Finite Group DatabasebetaFinite Group Databasebeta| order | 32364 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C31⋊C9)⋊#1181 |
| unambiguous semidirect product | (C31⋊#1181)⋊C9 |
| derived, Hall | C29×C31 ⋊ C4×C9 |
| Hall | C29×C31⋊C9 ⋊ C4 |
| Hall | C31⋊#1181 ⋊ C9 |
| Hall | C31⋊C9 ⋊ #1181 |
| Sylow | C31 ⋊ C9×#1181 |
| Sylow | C29 ⋊ Dic31⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C31⋊C3)⋊#1181 |
| commutator, hypocenter | C29×C31 | C4×C9 |
| Fitting, socle | C3×C29×C31 | C3×C4 |
| prime radical, cosocle | C3×C31×D29 | C2×C3 |
| LCS | G ▷ C29×C31 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8091 |
Polycyclic presentation:
2,3,2,29,31,3|a^2=c,b^3=f,d^a=d^17,e^a=e^30,e^b=e^5,d^c=d^28339 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32364, 14);