Finite Group DatabasebetaFinite Group Databasebeta| order | 32364 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C3 |
| direct product | C31×C3⋊(C3⋊#1181) |
| unambiguous semidirect product | C3⋊(C31×C3⋊#1181) |
| Fitting, socle, Hall | C32×C29×C31 ⋊ C4 |
| derived, Hall | C32×C29 ⋊ C4×C31 |
| Hall | C29×C31 ⋊ C3⋊Dic3 |
| Hall | C32×C31 ⋊ #1181 |
| Sylow | C29 ⋊ C31×C3⋊Dic3 |
| Sylow | C32 ⋊ C31×#1181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | C3⋊(C3⋊#1181) |
| commutator, hypocenter | C32×C29 | C4×C31 |
| Frattini | C1 | G |
| Fitting, socle | C32×C29×C31 | C4 |
| prime radical | C32×C31×D29 | C2 |
| cosocle | C32×D29 | C2×C31 |
| LCS | G ▷ C32×C29 | |
| UCS | C1 ◁ C31 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8091 |
2325 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32364, 109);