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G = D7×C29order 406 = 2·7·29

Direct product of C29 and D7

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

Aliases: D7×C29, C7⋊C58, C2033C2, SmallGroup(406,3)

Series: Derived Chief Lower central Upper central

C1C7 — D7×C29
C1C7C203 — D7×C29
C7 — D7×C29
C1C29

Generators and relations for D7×C29
 G = < a,b,c | a29=b7=c2=1, ab=ba, ac=ca, cbc=b-1 >

7C2
7C58

Smallest permutation representation of D7×C29
On 203 points
Generators in S203
(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 39 99 128 85 166 179)(2 40 100 129 86 167 180)(3 41 101 130 87 168 181)(4 42 102 131 59 169 182)(5 43 103 132 60 170 183)(6 44 104 133 61 171 184)(7 45 105 134 62 172 185)(8 46 106 135 63 173 186)(9 47 107 136 64 174 187)(10 48 108 137 65 146 188)(11 49 109 138 66 147 189)(12 50 110 139 67 148 190)(13 51 111 140 68 149 191)(14 52 112 141 69 150 192)(15 53 113 142 70 151 193)(16 54 114 143 71 152 194)(17 55 115 144 72 153 195)(18 56 116 145 73 154 196)(19 57 88 117 74 155 197)(20 58 89 118 75 156 198)(21 30 90 119 76 157 199)(22 31 91 120 77 158 200)(23 32 92 121 78 159 201)(24 33 93 122 79 160 202)(25 34 94 123 80 161 203)(26 35 95 124 81 162 175)(27 36 96 125 82 163 176)(28 37 97 126 83 164 177)(29 38 98 127 84 165 178)
(1 179)(2 180)(3 181)(4 182)(5 183)(6 184)(7 185)(8 186)(9 187)(10 188)(11 189)(12 190)(13 191)(14 192)(15 193)(16 194)(17 195)(18 196)(19 197)(20 198)(21 199)(22 200)(23 201)(24 202)(25 203)(26 175)(27 176)(28 177)(29 178)(30 157)(31 158)(32 159)(33 160)(34 161)(35 162)(36 163)(37 164)(38 165)(39 166)(40 167)(41 168)(42 169)(43 170)(44 171)(45 172)(46 173)(47 174)(48 146)(49 147)(50 148)(51 149)(52 150)(53 151)(54 152)(55 153)(56 154)(57 155)(58 156)(59 102)(60 103)(61 104)(62 105)(63 106)(64 107)(65 108)(66 109)(67 110)(68 111)(69 112)(70 113)(71 114)(72 115)(73 116)(74 88)(75 89)(76 90)(77 91)(78 92)(79 93)(80 94)(81 95)(82 96)(83 97)(84 98)(85 99)(86 100)(87 101)

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

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

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

145 conjugacy classes

class 1  2 7A7B7C29A···29AB58A···58AB203A···203CF
order1277729···2958···58203···203
size172221···17···72···2

145 irreducible representations

dim111122
type+++
imageC1C2C29C58D7D7×C29
kernelD7×C29C203D7C7C29C1
# reps112828384

Matrix representation of D7×C29 in GL2(𝔽2437) generated by

17030
01703
,
9901
20111415
,
14152405
4261022
G:=sub<GL(2,GF(2437))| [1703,0,0,1703],[990,2011,1,1415],[1415,426,2405,1022] >;

D7×C29 in GAP, Magma, Sage, TeX

D_7\times C_{29}
% in TeX

G:=Group("D7xC29");
// GroupNames label

G:=SmallGroup(406,3);
// by ID

G=gap.SmallGroup(406,3);
# by ID

G:=PCGroup([3,-2,-29,-7,3134]);
// Polycyclic

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

Export

Subgroup lattice of D7×C29 in TeX

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