Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | (C31⋊C3)⋊((C31⋊C3)⋊C4) |
| unambiguous semidirect product | #26040335⋊C3 |
| unambiguous semidirect product | #26040336⋊C3 |
| unambiguous semidirect product | ((C31⋊C3)⋊Dic31)⋊C3 |
| derived, Sylow | C312 ⋊ C32×C4 |
| Hall | C31⋊C32 ⋊ C4 |
| Hall | C31⋊Dic31 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C31⋊C3)⋊(D31⋊C3) |
| commutator, hypocenter | C312 | C32×C4 |
| Fitting, socle, cosocle | C2×C312 | C2×C32 |
| prime radical | C2×C31⋊C32 | C2 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C2 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 372 |
Polycyclic presentation:
2,3^2,31^2,2|a^2=f,d^a=d^30,e^a=e^30,e^b=e^5,d^c=d^5196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 99);