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G = D47order 94 = 2·47

Dihedral group

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

Aliases: D47, C47⋊C2, sometimes denoted D94 or Dih47 or Dih94, SmallGroup(94,1)

Series: Derived Chief Lower central Upper central

C1C47 — D47
C1C47 — D47
C47 — D47
C1

Generators and relations for D47
 G = < a,b | a47=b2=1, bab=a-1 >

47C2

Character table of D47

 class 1247A47B47C47D47E47F47G47H47I47J47K47L47M47N47O47P47Q47R47S47T47U47V47W
 size 14722222222222222222222222
ρ11111111111111111111111111    trivial
ρ21-111111111111111111111111    linear of order 2
ρ320ζ47254722ζ47334714ζ4744473ζ4739478ζ47284719ζ47304717ζ4741476ζ4742475ζ47314716ζ47274720ζ4738479ζ4745472ζ47344713ζ47244723ζ47354712ζ474647ζ47374710ζ47264721ζ47324715ζ4743474ζ4740477ζ47294718ζ47364711    orthogonal faithful
ρ420ζ47324715ζ474647ζ47304717ζ47334714ζ4745472ζ47294718ζ47344713ζ4744473ζ47284719ζ47354712ζ4743474ζ47274720ζ47364711ζ4742475ζ47264721ζ47374710ζ4741476ζ47254722ζ4738479ζ4740477ζ47244723ζ4739478ζ47314716    orthogonal faithful
ρ520ζ47344713ζ4743474ζ47264721ζ4738479ζ4739478ζ47254722ζ4742475ζ47354712ζ47294718ζ474647ζ47314716ζ47334714ζ4744473ζ47274720ζ47374710ζ4740477ζ47244723ζ4741476ζ47364711ζ47284719ζ4745472ζ47324715ζ47304717    orthogonal faithful
ρ620ζ4745472ζ4744473ζ4743474ζ4742475ζ4741476ζ4740477ζ4739478ζ4738479ζ47374710ζ47364711ζ47354712ζ47344713ζ47334714ζ47324715ζ47314716ζ47304717ζ47294718ζ47284719ζ47274720ζ47264721ζ47254722ζ47244723ζ474647    orthogonal faithful
ρ720ζ47354712ζ47294718ζ47244723ζ47304717ζ47364711ζ4742475ζ474647ζ4740477ζ47344713ζ47284719ζ47254722ζ47314716ζ47374710ζ4743474ζ4745472ζ4739478ζ47334714ζ47274720ζ47264721ζ47324715ζ4738479ζ4744473ζ4741476    orthogonal faithful
ρ820ζ4741476ζ4738479ζ47354712ζ47324715ζ47294718ζ47264721ζ47244723ζ47274720ζ47304717ζ47334714ζ47364711ζ4739478ζ4742475ζ4745472ζ474647ζ4743474ζ4740477ζ47374710ζ47344713ζ47314716ζ47284719ζ47254722ζ4744473    orthogonal faithful
ρ920ζ4739478ζ47354712ζ47314716ζ47274720ζ47244723ζ47284719ζ47324715ζ47364711ζ4740477ζ4744473ζ474647ζ4742475ζ4738479ζ47344713ζ47304717ζ47264721ζ47254722ζ47294718ζ47334714ζ47374710ζ4741476ζ4745472ζ4743474    orthogonal faithful
ρ1020ζ474647ζ47254722ζ4745472ζ47264721ζ4744473ζ47274720ζ4743474ζ47284719ζ4742475ζ47294718ζ4741476ζ47304717ζ4740477ζ47314716ζ4739478ζ47324715ζ4738479ζ47334714ζ47374710ζ47344713ζ47364711ζ47354712ζ47244723    orthogonal faithful
ρ1120ζ47364711ζ4740477ζ47254722ζ4743474ζ47334714ζ47324715ζ4744473ζ47264721ζ4739478ζ47374710ζ47284719ζ474647ζ47304717ζ47354712ζ4741476ζ47244723ζ4742475ζ47344713ζ47314716ζ4745472ζ47274720ζ4738479ζ47294718    orthogonal faithful
ρ1220ζ47294718ζ47274720ζ47364711ζ4745472ζ4740477ζ47314716ζ47254722ζ47344713ζ4743474ζ4742475ζ47334714ζ47244723ζ47324715ζ4741476ζ4744473ζ47354712ζ47264721ζ47304717ζ4739478ζ474647ζ47374710ζ47284719ζ4738479    orthogonal faithful
ρ1320ζ47244723ζ47364711ζ474647ζ47344713ζ47254722ζ47374710ζ4745472ζ47334714ζ47264721ζ4738479ζ4744473ζ47324715ζ47274720ζ4739478ζ4743474ζ47314716ζ47284719ζ4740477ζ4742475ζ47304717ζ47294718ζ4741476ζ47354712    orthogonal faithful
ρ1420ζ47374710ζ47324715ζ47274720ζ47254722ζ47304717ζ47354712ζ4740477ζ4745472ζ4744473ζ4739478ζ47344713ζ47294718ζ47244723ζ47284719ζ47334714ζ4738479ζ4743474ζ474647ζ4741476ζ47364711ζ47314716ζ47264721ζ4742475    orthogonal faithful
ρ1520ζ4742475ζ47314716ζ47374710ζ47364711ζ47324715ζ4741476ζ47274720ζ474647ζ47254722ζ4743474ζ47304717ζ4738479ζ47354712ζ47334714ζ4740477ζ47284719ζ4745472ζ47244723ζ4744473ζ47294718ζ4739478ζ47344713ζ47264721    orthogonal faithful
ρ1620ζ47274720ζ47304717ζ4740477ζ4744473ζ47344713ζ47244723ζ47334714ζ4743474ζ4741476ζ47314716ζ47264721ζ47364711ζ474647ζ4738479ζ47284719ζ47294718ζ4739478ζ4745472ζ47354712ζ47254722ζ47324715ζ4742475ζ47374710    orthogonal faithful
ρ1720ζ47264721ζ4739478ζ4742475ζ47294718ζ47314716ζ4744473ζ47374710ζ47244723ζ47364711ζ4745472ζ47324715ζ47284719ζ4741476ζ4740477ζ47274720ζ47334714ζ474647ζ47354712ζ47254722ζ4738479ζ4743474ζ47304717ζ47344713    orthogonal faithful
ρ1820ζ47304717ζ4745472ζ47344713ζ47284719ζ4743474ζ47364711ζ47264721ζ4741476ζ4738479ζ47244723ζ4739478ζ4740477ζ47254722ζ47374710ζ4742475ζ47274720ζ47354712ζ4744473ζ47294718ζ47334714ζ474647ζ47314716ζ47324715    orthogonal faithful
ρ1920ζ4738479ζ47374710ζ47294718ζ474647ζ47274720ζ4739478ζ47364711ζ47304717ζ4745472ζ47264721ζ4740477ζ47354712ζ47314716ζ4744473ζ47254722ζ4741476ζ47344713ζ47324715ζ4743474ζ47244723ζ4742475ζ47334714ζ47284719    orthogonal faithful
ρ2020ζ47284719ζ4742475ζ4738479ζ47244723ζ47374710ζ4743474ζ47294718ζ47324715ζ474647ζ47344713ζ47274720ζ4741476ζ4739478ζ47254722ζ47364711ζ4744473ζ47304717ζ47314716ζ4745472ζ47354712ζ47264721ζ4740477ζ47334714    orthogonal faithful
ρ2120ζ4744473ζ47284719ζ4741476ζ47314716ζ4738479ζ47344713ζ47354712ζ47374710ζ47324715ζ4740477ζ47294718ζ4743474ζ47264721ζ474647ζ47244723ζ4745472ζ47274720ζ4742475ζ47304717ζ4739478ζ47334714ζ47364711ζ47254722    orthogonal faithful
ρ2220ζ4743474ζ4741476ζ4739478ζ47374710ζ47354712ζ47334714ζ47314716ζ47294718ζ47274720ζ47254722ζ47244723ζ47264721ζ47284719ζ47304717ζ47324715ζ47344713ζ47364711ζ4738479ζ4740477ζ4742475ζ4744473ζ474647ζ4745472    orthogonal faithful
ρ2320ζ47314716ζ47244723ζ47324715ζ4740477ζ474647ζ4738479ζ47304717ζ47254722ζ47334714ζ4741476ζ4745472ζ47374710ζ47294718ζ47264721ζ47344713ζ4742475ζ4744473ζ47364711ζ47284719ζ47274720ζ47354712ζ4743474ζ4739478    orthogonal faithful
ρ2420ζ47334714ζ47264721ζ47284719ζ47354712ζ4742475ζ4745472ζ4738479ζ47314716ζ47244723ζ47304717ζ47374710ζ4744473ζ4743474ζ47364711ζ47294718ζ47254722ζ47324715ζ4739478ζ474647ζ4741476ζ47344713ζ47274720ζ4740477    orthogonal faithful
ρ2520ζ4740477ζ47344713ζ47334714ζ4741476ζ47264721ζ474647ζ47284719ζ4739478ζ47354712ζ47324715ζ4742475ζ47254722ζ4745472ζ47294718ζ4738479ζ47364711ζ47314716ζ4743474ζ47244723ζ4744473ζ47304717ζ47374710ζ47274720    orthogonal faithful

Smallest permutation representation of D47
On 47 points: primitive
Generators in S47
(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 44 45 46 47)
(1 47)(2 46)(3 45)(4 44)(5 43)(6 42)(7 41)(8 40)(9 39)(10 38)(11 37)(12 36)(13 35)(14 34)(15 33)(16 32)(17 31)(18 30)(19 29)(20 28)(21 27)(22 26)(23 25)

G:=sub<Sym(47)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47), (1,47)(2,46)(3,45)(4,44)(5,43)(6,42)(7,41)(8,40)(9,39)(10,38)(11,37)(12,36)(13,35)(14,34)(15,33)(16,32)(17,31)(18,30)(19,29)(20,28)(21,27)(22,26)(23,25)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47), (1,47)(2,46)(3,45)(4,44)(5,43)(6,42)(7,41)(8,40)(9,39)(10,38)(11,37)(12,36)(13,35)(14,34)(15,33)(16,32)(17,31)(18,30)(19,29)(20,28)(21,27)(22,26)(23,25) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)], [(1,47),(2,46),(3,45),(4,44),(5,43),(6,42),(7,41),(8,40),(9,39),(10,38),(11,37),(12,36),(13,35),(14,34),(15,33),(16,32),(17,31),(18,30),(19,29),(20,28),(21,27),(22,26),(23,25)])

D47 is a maximal subgroup of   D141  D235
D47 is a maximal quotient of   Dic47  D141  D235

Matrix representation of D47 in GL2(𝔽283) generated by

27282
10
,
27282
162256
G:=sub<GL(2,GF(283))| [27,1,282,0],[27,162,282,256] >;

D47 in GAP, Magma, Sage, TeX

D_{47}
% in TeX

G:=Group("D47");
// GroupNames label

G:=SmallGroup(94,1);
// by ID

G=gap.SmallGroup(94,1);
# by ID

G:=PCGroup([2,-2,-47,369]);
// Polycyclic

G:=Group<a,b|a^47=b^2=1,b*a*b=a^-1>;
// generators/relations

Export

Subgroup lattice of D47 in TeX
Character table of D47 in TeX

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