Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C9×C11 ⋊ SD16 |
| Sylow | C11 ⋊ #3664 |
| Sylow | C9 ⋊ #4324 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 792 |
Polycyclic presentation:
2^4,3,11,3|a^2=c,c^2=d,e^3=g,b^a=bcd,f^a=f^10,c^b=cd,e^b=e^2g^2,g^b=g^2144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 9);