Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C22×D32×C11 |
| unambiguous semidirect product | (C3×D3)⋊(C23×C11) |
| unambiguous semidirect product | (C3⋊D3)⋊(C23×C11) |
| Fitting, socle | C22×C32×C11 ⋊ C22 |
| derived, Sylow | C32 ⋊ C24×C11 |
| Hall | C32×C11 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C11 | D32 |
| commutator, cosocle, hypocenter | C32 | C24×C11 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C11 | C22 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C22×C11 | |
568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
396 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 687);