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G = C14×D17order 476 = 22·7·17

Direct product of C14 and D17

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

Aliases: C14×D17, C34⋊C14, C2382C2, C1193C22, C17⋊(C2×C14), SmallGroup(476,8)

Series: Derived Chief Lower central Upper central

C1C17 — C14×D17
C1C17C119C7×D17 — C14×D17
C17 — C14×D17
C1C14

Generators and relations for C14×D17
 G = < a,b,c | a14=b17=c2=1, ab=ba, ac=ca, cbc=b-1 >

17C2
17C2
17C22
17C14
17C14
17C2×C14

Smallest permutation representation of C14×D17
On 238 points
Generators in S238
(1 171 107 166 92 153 84 136 66 238 42 221 23 198)(2 172 108 167 93 137 85 120 67 222 43 205 24 199)(3 173 109 168 94 138 69 121 68 223 44 206 25 200)(4 174 110 169 95 139 70 122 52 224 45 207 26 201)(5 175 111 170 96 140 71 123 53 225 46 208 27 202)(6 176 112 154 97 141 72 124 54 226 47 209 28 203)(7 177 113 155 98 142 73 125 55 227 48 210 29 204)(8 178 114 156 99 143 74 126 56 228 49 211 30 188)(9 179 115 157 100 144 75 127 57 229 50 212 31 189)(10 180 116 158 101 145 76 128 58 230 51 213 32 190)(11 181 117 159 102 146 77 129 59 231 35 214 33 191)(12 182 118 160 86 147 78 130 60 232 36 215 34 192)(13 183 119 161 87 148 79 131 61 233 37 216 18 193)(14 184 103 162 88 149 80 132 62 234 38 217 19 194)(15 185 104 163 89 150 81 133 63 235 39 218 20 195)(16 186 105 164 90 151 82 134 64 236 40 219 21 196)(17 187 106 165 91 152 83 135 65 237 41 220 22 197)
(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)(222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238)
(1 135)(2 134)(3 133)(4 132)(5 131)(6 130)(7 129)(8 128)(9 127)(10 126)(11 125)(12 124)(13 123)(14 122)(15 121)(16 120)(17 136)(18 140)(19 139)(20 138)(21 137)(22 153)(23 152)(24 151)(25 150)(26 149)(27 148)(28 147)(29 146)(30 145)(31 144)(32 143)(33 142)(34 141)(35 155)(36 154)(37 170)(38 169)(39 168)(40 167)(41 166)(42 165)(43 164)(44 163)(45 162)(46 161)(47 160)(48 159)(49 158)(50 157)(51 156)(52 184)(53 183)(54 182)(55 181)(56 180)(57 179)(58 178)(59 177)(60 176)(61 175)(62 174)(63 173)(64 172)(65 171)(66 187)(67 186)(68 185)(69 195)(70 194)(71 193)(72 192)(73 191)(74 190)(75 189)(76 188)(77 204)(78 203)(79 202)(80 201)(81 200)(82 199)(83 198)(84 197)(85 196)(86 209)(87 208)(88 207)(89 206)(90 205)(91 221)(92 220)(93 219)(94 218)(95 217)(96 216)(97 215)(98 214)(99 213)(100 212)(101 211)(102 210)(103 224)(104 223)(105 222)(106 238)(107 237)(108 236)(109 235)(110 234)(111 233)(112 232)(113 231)(114 230)(115 229)(116 228)(117 227)(118 226)(119 225)

G:=sub<Sym(238)| (1,171,107,166,92,153,84,136,66,238,42,221,23,198)(2,172,108,167,93,137,85,120,67,222,43,205,24,199)(3,173,109,168,94,138,69,121,68,223,44,206,25,200)(4,174,110,169,95,139,70,122,52,224,45,207,26,201)(5,175,111,170,96,140,71,123,53,225,46,208,27,202)(6,176,112,154,97,141,72,124,54,226,47,209,28,203)(7,177,113,155,98,142,73,125,55,227,48,210,29,204)(8,178,114,156,99,143,74,126,56,228,49,211,30,188)(9,179,115,157,100,144,75,127,57,229,50,212,31,189)(10,180,116,158,101,145,76,128,58,230,51,213,32,190)(11,181,117,159,102,146,77,129,59,231,35,214,33,191)(12,182,118,160,86,147,78,130,60,232,36,215,34,192)(13,183,119,161,87,148,79,131,61,233,37,216,18,193)(14,184,103,162,88,149,80,132,62,234,38,217,19,194)(15,185,104,163,89,150,81,133,63,235,39,218,20,195)(16,186,105,164,90,151,82,134,64,236,40,219,21,196)(17,187,106,165,91,152,83,135,65,237,41,220,22,197), (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)(222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238), (1,135)(2,134)(3,133)(4,132)(5,131)(6,130)(7,129)(8,128)(9,127)(10,126)(11,125)(12,124)(13,123)(14,122)(15,121)(16,120)(17,136)(18,140)(19,139)(20,138)(21,137)(22,153)(23,152)(24,151)(25,150)(26,149)(27,148)(28,147)(29,146)(30,145)(31,144)(32,143)(33,142)(34,141)(35,155)(36,154)(37,170)(38,169)(39,168)(40,167)(41,166)(42,165)(43,164)(44,163)(45,162)(46,161)(47,160)(48,159)(49,158)(50,157)(51,156)(52,184)(53,183)(54,182)(55,181)(56,180)(57,179)(58,178)(59,177)(60,176)(61,175)(62,174)(63,173)(64,172)(65,171)(66,187)(67,186)(68,185)(69,195)(70,194)(71,193)(72,192)(73,191)(74,190)(75,189)(76,188)(77,204)(78,203)(79,202)(80,201)(81,200)(82,199)(83,198)(84,197)(85,196)(86,209)(87,208)(88,207)(89,206)(90,205)(91,221)(92,220)(93,219)(94,218)(95,217)(96,216)(97,215)(98,214)(99,213)(100,212)(101,211)(102,210)(103,224)(104,223)(105,222)(106,238)(107,237)(108,236)(109,235)(110,234)(111,233)(112,232)(113,231)(114,230)(115,229)(116,228)(117,227)(118,226)(119,225)>;

G:=Group( (1,171,107,166,92,153,84,136,66,238,42,221,23,198)(2,172,108,167,93,137,85,120,67,222,43,205,24,199)(3,173,109,168,94,138,69,121,68,223,44,206,25,200)(4,174,110,169,95,139,70,122,52,224,45,207,26,201)(5,175,111,170,96,140,71,123,53,225,46,208,27,202)(6,176,112,154,97,141,72,124,54,226,47,209,28,203)(7,177,113,155,98,142,73,125,55,227,48,210,29,204)(8,178,114,156,99,143,74,126,56,228,49,211,30,188)(9,179,115,157,100,144,75,127,57,229,50,212,31,189)(10,180,116,158,101,145,76,128,58,230,51,213,32,190)(11,181,117,159,102,146,77,129,59,231,35,214,33,191)(12,182,118,160,86,147,78,130,60,232,36,215,34,192)(13,183,119,161,87,148,79,131,61,233,37,216,18,193)(14,184,103,162,88,149,80,132,62,234,38,217,19,194)(15,185,104,163,89,150,81,133,63,235,39,218,20,195)(16,186,105,164,90,151,82,134,64,236,40,219,21,196)(17,187,106,165,91,152,83,135,65,237,41,220,22,197), (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)(222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238), (1,135)(2,134)(3,133)(4,132)(5,131)(6,130)(7,129)(8,128)(9,127)(10,126)(11,125)(12,124)(13,123)(14,122)(15,121)(16,120)(17,136)(18,140)(19,139)(20,138)(21,137)(22,153)(23,152)(24,151)(25,150)(26,149)(27,148)(28,147)(29,146)(30,145)(31,144)(32,143)(33,142)(34,141)(35,155)(36,154)(37,170)(38,169)(39,168)(40,167)(41,166)(42,165)(43,164)(44,163)(45,162)(46,161)(47,160)(48,159)(49,158)(50,157)(51,156)(52,184)(53,183)(54,182)(55,181)(56,180)(57,179)(58,178)(59,177)(60,176)(61,175)(62,174)(63,173)(64,172)(65,171)(66,187)(67,186)(68,185)(69,195)(70,194)(71,193)(72,192)(73,191)(74,190)(75,189)(76,188)(77,204)(78,203)(79,202)(80,201)(81,200)(82,199)(83,198)(84,197)(85,196)(86,209)(87,208)(88,207)(89,206)(90,205)(91,221)(92,220)(93,219)(94,218)(95,217)(96,216)(97,215)(98,214)(99,213)(100,212)(101,211)(102,210)(103,224)(104,223)(105,222)(106,238)(107,237)(108,236)(109,235)(110,234)(111,233)(112,232)(113,231)(114,230)(115,229)(116,228)(117,227)(118,226)(119,225) );

G=PermutationGroup([(1,171,107,166,92,153,84,136,66,238,42,221,23,198),(2,172,108,167,93,137,85,120,67,222,43,205,24,199),(3,173,109,168,94,138,69,121,68,223,44,206,25,200),(4,174,110,169,95,139,70,122,52,224,45,207,26,201),(5,175,111,170,96,140,71,123,53,225,46,208,27,202),(6,176,112,154,97,141,72,124,54,226,47,209,28,203),(7,177,113,155,98,142,73,125,55,227,48,210,29,204),(8,178,114,156,99,143,74,126,56,228,49,211,30,188),(9,179,115,157,100,144,75,127,57,229,50,212,31,189),(10,180,116,158,101,145,76,128,58,230,51,213,32,190),(11,181,117,159,102,146,77,129,59,231,35,214,33,191),(12,182,118,160,86,147,78,130,60,232,36,215,34,192),(13,183,119,161,87,148,79,131,61,233,37,216,18,193),(14,184,103,162,88,149,80,132,62,234,38,217,19,194),(15,185,104,163,89,150,81,133,63,235,39,218,20,195),(16,186,105,164,90,151,82,134,64,236,40,219,21,196),(17,187,106,165,91,152,83,135,65,237,41,220,22,197)], [(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),(222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238)], [(1,135),(2,134),(3,133),(4,132),(5,131),(6,130),(7,129),(8,128),(9,127),(10,126),(11,125),(12,124),(13,123),(14,122),(15,121),(16,120),(17,136),(18,140),(19,139),(20,138),(21,137),(22,153),(23,152),(24,151),(25,150),(26,149),(27,148),(28,147),(29,146),(30,145),(31,144),(32,143),(33,142),(34,141),(35,155),(36,154),(37,170),(38,169),(39,168),(40,167),(41,166),(42,165),(43,164),(44,163),(45,162),(46,161),(47,160),(48,159),(49,158),(50,157),(51,156),(52,184),(53,183),(54,182),(55,181),(56,180),(57,179),(58,178),(59,177),(60,176),(61,175),(62,174),(63,173),(64,172),(65,171),(66,187),(67,186),(68,185),(69,195),(70,194),(71,193),(72,192),(73,191),(74,190),(75,189),(76,188),(77,204),(78,203),(79,202),(80,201),(81,200),(82,199),(83,198),(84,197),(85,196),(86,209),(87,208),(88,207),(89,206),(90,205),(91,221),(92,220),(93,219),(94,218),(95,217),(96,216),(97,215),(98,214),(99,213),(100,212),(101,211),(102,210),(103,224),(104,223),(105,222),(106,238),(107,237),(108,236),(109,235),(110,234),(111,233),(112,232),(113,231),(114,230),(115,229),(116,228),(117,227),(118,226),(119,225)])

140 conjugacy classes

class 1 2A2B2C7A···7F14A···14F14G···14R17A···17H34A···34H119A···119AV238A···238AV
order12227···714···1414···1417···1734···34119···119238···238
size1117171···11···117···172···22···22···22···2

140 irreducible representations

dim1111112222
type+++++
imageC1C2C2C7C14C14D17D34C7×D17C14×D17
kernelC14×D17C7×D17C238D34D17C34C14C7C2C1
# reps1216126884848

Matrix representation of C14×D17 in GL2(𝔽239) generated by

1410
0141
,
961
1130
,
1561
12224
G:=sub<GL(2,GF(239))| [141,0,0,141],[96,11,1,30],[15,12,61,224] >;

C14×D17 in GAP, Magma, Sage, TeX

C_{14}\times D_{17}
% in TeX

G:=Group("C14xD17");
// GroupNames label

G:=SmallGroup(476,8);
// by ID

G=gap.SmallGroup(476,8);
# by ID

G:=PCGroup([4,-2,-2,-7,-17,7171]);
// Polycyclic

G:=Group<a,b,c|a^14=b^17=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C14×D17 in TeX

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