Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D279⋊D31 |
| Fitting, derived, Hall | C9×C312 ⋊ C22 |
| Sylow | C312 ⋊ C2×D9 |
| Sylow | C9 ⋊ D312 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C312 | C22 |
| Frattini | C3 | D93⋊D31 |
| socle | C3×C312 | C2×D3 |
| LCS | G ▷ C9×C312 | |
| UCS | C1 | |
150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 558 |
Polycyclic presentation:
2^2,3,31^2,3|c^3=f^2,c^a=c^2f,d^a=d^30,f^a=f^2,d^b=d^30,e^b=e^302217 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 84);