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G = Dic23order 92 = 22·23

Dicyclic group

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

Aliases: Dic23, C23⋊C4, C46.C2, C2.D23, SmallGroup(92,1)

Series: Derived Chief Lower central Upper central

C1C23 — Dic23
C1C23C46 — Dic23
C23 — Dic23
C1C2

Generators and relations for Dic23
 G = < a,b | a46=1, b2=a23, bab-1=a-1 >

23C4

Character table of Dic23

 class 124A4B23A23B23C23D23E23F23G23H23I23J23K46A46B46C46D46E46F46G46H46I46J46K
 size 1123232222222222222222222222
ρ111111111111111111111111111    trivial
ρ211-1-11111111111111111111111    linear of order 2
ρ31-1i-i11111111111-1-1-1-1-1-1-1-1-1-1-1    linear of order 4
ρ41-1-ii11111111111-1-1-1-1-1-1-1-1-1-1-1    linear of order 4
ρ52200ζ2315238ζ23132310ζ23122311ζ2314239ζ2316237ζ2318235ζ2320233ζ232223ζ2321232ζ2319234ζ2317236ζ2317236ζ2315238ζ23132310ζ23122311ζ2314239ζ2316237ζ2318235ζ2320233ζ232223ζ2321232ζ2319234    orthogonal lifted from D23
ρ62200ζ2319234ζ2318235ζ2317236ζ2316237ζ2315238ζ2314239ζ23132310ζ23122311ζ232223ζ2321232ζ2320233ζ2320233ζ2319234ζ2318235ζ2317236ζ2316237ζ2315238ζ2314239ζ23132310ζ23122311ζ232223ζ2321232    orthogonal lifted from D23
ρ72200ζ2316237ζ2320233ζ232223ζ2318235ζ2314239ζ23132310ζ2317236ζ2321232ζ2319234ζ2315238ζ23122311ζ23122311ζ2316237ζ2320233ζ232223ζ2318235ζ2314239ζ23132310ζ2317236ζ2321232ζ2319234ζ2315238    orthogonal lifted from D23
ρ82200ζ2317236ζ2319234ζ2314239ζ232223ζ23122311ζ2321232ζ2315238ζ2318235ζ23132310ζ2320233ζ2316237ζ2316237ζ2317236ζ2319234ζ2314239ζ232223ζ23122311ζ2321232ζ2315238ζ2318235ζ23132310ζ2320233    orthogonal lifted from D23
ρ92200ζ23132310ζ232223ζ2315238ζ2317236ζ2320233ζ23122311ζ2321232ζ2316237ζ2314239ζ2318235ζ2319234ζ2319234ζ23132310ζ232223ζ2315238ζ2317236ζ2320233ζ23122311ζ2321232ζ2316237ζ2314239ζ2318235    orthogonal lifted from D23
ρ102200ζ2320233ζ2321232ζ2316237ζ23122311ζ2317236ζ232223ζ2319234ζ2314239ζ2318235ζ23132310ζ2315238ζ2315238ζ2320233ζ2321232ζ2316237ζ23122311ζ2317236ζ232223ζ2319234ζ2314239ζ2318235ζ23132310    orthogonal lifted from D23
ρ112200ζ2318235ζ23122311ζ2319234ζ2320233ζ23132310ζ2317236ζ232223ζ2315238ζ2316237ζ2314239ζ2321232ζ2321232ζ2318235ζ23122311ζ2319234ζ2320233ζ23132310ζ2317236ζ232223ζ2315238ζ2316237ζ2314239    orthogonal lifted from D23
ρ122200ζ2314239ζ2317236ζ2321232ζ23132310ζ2318235ζ2320233ζ23122311ζ2319234ζ2315238ζ2316237ζ232223ζ232223ζ2314239ζ2317236ζ2321232ζ23132310ζ2318235ζ2320233ζ23122311ζ2319234ζ2315238ζ2316237    orthogonal lifted from D23
ρ132200ζ23122311ζ2315238ζ2318235ζ2321232ζ232223ζ2319234ζ2316237ζ23132310ζ2320233ζ2317236ζ2314239ζ2314239ζ23122311ζ2315238ζ2318235ζ2321232ζ232223ζ2319234ζ2316237ζ23132310ζ2320233ζ2317236    orthogonal lifted from D23
ρ142200ζ2321232ζ2314239ζ2320233ζ2315238ζ2319234ζ2316237ζ2318235ζ2317236ζ23122311ζ232223ζ23132310ζ23132310ζ2321232ζ2314239ζ2320233ζ2315238ζ2319234ζ2316237ζ2318235ζ2317236ζ23122311ζ232223    orthogonal lifted from D23
ρ152200ζ232223ζ2316237ζ23132310ζ2319234ζ2321232ζ2315238ζ2314239ζ2320233ζ2317236ζ23122311ζ2318235ζ2318235ζ232223ζ2316237ζ23132310ζ2319234ζ2321232ζ2315238ζ2314239ζ2320233ζ2317236ζ23122311    orthogonal lifted from D23
ρ162-200ζ2321232ζ2314239ζ2320233ζ2315238ζ2319234ζ2316237ζ2318235ζ2317236ζ23122311ζ232223ζ23132310231323102321232231423923202332315238231923423162372318235231723623122311232223    symplectic faithful, Schur index 2
ρ172-200ζ2320233ζ2321232ζ2316237ζ23122311ζ2317236ζ232223ζ2319234ζ2314239ζ2318235ζ23132310ζ2315238231523823202332321232231623723122311231723623222323192342314239231823523132310    symplectic faithful, Schur index 2
ρ182-200ζ2315238ζ23132310ζ23122311ζ2314239ζ2316237ζ2318235ζ2320233ζ232223ζ2321232ζ2319234ζ2317236231723623152382313231023122311231423923162372318235232023323222323212322319234    symplectic faithful, Schur index 2
ρ192-200ζ2318235ζ23122311ζ2319234ζ2320233ζ23132310ζ2317236ζ232223ζ2315238ζ2316237ζ2314239ζ2321232232123223182352312231123192342320233231323102317236232223231523823162372314239    symplectic faithful, Schur index 2
ρ202-200ζ2319234ζ2318235ζ2317236ζ2316237ζ2315238ζ2314239ζ23132310ζ23122311ζ232223ζ2321232ζ2320233232023323192342318235231723623162372315238231423923132310231223112322232321232    symplectic faithful, Schur index 2
ρ212-200ζ2314239ζ2317236ζ2321232ζ23132310ζ2318235ζ2320233ζ23122311ζ2319234ζ2315238ζ2316237ζ232223232223231423923172362321232231323102318235232023323122311231923423152382316237    symplectic faithful, Schur index 2
ρ222-200ζ232223ζ2316237ζ23132310ζ2319234ζ2321232ζ2315238ζ2314239ζ2320233ζ2317236ζ23122311ζ2318235231823523222323162372313231023192342321232231523823142392320233231723623122311    symplectic faithful, Schur index 2
ρ232-200ζ23122311ζ2315238ζ2318235ζ2321232ζ232223ζ2319234ζ2316237ζ23132310ζ2320233ζ2317236ζ2314239231423923122311231523823182352321232232223231923423162372313231023202332317236    symplectic faithful, Schur index 2
ρ242-200ζ23132310ζ232223ζ2315238ζ2317236ζ2320233ζ23122311ζ2321232ζ2316237ζ2314239ζ2318235ζ2319234231923423132310232223231523823172362320233231223112321232231623723142392318235    symplectic faithful, Schur index 2
ρ252-200ζ2317236ζ2319234ζ2314239ζ232223ζ23122311ζ2321232ζ2315238ζ2318235ζ23132310ζ2320233ζ2316237231623723172362319234231423923222323122311232123223152382318235231323102320233    symplectic faithful, Schur index 2
ρ262-200ζ2316237ζ2320233ζ232223ζ2318235ζ2314239ζ23132310ζ2317236ζ2321232ζ2319234ζ2315238ζ23122311231223112316237232023323222323182352314239231323102317236232123223192342315238    symplectic faithful, Schur index 2

Smallest permutation representation of Dic23
Regular action on 92 points
Generators in S92
(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 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92)
(1 81 24 58)(2 80 25 57)(3 79 26 56)(4 78 27 55)(5 77 28 54)(6 76 29 53)(7 75 30 52)(8 74 31 51)(9 73 32 50)(10 72 33 49)(11 71 34 48)(12 70 35 47)(13 69 36 92)(14 68 37 91)(15 67 38 90)(16 66 39 89)(17 65 40 88)(18 64 41 87)(19 63 42 86)(20 62 43 85)(21 61 44 84)(22 60 45 83)(23 59 46 82)

G:=sub<Sym(92)| (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)(47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92), (1,81,24,58)(2,80,25,57)(3,79,26,56)(4,78,27,55)(5,77,28,54)(6,76,29,53)(7,75,30,52)(8,74,31,51)(9,73,32,50)(10,72,33,49)(11,71,34,48)(12,70,35,47)(13,69,36,92)(14,68,37,91)(15,67,38,90)(16,66,39,89)(17,65,40,88)(18,64,41,87)(19,63,42,86)(20,62,43,85)(21,61,44,84)(22,60,45,83)(23,59,46,82)>;

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)(47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92), (1,81,24,58)(2,80,25,57)(3,79,26,56)(4,78,27,55)(5,77,28,54)(6,76,29,53)(7,75,30,52)(8,74,31,51)(9,73,32,50)(10,72,33,49)(11,71,34,48)(12,70,35,47)(13,69,36,92)(14,68,37,91)(15,67,38,90)(16,66,39,89)(17,65,40,88)(18,64,41,87)(19,63,42,86)(20,62,43,85)(21,61,44,84)(22,60,45,83)(23,59,46,82) );

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),(47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92)], [(1,81,24,58),(2,80,25,57),(3,79,26,56),(4,78,27,55),(5,77,28,54),(6,76,29,53),(7,75,30,52),(8,74,31,51),(9,73,32,50),(10,72,33,49),(11,71,34,48),(12,70,35,47),(13,69,36,92),(14,68,37,91),(15,67,38,90),(16,66,39,89),(17,65,40,88),(18,64,41,87),(19,63,42,86),(20,62,43,85),(21,61,44,84),(22,60,45,83),(23,59,46,82)])

Dic23 is a maximal subgroup of   Dic46  C4×D23  C23⋊D4  Dic69  Dic115  C23⋊F5
Dic23 is a maximal quotient of   C23⋊C8  Dic69  Dic115  C23⋊F5

Matrix representation of Dic23 in GL2(𝔽47) generated by

4130
171
,
3117
716
G:=sub<GL(2,GF(47))| [41,17,30,1],[31,7,17,16] >;

Dic23 in GAP, Magma, Sage, TeX

{\rm Dic}_{23}
% in TeX

G:=Group("Dic23");
// GroupNames label

G:=SmallGroup(92,1);
// by ID

G=gap.SmallGroup(92,1);
# by ID

G:=PCGroup([3,-2,-2,-23,6,794]);
// Polycyclic

G:=Group<a,b|a^46=1,b^2=a^23,b*a*b^-1=a^-1>;
// generators/relations

Export

Subgroup lattice of Dic23 in TeX
Character table of Dic23 in TeX

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