Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C31 |
| unambiguous semidirect product | C3⋊(C3⋊#16838652) |
| Fitting, socle, derived, Hall | C32×C312 ⋊ C4 |
| Sylow | C312 ⋊ C3⋊Dic3 |
| Sylow | C32 ⋊ #16838652 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C312 | C4 |
| prime radical, cosocle | C32×C31⋊D31 | C2 |
| LCS | G ▷ C32×C312 | |
| UCS | C1 | |
228 conjugacy classes of subgroups.
| transitive degree | μt(G) = 558 |
Polycyclic presentation:
2^2,3^2,31^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^27f^19,f^a=e^4f^4,e^b=e^30,f^b=f^302172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 209);