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G = C7×D29order 406 = 2·7·29

Direct product of C7 and D29

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

Aliases: C7×D29, C2032C2, C293C14, SmallGroup(406,4)

Series: Derived Chief Lower central Upper central

C1C29 — C7×D29
C1C29C203 — C7×D29
C29 — C7×D29
C1C7

Generators and relations for C7×D29
 G = < a,b,c | a7=b29=c2=1, ab=ba, ac=ca, cbc=b-1 >

29C2
29C14

Smallest permutation representation of C7×D29
On 203 points
Generators in S203
(1 188 153 121 88 66 46)(2 189 154 122 89 67 47)(3 190 155 123 90 68 48)(4 191 156 124 91 69 49)(5 192 157 125 92 70 50)(6 193 158 126 93 71 51)(7 194 159 127 94 72 52)(8 195 160 128 95 73 53)(9 196 161 129 96 74 54)(10 197 162 130 97 75 55)(11 198 163 131 98 76 56)(12 199 164 132 99 77 57)(13 200 165 133 100 78 58)(14 201 166 134 101 79 30)(15 202 167 135 102 80 31)(16 203 168 136 103 81 32)(17 175 169 137 104 82 33)(18 176 170 138 105 83 34)(19 177 171 139 106 84 35)(20 178 172 140 107 85 36)(21 179 173 141 108 86 37)(22 180 174 142 109 87 38)(23 181 146 143 110 59 39)(24 182 147 144 111 60 40)(25 183 148 145 112 61 41)(26 184 149 117 113 62 42)(27 185 150 118 114 63 43)(28 186 151 119 115 64 44)(29 187 152 120 116 65 45)
(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)(146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174)(175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203)
(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 32)(33 58)(34 57)(35 56)(36 55)(37 54)(38 53)(39 52)(40 51)(41 50)(42 49)(43 48)(44 47)(45 46)(59 72)(60 71)(61 70)(62 69)(63 68)(64 67)(65 66)(73 87)(74 86)(75 85)(76 84)(77 83)(78 82)(79 81)(88 116)(89 115)(90 114)(91 113)(92 112)(93 111)(94 110)(95 109)(96 108)(97 107)(98 106)(99 105)(100 104)(101 103)(117 124)(118 123)(119 122)(120 121)(125 145)(126 144)(127 143)(128 142)(129 141)(130 140)(131 139)(132 138)(133 137)(134 136)(146 159)(147 158)(148 157)(149 156)(150 155)(151 154)(152 153)(160 174)(161 173)(162 172)(163 171)(164 170)(165 169)(166 168)(175 200)(176 199)(177 198)(178 197)(179 196)(180 195)(181 194)(182 193)(183 192)(184 191)(185 190)(186 189)(187 188)(201 203)

G:=sub<Sym(203)| (1,188,153,121,88,66,46)(2,189,154,122,89,67,47)(3,190,155,123,90,68,48)(4,191,156,124,91,69,49)(5,192,157,125,92,70,50)(6,193,158,126,93,71,51)(7,194,159,127,94,72,52)(8,195,160,128,95,73,53)(9,196,161,129,96,74,54)(10,197,162,130,97,75,55)(11,198,163,131,98,76,56)(12,199,164,132,99,77,57)(13,200,165,133,100,78,58)(14,201,166,134,101,79,30)(15,202,167,135,102,80,31)(16,203,168,136,103,81,32)(17,175,169,137,104,82,33)(18,176,170,138,105,83,34)(19,177,171,139,106,84,35)(20,178,172,140,107,85,36)(21,179,173,141,108,86,37)(22,180,174,142,109,87,38)(23,181,146,143,110,59,39)(24,182,147,144,111,60,40)(25,183,148,145,112,61,41)(26,184,149,117,113,62,42)(27,185,150,118,114,63,43)(28,186,151,119,115,64,44)(29,187,152,120,116,65,45), (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)(146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174)(175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203), (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)(30,32)(33,58)(34,57)(35,56)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(45,46)(59,72)(60,71)(61,70)(62,69)(63,68)(64,67)(65,66)(73,87)(74,86)(75,85)(76,84)(77,83)(78,82)(79,81)(88,116)(89,115)(90,114)(91,113)(92,112)(93,111)(94,110)(95,109)(96,108)(97,107)(98,106)(99,105)(100,104)(101,103)(117,124)(118,123)(119,122)(120,121)(125,145)(126,144)(127,143)(128,142)(129,141)(130,140)(131,139)(132,138)(133,137)(134,136)(146,159)(147,158)(148,157)(149,156)(150,155)(151,154)(152,153)(160,174)(161,173)(162,172)(163,171)(164,170)(165,169)(166,168)(175,200)(176,199)(177,198)(178,197)(179,196)(180,195)(181,194)(182,193)(183,192)(184,191)(185,190)(186,189)(187,188)(201,203)>;

G:=Group( (1,188,153,121,88,66,46)(2,189,154,122,89,67,47)(3,190,155,123,90,68,48)(4,191,156,124,91,69,49)(5,192,157,125,92,70,50)(6,193,158,126,93,71,51)(7,194,159,127,94,72,52)(8,195,160,128,95,73,53)(9,196,161,129,96,74,54)(10,197,162,130,97,75,55)(11,198,163,131,98,76,56)(12,199,164,132,99,77,57)(13,200,165,133,100,78,58)(14,201,166,134,101,79,30)(15,202,167,135,102,80,31)(16,203,168,136,103,81,32)(17,175,169,137,104,82,33)(18,176,170,138,105,83,34)(19,177,171,139,106,84,35)(20,178,172,140,107,85,36)(21,179,173,141,108,86,37)(22,180,174,142,109,87,38)(23,181,146,143,110,59,39)(24,182,147,144,111,60,40)(25,183,148,145,112,61,41)(26,184,149,117,113,62,42)(27,185,150,118,114,63,43)(28,186,151,119,115,64,44)(29,187,152,120,116,65,45), (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)(146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174)(175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203), (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)(30,32)(33,58)(34,57)(35,56)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(45,46)(59,72)(60,71)(61,70)(62,69)(63,68)(64,67)(65,66)(73,87)(74,86)(75,85)(76,84)(77,83)(78,82)(79,81)(88,116)(89,115)(90,114)(91,113)(92,112)(93,111)(94,110)(95,109)(96,108)(97,107)(98,106)(99,105)(100,104)(101,103)(117,124)(118,123)(119,122)(120,121)(125,145)(126,144)(127,143)(128,142)(129,141)(130,140)(131,139)(132,138)(133,137)(134,136)(146,159)(147,158)(148,157)(149,156)(150,155)(151,154)(152,153)(160,174)(161,173)(162,172)(163,171)(164,170)(165,169)(166,168)(175,200)(176,199)(177,198)(178,197)(179,196)(180,195)(181,194)(182,193)(183,192)(184,191)(185,190)(186,189)(187,188)(201,203) );

G=PermutationGroup([(1,188,153,121,88,66,46),(2,189,154,122,89,67,47),(3,190,155,123,90,68,48),(4,191,156,124,91,69,49),(5,192,157,125,92,70,50),(6,193,158,126,93,71,51),(7,194,159,127,94,72,52),(8,195,160,128,95,73,53),(9,196,161,129,96,74,54),(10,197,162,130,97,75,55),(11,198,163,131,98,76,56),(12,199,164,132,99,77,57),(13,200,165,133,100,78,58),(14,201,166,134,101,79,30),(15,202,167,135,102,80,31),(16,203,168,136,103,81,32),(17,175,169,137,104,82,33),(18,176,170,138,105,83,34),(19,177,171,139,106,84,35),(20,178,172,140,107,85,36),(21,179,173,141,108,86,37),(22,180,174,142,109,87,38),(23,181,146,143,110,59,39),(24,182,147,144,111,60,40),(25,183,148,145,112,61,41),(26,184,149,117,113,62,42),(27,185,150,118,114,63,43),(28,186,151,119,115,64,44),(29,187,152,120,116,65,45)], [(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),(146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174),(175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203)], [(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),(30,32),(33,58),(34,57),(35,56),(36,55),(37,54),(38,53),(39,52),(40,51),(41,50),(42,49),(43,48),(44,47),(45,46),(59,72),(60,71),(61,70),(62,69),(63,68),(64,67),(65,66),(73,87),(74,86),(75,85),(76,84),(77,83),(78,82),(79,81),(88,116),(89,115),(90,114),(91,113),(92,112),(93,111),(94,110),(95,109),(96,108),(97,107),(98,106),(99,105),(100,104),(101,103),(117,124),(118,123),(119,122),(120,121),(125,145),(126,144),(127,143),(128,142),(129,141),(130,140),(131,139),(132,138),(133,137),(134,136),(146,159),(147,158),(148,157),(149,156),(150,155),(151,154),(152,153),(160,174),(161,173),(162,172),(163,171),(164,170),(165,169),(166,168),(175,200),(176,199),(177,198),(178,197),(179,196),(180,195),(181,194),(182,193),(183,192),(184,191),(185,190),(186,189),(187,188),(201,203)])

112 conjugacy classes

class 1  2 7A···7F14A···14F29A···29N203A···203CF
order127···714···1429···29203···203
size1291···129···292···22···2

112 irreducible representations

dim111122
type+++
imageC1C2C7C14D29C7×D29
kernelC7×D29C203D29C29C7C1
# reps11661484

Matrix representation of C7×D29 in GL2(𝔽2437) generated by

6450
0645
,
5831
24360
,
01
10
G:=sub<GL(2,GF(2437))| [645,0,0,645],[583,2436,1,0],[0,1,1,0] >;

C7×D29 in GAP, Magma, Sage, TeX

C_7\times D_{29}
% in TeX

G:=Group("C7xD29");
// GroupNames label

G:=SmallGroup(406,4);
// by ID

G=gap.SmallGroup(406,4);
# by ID

G:=PCGroup([3,-2,-7,-29,3530]);
// Polycyclic

G:=Group<a,b,c|a^7=b^29=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C7×D29 in TeX

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