Finite Group DatabasebetaFinite Group Databasebeta| order | 29865 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #23755835⋊C3 |
| Fitting, socle, derived, Hall | C11×C181 ⋊ C3×C5 |
| Hall | #23755835 ⋊ C3 |
| Hall | C11×C181⋊C3 ⋊ C5 |
| Hall | C181⋊C3 ⋊ C11⋊C5 |
| Sylow | C181 ⋊ C3×C11⋊C5 |
| Sylow | C11 ⋊ (C181⋊C3)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C181 | C3×C5 |
| LCS | G ▷ C11×C181 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1991 |
Polycyclic presentation:
3,5,11,181|d^a=d^48,c^b=c^4,d^b=d^59153 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29865, 11);