |
3675 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32715, 2);