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G = Dic29order 116 = 22·29

Dicyclic group

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

Aliases: Dic29, C292C4, C58.C2, C2.D29, SmallGroup(116,1)

Series: Derived Chief Lower central Upper central

C1C29 — Dic29
C1C29C58 — Dic29
C29 — Dic29
C1C2

Generators and relations for Dic29
 G = < a,b | a58=1, b2=a29, bab-1=a-1 >

29C4

Smallest permutation representation of Dic29
Regular action on 116 points
Generators in S116
(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 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116)
(1 70 30 99)(2 69 31 98)(3 68 32 97)(4 67 33 96)(5 66 34 95)(6 65 35 94)(7 64 36 93)(8 63 37 92)(9 62 38 91)(10 61 39 90)(11 60 40 89)(12 59 41 88)(13 116 42 87)(14 115 43 86)(15 114 44 85)(16 113 45 84)(17 112 46 83)(18 111 47 82)(19 110 48 81)(20 109 49 80)(21 108 50 79)(22 107 51 78)(23 106 52 77)(24 105 53 76)(25 104 54 75)(26 103 55 74)(27 102 56 73)(28 101 57 72)(29 100 58 71)

G:=sub<Sym(116)| (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)(59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116), (1,70,30,99)(2,69,31,98)(3,68,32,97)(4,67,33,96)(5,66,34,95)(6,65,35,94)(7,64,36,93)(8,63,37,92)(9,62,38,91)(10,61,39,90)(11,60,40,89)(12,59,41,88)(13,116,42,87)(14,115,43,86)(15,114,44,85)(16,113,45,84)(17,112,46,83)(18,111,47,82)(19,110,48,81)(20,109,49,80)(21,108,50,79)(22,107,51,78)(23,106,52,77)(24,105,53,76)(25,104,54,75)(26,103,55,74)(27,102,56,73)(28,101,57,72)(29,100,58,71)>;

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)(59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116), (1,70,30,99)(2,69,31,98)(3,68,32,97)(4,67,33,96)(5,66,34,95)(6,65,35,94)(7,64,36,93)(8,63,37,92)(9,62,38,91)(10,61,39,90)(11,60,40,89)(12,59,41,88)(13,116,42,87)(14,115,43,86)(15,114,44,85)(16,113,45,84)(17,112,46,83)(18,111,47,82)(19,110,48,81)(20,109,49,80)(21,108,50,79)(22,107,51,78)(23,106,52,77)(24,105,53,76)(25,104,54,75)(26,103,55,74)(27,102,56,73)(28,101,57,72)(29,100,58,71) );

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),(59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116)], [(1,70,30,99),(2,69,31,98),(3,68,32,97),(4,67,33,96),(5,66,34,95),(6,65,35,94),(7,64,36,93),(8,63,37,92),(9,62,38,91),(10,61,39,90),(11,60,40,89),(12,59,41,88),(13,116,42,87),(14,115,43,86),(15,114,44,85),(16,113,45,84),(17,112,46,83),(18,111,47,82),(19,110,48,81),(20,109,49,80),(21,108,50,79),(22,107,51,78),(23,106,52,77),(24,105,53,76),(25,104,54,75),(26,103,55,74),(27,102,56,73),(28,101,57,72),(29,100,58,71)])

Dic29 is a maximal subgroup of   C29⋊C8  Dic58  C4×D29  C29⋊D4  Dic87
Dic29 is a maximal quotient of   C292C8  Dic87

32 conjugacy classes

class 1  2 4A4B29A···29N58A···58N
order124429···2958···58
size1129292···22···2

32 irreducible representations

dim11122
type+++-
imageC1C2C4D29Dic29
kernelDic29C58C29C2C1
# reps1121414

Matrix representation of Dic29 in GL3(𝔽233) generated by

23200
028232
010
,
8900
022529
0388
G:=sub<GL(3,GF(233))| [232,0,0,0,28,1,0,232,0],[89,0,0,0,225,38,0,29,8] >;

Dic29 in GAP, Magma, Sage, TeX

{\rm Dic}_{29}
% in TeX

G:=Group("Dic29");
// GroupNames label

G:=SmallGroup(116,1);
// by ID

G=gap.SmallGroup(116,1);
# by ID

G:=PCGroup([3,-2,-2,-29,6,1010]);
// Polycyclic

G:=Group<a,b|a^58=1,b^2=a^29,b*a*b^-1=a^-1>;
// generators/relations

Export

Subgroup lattice of Dic29 in TeX

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