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G = D8×C29order 464 = 24·29

Direct product of C29 and D8

direct product, metacyclic, nilpotent (class 3), monomial, 2-elementary

Aliases: D8×C29, D4⋊C58, C81C58, C2325C2, C58.14D4, C116.17C22, (D4×C29)⋊4C2, C4.1(C2×C58), C2.3(D4×C29), SmallGroup(464,25)

Series: Derived Chief Lower central Upper central

C1C4 — D8×C29
C1C2C4C116D4×C29 — D8×C29
C1C2C4 — D8×C29
C1C58C116 — D8×C29

Generators and relations for D8×C29
 G = < a,b,c | a29=b8=c2=1, ab=ba, ac=ca, cbc=b-1 >

4C2
4C2
2C22
2C22
4C58
4C58
2C2×C58
2C2×C58

Smallest permutation representation of D8×C29
On 232 points
Generators in S232
(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)(204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232)
(1 112 40 230 71 199 135 165)(2 113 41 231 72 200 136 166)(3 114 42 232 73 201 137 167)(4 115 43 204 74 202 138 168)(5 116 44 205 75 203 139 169)(6 88 45 206 76 175 140 170)(7 89 46 207 77 176 141 171)(8 90 47 208 78 177 142 172)(9 91 48 209 79 178 143 173)(10 92 49 210 80 179 144 174)(11 93 50 211 81 180 145 146)(12 94 51 212 82 181 117 147)(13 95 52 213 83 182 118 148)(14 96 53 214 84 183 119 149)(15 97 54 215 85 184 120 150)(16 98 55 216 86 185 121 151)(17 99 56 217 87 186 122 152)(18 100 57 218 59 187 123 153)(19 101 58 219 60 188 124 154)(20 102 30 220 61 189 125 155)(21 103 31 221 62 190 126 156)(22 104 32 222 63 191 127 157)(23 105 33 223 64 192 128 158)(24 106 34 224 65 193 129 159)(25 107 35 225 66 194 130 160)(26 108 36 226 67 195 131 161)(27 109 37 227 68 196 132 162)(28 110 38 228 69 197 133 163)(29 111 39 229 70 198 134 164)
(30 125)(31 126)(32 127)(33 128)(34 129)(35 130)(36 131)(37 132)(38 133)(39 134)(40 135)(41 136)(42 137)(43 138)(44 139)(45 140)(46 141)(47 142)(48 143)(49 144)(50 145)(51 117)(52 118)(53 119)(54 120)(55 121)(56 122)(57 123)(58 124)(88 170)(89 171)(90 172)(91 173)(92 174)(93 146)(94 147)(95 148)(96 149)(97 150)(98 151)(99 152)(100 153)(101 154)(102 155)(103 156)(104 157)(105 158)(106 159)(107 160)(108 161)(109 162)(110 163)(111 164)(112 165)(113 166)(114 167)(115 168)(116 169)(175 206)(176 207)(177 208)(178 209)(179 210)(180 211)(181 212)(182 213)(183 214)(184 215)(185 216)(186 217)(187 218)(188 219)(189 220)(190 221)(191 222)(192 223)(193 224)(194 225)(195 226)(196 227)(197 228)(198 229)(199 230)(200 231)(201 232)(202 204)(203 205)

G:=sub<Sym(232)| (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)(204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232), (1,112,40,230,71,199,135,165)(2,113,41,231,72,200,136,166)(3,114,42,232,73,201,137,167)(4,115,43,204,74,202,138,168)(5,116,44,205,75,203,139,169)(6,88,45,206,76,175,140,170)(7,89,46,207,77,176,141,171)(8,90,47,208,78,177,142,172)(9,91,48,209,79,178,143,173)(10,92,49,210,80,179,144,174)(11,93,50,211,81,180,145,146)(12,94,51,212,82,181,117,147)(13,95,52,213,83,182,118,148)(14,96,53,214,84,183,119,149)(15,97,54,215,85,184,120,150)(16,98,55,216,86,185,121,151)(17,99,56,217,87,186,122,152)(18,100,57,218,59,187,123,153)(19,101,58,219,60,188,124,154)(20,102,30,220,61,189,125,155)(21,103,31,221,62,190,126,156)(22,104,32,222,63,191,127,157)(23,105,33,223,64,192,128,158)(24,106,34,224,65,193,129,159)(25,107,35,225,66,194,130,160)(26,108,36,226,67,195,131,161)(27,109,37,227,68,196,132,162)(28,110,38,228,69,197,133,163)(29,111,39,229,70,198,134,164), (30,125)(31,126)(32,127)(33,128)(34,129)(35,130)(36,131)(37,132)(38,133)(39,134)(40,135)(41,136)(42,137)(43,138)(44,139)(45,140)(46,141)(47,142)(48,143)(49,144)(50,145)(51,117)(52,118)(53,119)(54,120)(55,121)(56,122)(57,123)(58,124)(88,170)(89,171)(90,172)(91,173)(92,174)(93,146)(94,147)(95,148)(96,149)(97,150)(98,151)(99,152)(100,153)(101,154)(102,155)(103,156)(104,157)(105,158)(106,159)(107,160)(108,161)(109,162)(110,163)(111,164)(112,165)(113,166)(114,167)(115,168)(116,169)(175,206)(176,207)(177,208)(178,209)(179,210)(180,211)(181,212)(182,213)(183,214)(184,215)(185,216)(186,217)(187,218)(188,219)(189,220)(190,221)(191,222)(192,223)(193,224)(194,225)(195,226)(196,227)(197,228)(198,229)(199,230)(200,231)(201,232)(202,204)(203,205)>;

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)(204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232), (1,112,40,230,71,199,135,165)(2,113,41,231,72,200,136,166)(3,114,42,232,73,201,137,167)(4,115,43,204,74,202,138,168)(5,116,44,205,75,203,139,169)(6,88,45,206,76,175,140,170)(7,89,46,207,77,176,141,171)(8,90,47,208,78,177,142,172)(9,91,48,209,79,178,143,173)(10,92,49,210,80,179,144,174)(11,93,50,211,81,180,145,146)(12,94,51,212,82,181,117,147)(13,95,52,213,83,182,118,148)(14,96,53,214,84,183,119,149)(15,97,54,215,85,184,120,150)(16,98,55,216,86,185,121,151)(17,99,56,217,87,186,122,152)(18,100,57,218,59,187,123,153)(19,101,58,219,60,188,124,154)(20,102,30,220,61,189,125,155)(21,103,31,221,62,190,126,156)(22,104,32,222,63,191,127,157)(23,105,33,223,64,192,128,158)(24,106,34,224,65,193,129,159)(25,107,35,225,66,194,130,160)(26,108,36,226,67,195,131,161)(27,109,37,227,68,196,132,162)(28,110,38,228,69,197,133,163)(29,111,39,229,70,198,134,164), (30,125)(31,126)(32,127)(33,128)(34,129)(35,130)(36,131)(37,132)(38,133)(39,134)(40,135)(41,136)(42,137)(43,138)(44,139)(45,140)(46,141)(47,142)(48,143)(49,144)(50,145)(51,117)(52,118)(53,119)(54,120)(55,121)(56,122)(57,123)(58,124)(88,170)(89,171)(90,172)(91,173)(92,174)(93,146)(94,147)(95,148)(96,149)(97,150)(98,151)(99,152)(100,153)(101,154)(102,155)(103,156)(104,157)(105,158)(106,159)(107,160)(108,161)(109,162)(110,163)(111,164)(112,165)(113,166)(114,167)(115,168)(116,169)(175,206)(176,207)(177,208)(178,209)(179,210)(180,211)(181,212)(182,213)(183,214)(184,215)(185,216)(186,217)(187,218)(188,219)(189,220)(190,221)(191,222)(192,223)(193,224)(194,225)(195,226)(196,227)(197,228)(198,229)(199,230)(200,231)(201,232)(202,204)(203,205) );

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),(204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232)], [(1,112,40,230,71,199,135,165),(2,113,41,231,72,200,136,166),(3,114,42,232,73,201,137,167),(4,115,43,204,74,202,138,168),(5,116,44,205,75,203,139,169),(6,88,45,206,76,175,140,170),(7,89,46,207,77,176,141,171),(8,90,47,208,78,177,142,172),(9,91,48,209,79,178,143,173),(10,92,49,210,80,179,144,174),(11,93,50,211,81,180,145,146),(12,94,51,212,82,181,117,147),(13,95,52,213,83,182,118,148),(14,96,53,214,84,183,119,149),(15,97,54,215,85,184,120,150),(16,98,55,216,86,185,121,151),(17,99,56,217,87,186,122,152),(18,100,57,218,59,187,123,153),(19,101,58,219,60,188,124,154),(20,102,30,220,61,189,125,155),(21,103,31,221,62,190,126,156),(22,104,32,222,63,191,127,157),(23,105,33,223,64,192,128,158),(24,106,34,224,65,193,129,159),(25,107,35,225,66,194,130,160),(26,108,36,226,67,195,131,161),(27,109,37,227,68,196,132,162),(28,110,38,228,69,197,133,163),(29,111,39,229,70,198,134,164)], [(30,125),(31,126),(32,127),(33,128),(34,129),(35,130),(36,131),(37,132),(38,133),(39,134),(40,135),(41,136),(42,137),(43,138),(44,139),(45,140),(46,141),(47,142),(48,143),(49,144),(50,145),(51,117),(52,118),(53,119),(54,120),(55,121),(56,122),(57,123),(58,124),(88,170),(89,171),(90,172),(91,173),(92,174),(93,146),(94,147),(95,148),(96,149),(97,150),(98,151),(99,152),(100,153),(101,154),(102,155),(103,156),(104,157),(105,158),(106,159),(107,160),(108,161),(109,162),(110,163),(111,164),(112,165),(113,166),(114,167),(115,168),(116,169),(175,206),(176,207),(177,208),(178,209),(179,210),(180,211),(181,212),(182,213),(183,214),(184,215),(185,216),(186,217),(187,218),(188,219),(189,220),(190,221),(191,222),(192,223),(193,224),(194,225),(195,226),(196,227),(197,228),(198,229),(199,230),(200,231),(201,232),(202,204),(203,205)])

203 conjugacy classes

class 1 2A2B2C 4 8A8B29A···29AB58A···58AB58AC···58CF116A···116AB232A···232BD
order122248829···2958···5858···58116···116232···232
size11442221···11···14···42···22···2

203 irreducible representations

dim1111112222
type+++++
imageC1C2C2C29C58C58D4D8D4×C29D8×C29
kernelD8×C29C232D4×C29D8C8D4C58C29C2C1
# reps112282856122856

Matrix representation of D8×C29 in GL2(𝔽233) generated by

1020
0102
,
15974
159159
,
10
0232
G:=sub<GL(2,GF(233))| [102,0,0,102],[159,159,74,159],[1,0,0,232] >;

D8×C29 in GAP, Magma, Sage, TeX

D_8\times C_{29}
% in TeX

G:=Group("D8xC29");
// GroupNames label

G:=SmallGroup(464,25);
// by ID

G=gap.SmallGroup(464,25);
# by ID

G:=PCGroup([5,-2,-2,-29,-2,-2,1181,6963,3488,58]);
// Polycyclic

G:=Group<a,b,c|a^29=b^8=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of D8×C29 in TeX

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