Finite Group DatabasebetaFinite Group Databasebeta| order | 1040 |
| automorphism | Aut(G) order 99840 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic260 |
| Hall | C5×C13 ⋊ Q16 |
| Sylow | C13 ⋊ Dic20 |
| Sylow | C5 ⋊ Dic52 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 1040 |
A minimal faithful permutation representation — 2 generators on 34 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);(1,9,5,13)(2,10,6,14)(3,11,7,15)(4,12,8,16)(18,21)(19,20)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)Polycyclic presentation:
2^4,5,13|a^2=d,b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^4,f^a=f^12263 conjugacy classes — view the full character table.
| maximal subgroup of | Dic520, Dic780, Dic1300, … |
| maximal normal subgroup of | Dic520 |
| maximal quotient of | Dic780, Dic1300, Dic1820, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1040, 72);