Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| automorphism | Aut(G) order 98784 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic294 |
| Hall | C3×C49 ⋊ Q8 |
| Sylow | C49 ⋊ Dic6 |
| Sylow | C3 ⋊ Dic98 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 60 |
| transitive degree | μt(G) = 1176 |
A minimal faithful permutation representation — 2 generators on 60 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);(1,5,3,7)(2,6,4,8)(10,11)(13,60)(14,59)(15,58)(16,57)(17,56)(18,55)(19,54)(20,53)(21,52)(22,51)(23,50)(24,49)(25,48)(26,47)(27,46)(28,45)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)Polycyclic presentation:
2^3,3,7^2|a^2=c,b^2=c,e^7=f,b^a=bc,d^a=d^2,e^a=e^6f^6,f^a=f^6297 conjugacy classes — view the full character table.
| maximal subgroup of | Dic588, Dic882, Dic1470, … |
| maximal normal subgroup of | Dic588 |
| maximal quotient of | Dic882, Dic1470, Dic2058, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 34);