Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊(D31⋊C3))⋊D31 |
| unambiguous semidirect product | ((C31⋊C3)⋊D31)⋊D3 |
| Fitting, socle, derived | C3×C312 ⋊ C22×C3 |
| Hall | C3×C31×C31⋊C3 ⋊ C22 |
| Sylow | C312 ⋊ C2×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C312 | C22×C3 |
| LCS | G ▷ C3×C312 | |
| UCS | C1 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 558 |
Polycyclic presentation:
2^2,3^2,31^2|d^a=d^2,f^a=f^30,e^b=e^30,f^b=f^30,e^c=e^5393 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 156);