Finite Group DatabasebetaFinite Group Databasebeta| order | 27335 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×(C71⋊C5)⋊C7 |
| unambiguous semidirect product | (C71⋊C5)⋊(C7×C11) |
| unambiguous semidirect product | (C71⋊C7)⋊(C5×C11) |
| unambiguous semidirect product | (C11×C71⋊C5)⋊C7 |
| Fitting, socle, Hall | C11×C71 ⋊ C5×C7 |
| derived, Sylow | C71 ⋊ C5×C7×C11 |
| Hall | C11×C71⋊C7 ⋊ C5 |
| Hall | C11×C71⋊C5 ⋊ C7 |
| Hall | C71⋊C7 ⋊ C5×C11 |
| Hall | C71⋊C5 ⋊ C7×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | (C71⋊C5)⋊C7 |
| commutator, cosocle, hypocenter | C71 | C5×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C71 | C5×C7 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 781 |
407 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27335, 9);