Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| automorphism | Aut(G) order 329280 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic490 |
| Hall | C5×C49 ⋊ Q8 |
| Sylow | C49 ⋊ Dic10 |
| Sylow | C5 ⋊ Dic98 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 62 |
| transitive degree | μt(G) = 1960 |
A minimal faithful permutation representation — 2 generators on 62 points:
(1,2,3,4)(5,8,7,6)(9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62);(1,5,3,7)(2,6,4,8)(10,13)(11,12)(15,62)(16,61)(17,60)(18,59)(19,58)(20,57)(21,56)(22,55)(23,54)(24,53)(25,52)(26,51)(27,50)(28,49)(29,48)(30,47)(31,46)(32,45)(33,44)(34,43)(35,42)(36,41)(37,40)(38,39)Polycyclic presentation:
2^3,5,7^2|a^2=c,b^2=c,e^7=f,b^a=bc,d^a=d^4,e^a=e^6f^6,f^a=f^6493 conjugacy classes — view the full character table.
| maximal subgroup of | Dic980, Dic1470, Dic2450, … |
| maximal normal subgroup of | Dic980 |
| maximal quotient of | Dic1470, Dic2450, Dic3430, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 24);