Finite Group DatabasebetaFinite Group Databasebeta| order | 27885 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×#92788 |
| unambiguous semidirect product | C11⋊(C5×#92788) |
| unambiguous semidirect product | (C11×#92788)⋊C5 |
| Fitting, socle, derived, Hall | C11×C132 ⋊ C3×C5 |
| Hall | C132×C11⋊C5 ⋊ C3 |
| Hall | C11×#92788 ⋊ C5 |
| Sylow | C132 ⋊ C3×C11⋊C5 |
| Sylow | C11 ⋊ C5×#92788 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C132 | C3×C5 |
| LCS | G ▷ C11×C132 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1859 |
413 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27885, 7);