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G = D46order 92 = 22·23

Dihedral group

direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary

Aliases: D46, C2×D23, C46⋊C2, C23⋊C22, sometimes denoted D92 or Dih46 or Dih92, SmallGroup(92,3)

Series: Derived Chief Lower central Upper central

C1C23 — D46
C1C23D23 — D46
C23 — D46
C1C2

Generators and relations for D46
 G = < a,b | a46=b2=1, bab=a-1 >

23C2
23C2
23C22

Character table of D46

 class 12A2B2C23A23B23C23D23E23F23G23H23I23J23K46A46B46C46D46E46F46G46H46I46J46K
 size 1123232222222222222222222222
ρ111111111111111111111111111    trivial
ρ21-11-111111111111-1-1-1-1-1-1-1-1-1-1-1    linear of order 2
ρ31-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1    linear of order 2
ρ411-1-11111111111111111111111    linear of order 2
ρ52200ζ2315238ζ23132310ζ23122311ζ2314239ζ2316237ζ2318235ζ2320233ζ232223ζ2321232ζ2319234ζ2317236ζ2317236ζ2315238ζ23132310ζ23122311ζ2314239ζ2316237ζ2318235ζ2320233ζ232223ζ2321232ζ2319234    orthogonal lifted from D23
ρ62200ζ2319234ζ2318235ζ2317236ζ2316237ζ2315238ζ2314239ζ23132310ζ23122311ζ232223ζ2321232ζ2320233ζ2320233ζ2319234ζ2318235ζ2317236ζ2316237ζ2315238ζ2314239ζ23132310ζ23122311ζ232223ζ2321232    orthogonal lifted from D23
ρ72-200ζ2320233ζ2321232ζ2316237ζ23122311ζ2317236ζ232223ζ2319234ζ2314239ζ2318235ζ23132310ζ2315238231523823202332321232231623723122311231723623222323192342314239231823523132310    orthogonal faithful
ρ82-200ζ2321232ζ2314239ζ2320233ζ2315238ζ2319234ζ2316237ζ2318235ζ2317236ζ23122311ζ232223ζ23132310231323102321232231423923202332315238231923423162372318235231723623122311232223    orthogonal faithful
ρ92-200ζ2314239ζ2317236ζ2321232ζ23132310ζ2318235ζ2320233ζ23122311ζ2319234ζ2315238ζ2316237ζ232223232223231423923172362321232231323102318235232023323122311231923423152382316237    orthogonal faithful
ρ102200ζ2320233ζ2321232ζ2316237ζ23122311ζ2317236ζ232223ζ2319234ζ2314239ζ2318235ζ23132310ζ2315238ζ2315238ζ2320233ζ2321232ζ2316237ζ23122311ζ2317236ζ232223ζ2319234ζ2314239ζ2318235ζ23132310    orthogonal lifted from D23
ρ112200ζ2316237ζ2320233ζ232223ζ2318235ζ2314239ζ23132310ζ2317236ζ2321232ζ2319234ζ2315238ζ23122311ζ23122311ζ2316237ζ2320233ζ232223ζ2318235ζ2314239ζ23132310ζ2317236ζ2321232ζ2319234ζ2315238    orthogonal lifted from D23
ρ122-200ζ2315238ζ23132310ζ23122311ζ2314239ζ2316237ζ2318235ζ2320233ζ232223ζ2321232ζ2319234ζ2317236231723623152382313231023122311231423923162372318235232023323222323212322319234    orthogonal faithful
ρ132-200ζ2317236ζ2319234ζ2314239ζ232223ζ23122311ζ2321232ζ2315238ζ2318235ζ23132310ζ2320233ζ2316237231623723172362319234231423923222323122311232123223152382318235231323102320233    orthogonal faithful
ρ142-200ζ232223ζ2316237ζ23132310ζ2319234ζ2321232ζ2315238ζ2314239ζ2320233ζ2317236ζ23122311ζ2318235231823523222323162372313231023192342321232231523823142392320233231723623122311    orthogonal faithful
ρ152-200ζ2318235ζ23122311ζ2319234ζ2320233ζ23132310ζ2317236ζ232223ζ2315238ζ2316237ζ2314239ζ2321232232123223182352312231123192342320233231323102317236232223231523823162372314239    orthogonal faithful
ρ162-200ζ2319234ζ2318235ζ2317236ζ2316237ζ2315238ζ2314239ζ23132310ζ23122311ζ232223ζ2321232ζ2320233232023323192342318235231723623162372315238231423923132310231223112322232321232    orthogonal faithful
ρ172200ζ23132310ζ232223ζ2315238ζ2317236ζ2320233ζ23122311ζ2321232ζ2316237ζ2314239ζ2318235ζ2319234ζ2319234ζ23132310ζ232223ζ2315238ζ2317236ζ2320233ζ23122311ζ2321232ζ2316237ζ2314239ζ2318235    orthogonal lifted from D23
ρ182-200ζ2316237ζ2320233ζ232223ζ2318235ζ2314239ζ23132310ζ2317236ζ2321232ζ2319234ζ2315238ζ23122311231223112316237232023323222323182352314239231323102317236232123223192342315238    orthogonal faithful
ρ192200ζ2318235ζ23122311ζ2319234ζ2320233ζ23132310ζ2317236ζ232223ζ2315238ζ2316237ζ2314239ζ2321232ζ2321232ζ2318235ζ23122311ζ2319234ζ2320233ζ23132310ζ2317236ζ232223ζ2315238ζ2316237ζ2314239    orthogonal lifted from D23
ρ202200ζ2317236ζ2319234ζ2314239ζ232223ζ23122311ζ2321232ζ2315238ζ2318235ζ23132310ζ2320233ζ2316237ζ2316237ζ2317236ζ2319234ζ2314239ζ232223ζ23122311ζ2321232ζ2315238ζ2318235ζ23132310ζ2320233    orthogonal lifted from D23
ρ212200ζ2314239ζ2317236ζ2321232ζ23132310ζ2318235ζ2320233ζ23122311ζ2319234ζ2315238ζ2316237ζ232223ζ232223ζ2314239ζ2317236ζ2321232ζ23132310ζ2318235ζ2320233ζ23122311ζ2319234ζ2315238ζ2316237    orthogonal lifted from D23
ρ222200ζ23122311ζ2315238ζ2318235ζ2321232ζ232223ζ2319234ζ2316237ζ23132310ζ2320233ζ2317236ζ2314239ζ2314239ζ23122311ζ2315238ζ2318235ζ2321232ζ232223ζ2319234ζ2316237ζ23132310ζ2320233ζ2317236    orthogonal lifted from D23
ρ232-200ζ23122311ζ2315238ζ2318235ζ2321232ζ232223ζ2319234ζ2316237ζ23132310ζ2320233ζ2317236ζ2314239231423923122311231523823182352321232232223231923423162372313231023202332317236    orthogonal faithful
ρ242-200ζ23132310ζ232223ζ2315238ζ2317236ζ2320233ζ23122311ζ2321232ζ2316237ζ2314239ζ2318235ζ2319234231923423132310232223231523823172362320233231223112321232231623723142392318235    orthogonal faithful
ρ252200ζ2321232ζ2314239ζ2320233ζ2315238ζ2319234ζ2316237ζ2318235ζ2317236ζ23122311ζ232223ζ23132310ζ23132310ζ2321232ζ2314239ζ2320233ζ2315238ζ2319234ζ2316237ζ2318235ζ2317236ζ23122311ζ232223    orthogonal lifted from D23
ρ262200ζ232223ζ2316237ζ23132310ζ2319234ζ2321232ζ2315238ζ2314239ζ2320233ζ2317236ζ23122311ζ2318235ζ2318235ζ232223ζ2316237ζ23132310ζ2319234ζ2321232ζ2315238ζ2314239ζ2320233ζ2317236ζ23122311    orthogonal lifted from D23

Smallest permutation representation of D46
On 46 points
Generators in S46
(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)
(1 46)(2 45)(3 44)(4 43)(5 42)(6 41)(7 40)(8 39)(9 38)(10 37)(11 36)(12 35)(13 34)(14 33)(15 32)(16 31)(17 30)(18 29)(19 28)(20 27)(21 26)(22 25)(23 24)

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

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

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

D46 is a maximal subgroup of   D92  C23⋊D4
D46 is a maximal quotient of   Dic46  D92  C23⋊D4

Matrix representation of D46 in GL2(𝔽47) generated by

046
113
,
1327
4634
G:=sub<GL(2,GF(47))| [0,1,46,13],[13,46,27,34] >;

D46 in GAP, Magma, Sage, TeX

D_{46}
% in TeX

G:=Group("D46");
// GroupNames label

G:=SmallGroup(92,3);
// by ID

G=gap.SmallGroup(92,3);
# by ID

G:=PCGroup([3,-2,-2,-23,794]);
// Polycyclic

G:=Group<a,b|a^46=b^2=1,b*a*b=a^-1>;
// generators/relations

Export

Subgroup lattice of D46 in TeX
Character table of D46 in TeX

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