Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C32×C11 ⋊ Q16 |
| Sylow | C11 ⋊ #3718 |
| Sylow | C32 ⋊ #4326 |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 528 |
Polycyclic presentation:
2^4,3^2,11|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^2,g^a=g^10,c^b=cd,f^b=f^2156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 249);