Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C31⋊C9)⋊Dic31 |
| derived, Sylow | C312 ⋊ C4×C9 |
| Hall | C31×C31⋊C9 ⋊ C4 |
| Hall | C31⋊Dic31 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | (C31⋊C3)⋊D31 |
| commutator, hypocenter | C312 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C312 | C2×C3 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C2×C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1116 |
Polycyclic presentation:
2,3,31^2,2,3|a^2=e,b^3=f,c^a=c^30,d^a=d^30,c^b=c^51236 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 53);