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G = D43order 86 = 2·43

Dihedral group

metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary

Aliases: D43, C43⋊C2, sometimes denoted D86 or Dih43 or Dih86, SmallGroup(86,1)

Series: Derived Chief Lower central Upper central

C1C43 — D43
C1C43 — D43
C43 — D43
C1

Generators and relations for D43
 G = < a,b | a43=b2=1, bab=a-1 >

43C2

Character table of D43

 class 1243A43B43C43D43E43F43G43H43I43J43K43L43M43N43O43P43Q43R43S43T43U
 size 143222222222222222222222
ρ111111111111111111111111    trivial
ρ21-1111111111111111111111    linear of order 2
ρ320ζ4341432ζ4340433ζ4339434ζ4338435ζ4337436ζ4336437ζ4335438ζ4334439ζ43334310ζ43324311ζ43314312ζ43304313ζ43294314ζ43284315ζ43274316ζ43264317ζ43254318ζ43244319ζ43234320ζ43224321ζ434243    orthogonal faithful
ρ420ζ43334310ζ43284315ζ43234320ζ43254318ζ43304313ζ4335438ζ4340433ζ4341432ζ4336437ζ43314312ζ43264317ζ43224321ζ43274316ζ43324311ζ4337436ζ434243ζ4339434ζ4334439ζ43294314ζ43244319ζ4338435    orthogonal faithful
ρ520ζ43274316ζ43244319ζ43324311ζ4340433ζ4338435ζ43304313ζ43224321ζ43294314ζ4337436ζ4341432ζ43334310ζ43254318ζ43264317ζ4334439ζ434243ζ4336437ζ43284315ζ43234320ζ43314312ζ4339434ζ4335438    orthogonal faithful
ρ620ζ43294314ζ43224321ζ43284315ζ4335438ζ434243ζ4337436ζ43304313ζ43234320ζ43274316ζ4334439ζ4341432ζ4338435ζ43314312ζ43244319ζ43264317ζ43334310ζ4340433ζ4339434ζ43324311ζ43254318ζ4336437    orthogonal faithful
ρ720ζ4337436ζ4334439ζ43314312ζ43284315ζ43254318ζ43224321ζ43244319ζ43274316ζ43304313ζ43334310ζ4336437ζ4339434ζ434243ζ4341432ζ4338435ζ4335438ζ43324311ζ43294314ζ43264317ζ43234320ζ4340433    orthogonal faithful
ρ820ζ43314312ζ43254318ζ43244319ζ43304313ζ4336437ζ434243ζ4338435ζ43324311ζ43264317ζ43234320ζ43294314ζ4335438ζ4341432ζ4339434ζ43334310ζ43274316ζ43224321ζ43284315ζ4334439ζ4340433ζ4337436    orthogonal faithful
ρ920ζ43244319ζ4336437ζ4338435ζ43264317ζ43294314ζ4341432ζ43334310ζ43224321ζ4334439ζ4340433ζ43284315ζ43274316ζ4339434ζ4335438ζ43234320ζ43324311ζ434243ζ43304313ζ43254318ζ4337436ζ43314312    orthogonal faithful
ρ1020ζ43224321ζ43334310ζ434243ζ43314312ζ43234320ζ4334439ζ4341432ζ43304313ζ43244319ζ4335438ζ4340433ζ43294314ζ43254318ζ4336437ζ4339434ζ43284315ζ43264317ζ4337436ζ4338435ζ43274316ζ43324311    orthogonal faithful
ρ1120ζ43234320ζ43304313ζ4340433ζ4336437ζ43264317ζ43274316ζ4337436ζ4339434ζ43294314ζ43244319ζ4334439ζ434243ζ43324311ζ43224321ζ43314312ζ4341432ζ4335438ζ43254318ζ43284315ζ4338435ζ43334310    orthogonal faithful
ρ1220ζ434243ζ43234320ζ4341432ζ43244319ζ4340433ζ43254318ζ4339434ζ43264317ζ4338435ζ43274316ζ4337436ζ43284315ζ4336437ζ43294314ζ4335438ζ43304313ζ4334439ζ43314312ζ43334310ζ43324311ζ43224321    orthogonal faithful
ρ1320ζ4338435ζ43294314ζ43334310ζ4334439ζ43284315ζ4339434ζ43234320ζ434243ζ43254318ζ4337436ζ43304313ζ43324311ζ4335438ζ43274316ζ4340433ζ43224321ζ4341432ζ43264317ζ4336437ζ43314312ζ43244319    orthogonal faithful
ρ1420ζ4335438ζ43314312ζ43274316ζ43234320ζ43244319ζ43284315ζ43324311ζ4336437ζ4340433ζ434243ζ4338435ζ4334439ζ43304313ζ43264317ζ43224321ζ43254318ζ43294314ζ43334310ζ4337436ζ4341432ζ4339434    orthogonal faithful
ρ1520ζ43324311ζ4338435ζ43224321ζ4337436ζ43334310ζ43264317ζ434243ζ43284315ζ43314312ζ4339434ζ43234320ζ4336437ζ4334439ζ43254318ζ4341432ζ43294314ζ43304313ζ4340433ζ43244319ζ4335438ζ43274316    orthogonal faithful
ρ1620ζ43284315ζ434243ζ43304313ζ43274316ζ4341432ζ43314312ζ43264317ζ4340433ζ43324311ζ43254318ζ4339434ζ43334310ζ43244319ζ4338435ζ4334439ζ43234320ζ4337436ζ4335438ζ43224321ζ4336437ζ43294314    orthogonal faithful
ρ1720ζ4336437ζ43324311ζ43294314ζ4339434ζ43224321ζ4340433ζ43284315ζ43334310ζ4335438ζ43264317ζ434243ζ43244319ζ4337436ζ43314312ζ43304313ζ4338435ζ43234320ζ4341432ζ43274316ζ4334439ζ43254318    orthogonal faithful
ρ1820ζ43254318ζ43274316ζ4336437ζ4341432ζ43324311ζ43234320ζ43294314ζ4338435ζ4339434ζ43304313ζ43224321ζ43314312ζ4340433ζ4337436ζ43284315ζ43244319ζ43334310ζ434243ζ4335438ζ43264317ζ4334439    orthogonal faithful
ρ1920ζ43304313ζ4341432ζ43264317ζ43324311ζ4339434ζ43244319ζ4334439ζ4337436ζ43224321ζ4336437ζ4335438ζ43234320ζ4338435ζ43334310ζ43254318ζ4340433ζ43314312ζ43274316ζ434243ζ43294314ζ43284315    orthogonal faithful
ρ2020ζ43264317ζ4339434ζ4334439ζ43224321ζ4335438ζ4338435ζ43254318ζ43314312ζ434243ζ43294314ζ43274316ζ4340433ζ43334310ζ43234320ζ4336437ζ4337436ζ43244319ζ43324311ζ4341432ζ43284315ζ43304313    orthogonal faithful
ρ2120ζ4334439ζ4335438ζ43254318ζ434243ζ43274316ζ43334310ζ4336437ζ43244319ζ4341432ζ43284315ζ43324311ζ4337436ζ43234320ζ4340433ζ43294314ζ43314312ζ4338435ζ43224321ζ4339434ζ43304313ζ43264317    orthogonal faithful
ρ2220ζ4340433ζ43264317ζ4337436ζ43294314ζ4334439ζ43324311ζ43314312ζ4335438ζ43284315ζ4338435ζ43254318ζ4341432ζ43224321ζ434243ζ43244319ζ4339434ζ43274316ζ4336437ζ43304313ζ43334310ζ43234320    orthogonal faithful
ρ2320ζ4339434ζ4337436ζ4335438ζ43334310ζ43314312ζ43294314ζ43274316ζ43254318ζ43234320ζ43224321ζ43244319ζ43264317ζ43284315ζ43304313ζ43324311ζ4334439ζ4336437ζ4338435ζ4340433ζ434243ζ4341432    orthogonal faithful

Smallest permutation representation of D43
On 43 points: primitive
Generators in S43
(1 2 3 4 5 6 7 8 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)
(1 43)(2 42)(3 41)(4 40)(5 39)(6 38)(7 37)(8 36)(9 35)(10 34)(11 33)(12 32)(13 31)(14 30)(15 29)(16 28)(17 27)(18 26)(19 25)(20 24)(21 23)

G:=sub<Sym(43)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43), (1,43)(2,42)(3,41)(4,40)(5,39)(6,38)(7,37)(8,36)(9,35)(10,34)(11,33)(12,32)(13,31)(14,30)(15,29)(16,28)(17,27)(18,26)(19,25)(20,24)(21,23)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43), (1,43)(2,42)(3,41)(4,40)(5,39)(6,38)(7,37)(8,36)(9,35)(10,34)(11,33)(12,32)(13,31)(14,30)(15,29)(16,28)(17,27)(18,26)(19,25)(20,24)(21,23) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43)], [(1,43),(2,42),(3,41),(4,40),(5,39),(6,38),(7,37),(8,36),(9,35),(10,34),(11,33),(12,32),(13,31),(14,30),(15,29),(16,28),(17,27),(18,26),(19,25),(20,24),(21,23)])

D43 is a maximal subgroup of   C43⋊C6  D129  D215
D43 is a maximal quotient of   Dic43  D129  D215

Matrix representation of D43 in GL2(𝔽173) generated by

39172
10
,
39172
136134
G:=sub<GL(2,GF(173))| [39,1,172,0],[39,136,172,134] >;

D43 in GAP, Magma, Sage, TeX

D_{43}
% in TeX

G:=Group("D43");
// GroupNames label

G:=SmallGroup(86,1);
// by ID

G=gap.SmallGroup(86,1);
# by ID

G:=PCGroup([2,-2,-43,337]);
// Polycyclic

G:=Group<a,b|a^43=b^2=1,b*a*b=a^-1>;
// generators/relations

Export

Subgroup lattice of D43 in TeX
Character table of D43 in TeX

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