Finite Group DatabasebetaFinite Group Databasebeta| order | 1520 |
| automorphism | Aut(G) order 218880 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic380 |
| Hall | C5×C19 ⋊ Q16 |
| Sylow | C19 ⋊ Dic20 |
| Sylow | C5 ⋊ Dic76 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 1520 |
A minimal faithful permutation representation — 2 generators on 40 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);(1,9,5,13)(2,10,6,14)(3,11,7,15)(4,12,8,16)(18,21)(19,20)(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(31,32)Polycyclic presentation:
2^4,5,19|a^2=d,b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^4,f^a=f^18383 conjugacy classes — view the full character table.
| maximal subgroup of | Dic760, Dic1140, Dic1900, … |
| maximal normal subgroup of | Dic760 |
| maximal quotient of | Dic1140, Dic1900, Dic2660, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1520, 68);