Finite Group DatabasebetaFinite Group Databasebeta| order | 32094 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #30631032⋊C2 |
| Fitting, socle, derived, Sylow | C1783 ⋊ C2×C9 |
| Hall | #30631032 ⋊ C2 |
| Hall | D1783 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1783 | C2×C9 |
| prime radical | D1783⋊C3 | C3 |
| cosocle | C1783⋊C3 | C2×C3 |
| LCS | G ▷ C1783 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1783 |
Polycyclic presentation:
2,3^2,1783|b^3=c,d^a=d^1782,d^b=d^920,d^c=d^193117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32094, 8);