Finite Group DatabasebetaFinite Group Databasebeta| order | 27585 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C5×C613 ⋊ C3 |
| derived, Sylow | C613 ⋊ C32×C5 |
| Hall | C5×C613 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C613⋊C3 |
| commutator, cosocle, hypocenter | C613 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C613 | C3 |
| LCS | G ▷ C613 | |
| UCS | C1 ◁ C3×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9195 |
3105 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27585, 5);