Finite Group DatabasebetaFinite Group Databasebeta| order | 32364 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D87×D31⋊C3 |
| unambiguous semidirect product | D31⋊(C3×D87) |
| unambiguous semidirect product | (C3×D31⋊C3)⋊D29 |
| unambiguous semidirect product | (C29×D31⋊C3)⋊D3 |
| unambiguous semidirect product | (D31×D87)⋊C3 |
| Fitting, socle, derived | C3×C29×C31 ⋊ C22×C3 |
| Hall | C3×C29×C31⋊C3 ⋊ C22 |
| Hall | C29×C31 ⋊ C2×C3×D3 |
| Hall | C3×C31⋊C3 ⋊ C2×D29 |
| Sylow | C31 ⋊ C2×C3×D87 |
| Sylow | C29 ⋊ D3×D31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C29×C31 | C22×C3 |
| LCS | G ▷ C3×C29×C31 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2697 |
495 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32364, 68);