Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| automorphism | Aut(G) order 190080 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic396 |
| Hall | C9×C11 ⋊ Q16 |
| Sylow | C11 ⋊ Dic36 |
| Sylow | C9 ⋊ Dic44 |
54 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 1584 |
A minimal faithful permutation representation — 2 generators on 36 points:
(1,2,3,4,5,6,7,8)(9,16,15,14,13,12,11,10)(17,18,19,20,21,22,23,24,25)(26,27,28,29,30,31,32,33,34,35,36);(1,9,5,13)(2,10,6,14)(3,11,7,15)(4,12,8,16)(18,25)(19,24)(20,23)(21,22)(27,36)(28,35)(29,34)(30,33)(31,32)Polycyclic presentation:
2^4,3,11,3|a^2=d,b^2=cd,c^2=d,e^3=g,b^a=bc,c^a=cd,e^a=e^2g^2,f^a=f^10,g^a=g^2399 conjugacy classes — view the full character table.
| maximal subgroup of | Dic792, Dic1188, Dic1980, … |
| maximal normal subgroup of | Dic792 |
| maximal quotient of | Dic1188, Dic1980, Dic2772, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 63);