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G = D23order 46 = 2·23

Dihedral group

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

Aliases: D23, C23⋊C2, sometimes denoted D46 or Dih23 or Dih46, SmallGroup(46,1)

Series: Derived Chief Lower central Upper central

C1C23 — D23
C1C23 — D23
C23 — D23
C1

Generators and relations for D23
 G = < a,b | a23=b2=1, bab=a-1 >

23C2

Character table of D23

 class 1223A23B23C23D23E23F23G23H23I23J23K
 size 12322222222222
ρ11111111111111    trivial
ρ21-111111111111    linear of order 2
ρ320ζ2316237ζ232223ζ2314239ζ2317236ζ2321232ζ23132310ζ2318235ζ2320233ζ23122311ζ2319234ζ2315238    orthogonal faithful
ρ420ζ2318235ζ2319234ζ23132310ζ232223ζ2315238ζ2317236ζ2320233ζ23122311ζ2321232ζ2316237ζ2314239    orthogonal faithful
ρ520ζ2319234ζ2317236ζ2315238ζ23132310ζ23122311ζ2314239ζ2316237ζ2318235ζ2320233ζ232223ζ2321232    orthogonal faithful
ρ620ζ2321232ζ2320233ζ2319234ζ2318235ζ2317236ζ2316237ζ2315238ζ2314239ζ23132310ζ23122311ζ232223    orthogonal faithful
ρ720ζ2317236ζ2314239ζ23122311ζ2315238ζ2318235ζ2321232ζ232223ζ2319234ζ2316237ζ23132310ζ2320233    orthogonal faithful
ρ820ζ232223ζ23132310ζ2321232ζ2314239ζ2320233ζ2315238ζ2319234ζ2316237ζ2318235ζ2317236ζ23122311    orthogonal faithful
ρ920ζ23132310ζ2315238ζ2320233ζ2321232ζ2316237ζ23122311ζ2317236ζ232223ζ2319234ζ2314239ζ2318235    orthogonal faithful
ρ1020ζ2315238ζ23122311ζ2316237ζ2320233ζ232223ζ2318235ζ2314239ζ23132310ζ2317236ζ2321232ζ2319234    orthogonal faithful
ρ1120ζ2320233ζ2316237ζ2317236ζ2319234ζ2314239ζ232223ζ23122311ζ2321232ζ2315238ζ2318235ζ23132310    orthogonal faithful
ρ1220ζ2314239ζ2321232ζ2318235ζ23122311ζ2319234ζ2320233ζ23132310ζ2317236ζ232223ζ2315238ζ2316237    orthogonal faithful
ρ1320ζ23122311ζ2318235ζ232223ζ2316237ζ23132310ζ2319234ζ2321232ζ2315238ζ2314239ζ2320233ζ2317236    orthogonal faithful

Permutation representations of D23
On 23 points: primitive - transitive group 23T2
Generators in S23
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23)
(1 23)(2 22)(3 21)(4 20)(5 19)(6 18)(7 17)(8 16)(9 15)(10 14)(11 13)

G:=sub<Sym(23)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23), (1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)>;

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), (1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13) );

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)], [(1,23),(2,22),(3,21),(4,20),(5,19),(6,18),(7,17),(8,16),(9,15),(10,14),(11,13)])

G:=TransitiveGroup(23,2);

Matrix representation of D23 in GL2(𝔽47) generated by

646
10
,
646
3541
G:=sub<GL(2,GF(47))| [6,1,46,0],[6,35,46,41] >;

D23 in GAP, Magma, Sage, TeX

D_{23}
% in TeX

G:=Group("D23");
// GroupNames label

G:=SmallGroup(46,1);
// by ID

G=gap.SmallGroup(46,1);
# by ID

G:=PCGroup([2,-2,-23,177]);
// Polycyclic

G:=Group<a,b|a^23=b^2=1,b*a*b=a^-1>;
// generators/relations

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