Finite Group DatabasebetaFinite Group Databasebeta| order | 27335 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16840846⋊C7 |
| Fitting, socle, derived, Hall | C11×C71 ⋊ C5×C7 |
| Hall | C11×C71⋊C7 ⋊ C5 |
| Hall | #16840846 ⋊ C7 |
| Hall | C71⋊C7 ⋊ C11⋊C5 |
| Sylow | C71 ⋊ C7×C11⋊C5 |
| Sylow | C11 ⋊ (C71⋊C5)⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C71 | C5×C7 |
| LCS | G ▷ C11×C71 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 781 |
Polycyclic presentation:
5,7,11,71|c^a=c^4,d^a=d^57,d^b=d^4571 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27335, 13);