Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D99⋊Q8 |
| Hall | C9×C11 ⋊ C2×Q8 |
| Sylow | C11 ⋊ Q8×D9 |
| Sylow | C9 ⋊ Q8×D11 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 792 |
Polycyclic presentation:
2^4,3,11,3|a^2=d,b^2=d,c^2=d,e^3=g,c^a=cd,f^a=f^10,c^b=cd,e^b=e^2g^2,g^b=g^2135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 105);