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G = C5×D29order 290 = 2·5·29

Direct product of C5 and D29

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

Aliases: C5×D29, C29⋊C10, C1452C2, SmallGroup(290,2)

Series: Derived Chief Lower central Upper central

C1C29 — C5×D29
C1C29C145 — C5×D29
C29 — C5×D29
C1C5

Generators and relations for C5×D29
 G = < a,b,c | a5=b29=c2=1, ab=ba, ac=ca, cbc=b-1 >

29C2
29C10

Smallest permutation representation of C5×D29
On 145 points
Generators in S145
(1 130 114 79 34)(2 131 115 80 35)(3 132 116 81 36)(4 133 88 82 37)(5 134 89 83 38)(6 135 90 84 39)(7 136 91 85 40)(8 137 92 86 41)(9 138 93 87 42)(10 139 94 59 43)(11 140 95 60 44)(12 141 96 61 45)(13 142 97 62 46)(14 143 98 63 47)(15 144 99 64 48)(16 145 100 65 49)(17 117 101 66 50)(18 118 102 67 51)(19 119 103 68 52)(20 120 104 69 53)(21 121 105 70 54)(22 122 106 71 55)(23 123 107 72 56)(24 124 108 73 57)(25 125 109 74 58)(26 126 110 75 30)(27 127 111 76 31)(28 128 112 77 32)(29 129 113 78 33)
(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 29)(2 28)(3 27)(4 26)(5 25)(6 24)(7 23)(8 22)(9 21)(10 20)(11 19)(12 18)(13 17)(14 16)(30 37)(31 36)(32 35)(33 34)(38 58)(39 57)(40 56)(41 55)(42 54)(43 53)(44 52)(45 51)(46 50)(47 49)(59 69)(60 68)(61 67)(62 66)(63 65)(70 87)(71 86)(72 85)(73 84)(74 83)(75 82)(76 81)(77 80)(78 79)(88 110)(89 109)(90 108)(91 107)(92 106)(93 105)(94 104)(95 103)(96 102)(97 101)(98 100)(111 116)(112 115)(113 114)(117 142)(118 141)(119 140)(120 139)(121 138)(122 137)(123 136)(124 135)(125 134)(126 133)(127 132)(128 131)(129 130)(143 145)

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

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

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

80 conjugacy classes

class 1  2 5A5B5C5D10A10B10C10D29A···29N145A···145BD
order1255551010101029···29145···145
size1291111292929292···22···2

80 irreducible representations

dim111122
type+++
imageC1C2C5C10D29C5×D29
kernelC5×D29C145D29C29C5C1
# reps11441456

Matrix representation of C5×D29 in GL2(𝔽1451) generated by

5450
0545
,
01
1450127
,
01
10
G:=sub<GL(2,GF(1451))| [545,0,0,545],[0,1450,1,127],[0,1,1,0] >;

C5×D29 in GAP, Magma, Sage, TeX

C_5\times D_{29}
% in TeX

G:=Group("C5xD29");
// GroupNames label

G:=SmallGroup(290,2);
// by ID

G=gap.SmallGroup(290,2);
# by ID

G:=PCGroup([3,-2,-5,-29,2522]);
// Polycyclic

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

Export

Subgroup lattice of C5×D29 in TeX

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