Finite Group DatabasebetaFinite Group Databasebeta| order | 1392 |
| automorphism | Aut(G) order 155904 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic348 |
| Hall | C3×C29 ⋊ Q16 |
| Sylow | C29 ⋊ Dic12 |
| Sylow | C3 ⋊ Dic116 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 48 |
| transitive degree | μt(G) = 1392 |
A minimal faithful permutation representation — 2 generators on 48 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);(1,9,5,13)(2,10,6,14)(3,11,7,15)(4,12,8,16)(18,19)(21,48)(22,47)(23,46)(24,45)(25,44)(26,43)(27,42)(28,41)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)Polycyclic presentation:
2^4,3,29|a^2=d,b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^28351 conjugacy classes — view the full character table.
| maximal subgroup of | Dic696, Dic1044, Dic1740, … |
| maximal normal subgroup of | Dic696 |
| maximal quotient of | Dic1044, Dic1740, Dic2436, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1392, 69);