Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C32×C11 ⋊ SD16 |
| Sylow | C11 ⋊ #3775 |
| Sylow | C32 ⋊ #4325 |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 264 |
Polycyclic presentation:
2^4,3^2,11|b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=e^2f,g^a=g^10,c^b=cd,e^b=e^2f^2,e^c=e^2,f^c=f^290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 393);