Finite Group DatabasebetaFinite Group Databasebeta| order | 32364 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C31⋊C3)⋊#1181) |
| unambiguous semidirect product | (C31⋊C3)⋊(C3⋊#1181) |
| unambiguous semidirect product | (C3⋊(C31⋊#1181))⋊C3 |
| Fitting, socle, derived | C3×C29×C31 ⋊ C3×C4 |
| Hall | C3×C29×C31⋊C3 ⋊ C4 |
| Hall | C29×C31 ⋊ C3×Dic3 |
| Hall | C3×C31⋊C3 ⋊ #1181 |
| Sylow | C31 ⋊ C3×C3⋊#1181 |
| Sylow | C29 ⋊ C3⋊((C31⋊C3)⋊C4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C29×C31 | C3×C4 |
| prime radical | C3×D29×C31⋊C3 | C2 |
| cosocle | C3×C31×D29 | C2×C3 |
| LCS | G ▷ C3×C29×C31 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2697 |
Polycyclic presentation:
2,3,2,3,29,31|a^2=c,d^a=d^2,e^a=e^17,f^a=f^30,f^b=f^5,e^c=e^28321 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32364, 66);