Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic961⋊C9 |
| unambiguous semidirect product | (C961⋊C9)⋊C4 |
| derived, Sylow | C961 ⋊ C4×C9 |
| Hall | C961⋊C9 ⋊ C4 |
| Hall | Dic961 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D961⋊C3 |
| commutator, hypocenter | C961 | C4×C9 |
| Frattini, socle, prime radical | C2×C3×C31 | D31⋊C3 |
| Fitting, cosocle | C2×C3×C961 | C2×C3 |
| LCS | G ▷ C961 | |
| UCS | C1 ◁ C2×C3 | |
27 conjugacy classes of subgroups.
| transitive degree | μt(G) = 34596 |
Polycyclic presentation:
2,3,31,2,3,31|a^2=d,b^3=e,c^31=f^30,c^a=c^30f,f^a=f^30,c^b=c^25f^15,f^b=f^25996 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 2);