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G = D5×C29order 290 = 2·5·29

Direct product of C29 and D5

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

Aliases: D5×C29, C5⋊C58, C1453C2, SmallGroup(290,1)

Series: Derived Chief Lower central Upper central

C1C5 — D5×C29
C1C5C145 — D5×C29
C5 — D5×C29
C1C29

Generators and relations for D5×C29
 G = < a,b,c | a29=b5=c2=1, ab=ba, ac=ca, cbc=b-1 >

5C2
5C58

Smallest permutation representation of D5×C29
On 145 points
Generators in S145
(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)(117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145)
(1 127 56 113 86)(2 128 57 114 87)(3 129 58 115 59)(4 130 30 116 60)(5 131 31 88 61)(6 132 32 89 62)(7 133 33 90 63)(8 134 34 91 64)(9 135 35 92 65)(10 136 36 93 66)(11 137 37 94 67)(12 138 38 95 68)(13 139 39 96 69)(14 140 40 97 70)(15 141 41 98 71)(16 142 42 99 72)(17 143 43 100 73)(18 144 44 101 74)(19 145 45 102 75)(20 117 46 103 76)(21 118 47 104 77)(22 119 48 105 78)(23 120 49 106 79)(24 121 50 107 80)(25 122 51 108 81)(26 123 52 109 82)(27 124 53 110 83)(28 125 54 111 84)(29 126 55 112 85)
(1 86)(2 87)(3 59)(4 60)(5 61)(6 62)(7 63)(8 64)(9 65)(10 66)(11 67)(12 68)(13 69)(14 70)(15 71)(16 72)(17 73)(18 74)(19 75)(20 76)(21 77)(22 78)(23 79)(24 80)(25 81)(26 82)(27 83)(28 84)(29 85)(88 131)(89 132)(90 133)(91 134)(92 135)(93 136)(94 137)(95 138)(96 139)(97 140)(98 141)(99 142)(100 143)(101 144)(102 145)(103 117)(104 118)(105 119)(106 120)(107 121)(108 122)(109 123)(110 124)(111 125)(112 126)(113 127)(114 128)(115 129)(116 130)

G:=sub<Sym(145)| (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)(117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145), (1,127,56,113,86)(2,128,57,114,87)(3,129,58,115,59)(4,130,30,116,60)(5,131,31,88,61)(6,132,32,89,62)(7,133,33,90,63)(8,134,34,91,64)(9,135,35,92,65)(10,136,36,93,66)(11,137,37,94,67)(12,138,38,95,68)(13,139,39,96,69)(14,140,40,97,70)(15,141,41,98,71)(16,142,42,99,72)(17,143,43,100,73)(18,144,44,101,74)(19,145,45,102,75)(20,117,46,103,76)(21,118,47,104,77)(22,119,48,105,78)(23,120,49,106,79)(24,121,50,107,80)(25,122,51,108,81)(26,123,52,109,82)(27,124,53,110,83)(28,125,54,111,84)(29,126,55,112,85), (1,86)(2,87)(3,59)(4,60)(5,61)(6,62)(7,63)(8,64)(9,65)(10,66)(11,67)(12,68)(13,69)(14,70)(15,71)(16,72)(17,73)(18,74)(19,75)(20,76)(21,77)(22,78)(23,79)(24,80)(25,81)(26,82)(27,83)(28,84)(29,85)(88,131)(89,132)(90,133)(91,134)(92,135)(93,136)(94,137)(95,138)(96,139)(97,140)(98,141)(99,142)(100,143)(101,144)(102,145)(103,117)(104,118)(105,119)(106,120)(107,121)(108,122)(109,123)(110,124)(111,125)(112,126)(113,127)(114,128)(115,129)(116,130)>;

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)(117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145), (1,127,56,113,86)(2,128,57,114,87)(3,129,58,115,59)(4,130,30,116,60)(5,131,31,88,61)(6,132,32,89,62)(7,133,33,90,63)(8,134,34,91,64)(9,135,35,92,65)(10,136,36,93,66)(11,137,37,94,67)(12,138,38,95,68)(13,139,39,96,69)(14,140,40,97,70)(15,141,41,98,71)(16,142,42,99,72)(17,143,43,100,73)(18,144,44,101,74)(19,145,45,102,75)(20,117,46,103,76)(21,118,47,104,77)(22,119,48,105,78)(23,120,49,106,79)(24,121,50,107,80)(25,122,51,108,81)(26,123,52,109,82)(27,124,53,110,83)(28,125,54,111,84)(29,126,55,112,85), (1,86)(2,87)(3,59)(4,60)(5,61)(6,62)(7,63)(8,64)(9,65)(10,66)(11,67)(12,68)(13,69)(14,70)(15,71)(16,72)(17,73)(18,74)(19,75)(20,76)(21,77)(22,78)(23,79)(24,80)(25,81)(26,82)(27,83)(28,84)(29,85)(88,131)(89,132)(90,133)(91,134)(92,135)(93,136)(94,137)(95,138)(96,139)(97,140)(98,141)(99,142)(100,143)(101,144)(102,145)(103,117)(104,118)(105,119)(106,120)(107,121)(108,122)(109,123)(110,124)(111,125)(112,126)(113,127)(114,128)(115,129)(116,130) );

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),(117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145)], [(1,127,56,113,86),(2,128,57,114,87),(3,129,58,115,59),(4,130,30,116,60),(5,131,31,88,61),(6,132,32,89,62),(7,133,33,90,63),(8,134,34,91,64),(9,135,35,92,65),(10,136,36,93,66),(11,137,37,94,67),(12,138,38,95,68),(13,139,39,96,69),(14,140,40,97,70),(15,141,41,98,71),(16,142,42,99,72),(17,143,43,100,73),(18,144,44,101,74),(19,145,45,102,75),(20,117,46,103,76),(21,118,47,104,77),(22,119,48,105,78),(23,120,49,106,79),(24,121,50,107,80),(25,122,51,108,81),(26,123,52,109,82),(27,124,53,110,83),(28,125,54,111,84),(29,126,55,112,85)], [(1,86),(2,87),(3,59),(4,60),(5,61),(6,62),(7,63),(8,64),(9,65),(10,66),(11,67),(12,68),(13,69),(14,70),(15,71),(16,72),(17,73),(18,74),(19,75),(20,76),(21,77),(22,78),(23,79),(24,80),(25,81),(26,82),(27,83),(28,84),(29,85),(88,131),(89,132),(90,133),(91,134),(92,135),(93,136),(94,137),(95,138),(96,139),(97,140),(98,141),(99,142),(100,143),(101,144),(102,145),(103,117),(104,118),(105,119),(106,120),(107,121),(108,122),(109,123),(110,124),(111,125),(112,126),(113,127),(114,128),(115,129),(116,130)])

116 conjugacy classes

class 1  2 5A5B29A···29AB58A···58AB145A···145BD
order125529···2958···58145···145
size15221···15···52···2

116 irreducible representations

dim111122
type+++
imageC1C2C29C58D5D5×C29
kernelD5×C29C145D5C5C29C1
# reps112828256

Matrix representation of D5×C29 in GL2(𝔽1451) generated by

6860
0686
,
11691170
14501450
,
1450281
01
G:=sub<GL(2,GF(1451))| [686,0,0,686],[1169,1450,1170,1450],[1450,0,281,1] >;

D5×C29 in GAP, Magma, Sage, TeX

D_5\times C_{29}
% in TeX

G:=Group("D5xC29");
// GroupNames label

G:=SmallGroup(290,1);
// by ID

G=gap.SmallGroup(290,1);
# by ID

G:=PCGroup([3,-2,-29,-5,2090]);
// Polycyclic

G:=Group<a,b,c|a^29=b^5=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of D5×C29 in TeX

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