Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D9)⋊Dic11 |
| Hall | C9×C11 ⋊ C22⋊C4 |
| Sylow | C11 ⋊ (C2×D9)⋊C4 |
| Sylow | C9 ⋊ C22⋊Dic11 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 792 |
Polycyclic presentation:
2^4,3,11,3|a^2=d,e^3=g,b^a=bc,f^a=f^10,e^b=e^2g^2,g^b=g^2162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 27);