Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic240 |
| Hall | C3×C5 ⋊ Q64 |
| Sylow | C5 ⋊ Dic48 |
| Sylow | C3 ⋊ Dic80 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 72 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 2 generators on 72 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32)(33,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34)(65,66,67)(68,69,70,71,72);(1,33,17,49)(2,34,18,50)(3,35,19,51)(4,36,20,52)(5,37,21,53)(6,38,22,54)(7,39,23,55)(8,40,24,56)(9,41,25,57)(10,42,26,58)(11,43,27,59)(12,44,28,60)(13,45,29,61)(14,46,30,62)(15,47,31,63)(16,48,32,64)(66,67)(69,72)(70,71)Polycyclic presentation:
2^6,3,5|a^2=f,b^2=cd,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,g^a=g^2,h^a=h^4243 conjugacy classes — view the full character table.
| maximal subgroup of | #14279819, #14279822, #14279826, … |
| maximal normal subgroup of | #14279819, #14279822, #14279826, … |
| maximal quotient of | #14279588, #14279718, C2×Dic240, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 466);