Finite Group DatabasebetaFinite Group Databasebeta| order | 1968 |
| automorphism | Aut(G) order 314880 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic492 |
| Hall | C3×C41 ⋊ Q16 |
| Sylow | C41 ⋊ Dic12 |
| Sylow | C3 ⋊ Dic164 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 60 |
| transitive degree | μt(G) = 1968 |
A minimal faithful permutation representation — 2 generators on 60 points:
(1,2,3,4,5,6,7,8)(9,16,15,14,13,12,11,10)(17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60);(1,9,5,13)(2,10,6,14)(3,11,7,15)(4,12,8,16)(18,19)(21,60)(22,59)(23,58)(24,57)(25,56)(26,55)(27,54)(28,53)(29,52)(30,51)(31,50)(32,49)(33,48)(34,47)(35,46)(36,45)(37,44)(38,43)(39,42)(40,41)Polycyclic presentation:
2^4,3,41|a^2=d,b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^40495 conjugacy classes — view the full character table.
| maximal subgroup of | Dic984, Dic1476, Dic2460, … |
| maximal normal subgroup of | Dic984 |
| maximal quotient of | Dic1476, Dic2460, Dic3444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1968, 69);