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G = C2×C182order 364 = 22·7·13

Abelian group of type [2,182]

direct product, abelian, monomial, 2-elementary

Aliases: C2×C182, SmallGroup(364,11)

Series: Derived Chief Lower central Upper central

C1 — C2×C182
C1C13C91C182 — C2×C182
C1 — C2×C182
C1 — C2×C182

Generators and relations for C2×C182
 G = < a,b | a2=b182=1, ab=ba >


Smallest permutation representation of C2×C182
Regular action on 364 points
Generators in S364
(1 235)(2 236)(3 237)(4 238)(5 239)(6 240)(7 241)(8 242)(9 243)(10 244)(11 245)(12 246)(13 247)(14 248)(15 249)(16 250)(17 251)(18 252)(19 253)(20 254)(21 255)(22 256)(23 257)(24 258)(25 259)(26 260)(27 261)(28 262)(29 263)(30 264)(31 265)(32 266)(33 267)(34 268)(35 269)(36 270)(37 271)(38 272)(39 273)(40 274)(41 275)(42 276)(43 277)(44 278)(45 279)(46 280)(47 281)(48 282)(49 283)(50 284)(51 285)(52 286)(53 287)(54 288)(55 289)(56 290)(57 291)(58 292)(59 293)(60 294)(61 295)(62 296)(63 297)(64 298)(65 299)(66 300)(67 301)(68 302)(69 303)(70 304)(71 305)(72 306)(73 307)(74 308)(75 309)(76 310)(77 311)(78 312)(79 313)(80 314)(81 315)(82 316)(83 317)(84 318)(85 319)(86 320)(87 321)(88 322)(89 323)(90 324)(91 325)(92 326)(93 327)(94 328)(95 329)(96 330)(97 331)(98 332)(99 333)(100 334)(101 335)(102 336)(103 337)(104 338)(105 339)(106 340)(107 341)(108 342)(109 343)(110 344)(111 345)(112 346)(113 347)(114 348)(115 349)(116 350)(117 351)(118 352)(119 353)(120 354)(121 355)(122 356)(123 357)(124 358)(125 359)(126 360)(127 361)(128 362)(129 363)(130 364)(131 183)(132 184)(133 185)(134 186)(135 187)(136 188)(137 189)(138 190)(139 191)(140 192)(141 193)(142 194)(143 195)(144 196)(145 197)(146 198)(147 199)(148 200)(149 201)(150 202)(151 203)(152 204)(153 205)(154 206)(155 207)(156 208)(157 209)(158 210)(159 211)(160 212)(161 213)(162 214)(163 215)(164 216)(165 217)(166 218)(167 219)(168 220)(169 221)(170 222)(171 223)(172 224)(173 225)(174 226)(175 227)(176 228)(177 229)(178 230)(179 231)(180 232)(181 233)(182 234)
(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)(183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364)

G:=sub<Sym(364)| (1,235)(2,236)(3,237)(4,238)(5,239)(6,240)(7,241)(8,242)(9,243)(10,244)(11,245)(12,246)(13,247)(14,248)(15,249)(16,250)(17,251)(18,252)(19,253)(20,254)(21,255)(22,256)(23,257)(24,258)(25,259)(26,260)(27,261)(28,262)(29,263)(30,264)(31,265)(32,266)(33,267)(34,268)(35,269)(36,270)(37,271)(38,272)(39,273)(40,274)(41,275)(42,276)(43,277)(44,278)(45,279)(46,280)(47,281)(48,282)(49,283)(50,284)(51,285)(52,286)(53,287)(54,288)(55,289)(56,290)(57,291)(58,292)(59,293)(60,294)(61,295)(62,296)(63,297)(64,298)(65,299)(66,300)(67,301)(68,302)(69,303)(70,304)(71,305)(72,306)(73,307)(74,308)(75,309)(76,310)(77,311)(78,312)(79,313)(80,314)(81,315)(82,316)(83,317)(84,318)(85,319)(86,320)(87,321)(88,322)(89,323)(90,324)(91,325)(92,326)(93,327)(94,328)(95,329)(96,330)(97,331)(98,332)(99,333)(100,334)(101,335)(102,336)(103,337)(104,338)(105,339)(106,340)(107,341)(108,342)(109,343)(110,344)(111,345)(112,346)(113,347)(114,348)(115,349)(116,350)(117,351)(118,352)(119,353)(120,354)(121,355)(122,356)(123,357)(124,358)(125,359)(126,360)(127,361)(128,362)(129,363)(130,364)(131,183)(132,184)(133,185)(134,186)(135,187)(136,188)(137,189)(138,190)(139,191)(140,192)(141,193)(142,194)(143,195)(144,196)(145,197)(146,198)(147,199)(148,200)(149,201)(150,202)(151,203)(152,204)(153,205)(154,206)(155,207)(156,208)(157,209)(158,210)(159,211)(160,212)(161,213)(162,214)(163,215)(164,216)(165,217)(166,218)(167,219)(168,220)(169,221)(170,222)(171,223)(172,224)(173,225)(174,226)(175,227)(176,228)(177,229)(178,230)(179,231)(180,232)(181,233)(182,234), (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)(183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364)>;

G:=Group( (1,235)(2,236)(3,237)(4,238)(5,239)(6,240)(7,241)(8,242)(9,243)(10,244)(11,245)(12,246)(13,247)(14,248)(15,249)(16,250)(17,251)(18,252)(19,253)(20,254)(21,255)(22,256)(23,257)(24,258)(25,259)(26,260)(27,261)(28,262)(29,263)(30,264)(31,265)(32,266)(33,267)(34,268)(35,269)(36,270)(37,271)(38,272)(39,273)(40,274)(41,275)(42,276)(43,277)(44,278)(45,279)(46,280)(47,281)(48,282)(49,283)(50,284)(51,285)(52,286)(53,287)(54,288)(55,289)(56,290)(57,291)(58,292)(59,293)(60,294)(61,295)(62,296)(63,297)(64,298)(65,299)(66,300)(67,301)(68,302)(69,303)(70,304)(71,305)(72,306)(73,307)(74,308)(75,309)(76,310)(77,311)(78,312)(79,313)(80,314)(81,315)(82,316)(83,317)(84,318)(85,319)(86,320)(87,321)(88,322)(89,323)(90,324)(91,325)(92,326)(93,327)(94,328)(95,329)(96,330)(97,331)(98,332)(99,333)(100,334)(101,335)(102,336)(103,337)(104,338)(105,339)(106,340)(107,341)(108,342)(109,343)(110,344)(111,345)(112,346)(113,347)(114,348)(115,349)(116,350)(117,351)(118,352)(119,353)(120,354)(121,355)(122,356)(123,357)(124,358)(125,359)(126,360)(127,361)(128,362)(129,363)(130,364)(131,183)(132,184)(133,185)(134,186)(135,187)(136,188)(137,189)(138,190)(139,191)(140,192)(141,193)(142,194)(143,195)(144,196)(145,197)(146,198)(147,199)(148,200)(149,201)(150,202)(151,203)(152,204)(153,205)(154,206)(155,207)(156,208)(157,209)(158,210)(159,211)(160,212)(161,213)(162,214)(163,215)(164,216)(165,217)(166,218)(167,219)(168,220)(169,221)(170,222)(171,223)(172,224)(173,225)(174,226)(175,227)(176,228)(177,229)(178,230)(179,231)(180,232)(181,233)(182,234), (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)(183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364) );

G=PermutationGroup([(1,235),(2,236),(3,237),(4,238),(5,239),(6,240),(7,241),(8,242),(9,243),(10,244),(11,245),(12,246),(13,247),(14,248),(15,249),(16,250),(17,251),(18,252),(19,253),(20,254),(21,255),(22,256),(23,257),(24,258),(25,259),(26,260),(27,261),(28,262),(29,263),(30,264),(31,265),(32,266),(33,267),(34,268),(35,269),(36,270),(37,271),(38,272),(39,273),(40,274),(41,275),(42,276),(43,277),(44,278),(45,279),(46,280),(47,281),(48,282),(49,283),(50,284),(51,285),(52,286),(53,287),(54,288),(55,289),(56,290),(57,291),(58,292),(59,293),(60,294),(61,295),(62,296),(63,297),(64,298),(65,299),(66,300),(67,301),(68,302),(69,303),(70,304),(71,305),(72,306),(73,307),(74,308),(75,309),(76,310),(77,311),(78,312),(79,313),(80,314),(81,315),(82,316),(83,317),(84,318),(85,319),(86,320),(87,321),(88,322),(89,323),(90,324),(91,325),(92,326),(93,327),(94,328),(95,329),(96,330),(97,331),(98,332),(99,333),(100,334),(101,335),(102,336),(103,337),(104,338),(105,339),(106,340),(107,341),(108,342),(109,343),(110,344),(111,345),(112,346),(113,347),(114,348),(115,349),(116,350),(117,351),(118,352),(119,353),(120,354),(121,355),(122,356),(123,357),(124,358),(125,359),(126,360),(127,361),(128,362),(129,363),(130,364),(131,183),(132,184),(133,185),(134,186),(135,187),(136,188),(137,189),(138,190),(139,191),(140,192),(141,193),(142,194),(143,195),(144,196),(145,197),(146,198),(147,199),(148,200),(149,201),(150,202),(151,203),(152,204),(153,205),(154,206),(155,207),(156,208),(157,209),(158,210),(159,211),(160,212),(161,213),(162,214),(163,215),(164,216),(165,217),(166,218),(167,219),(168,220),(169,221),(170,222),(171,223),(172,224),(173,225),(174,226),(175,227),(176,228),(177,229),(178,230),(179,231),(180,232),(181,233),(182,234)], [(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),(183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364)])

364 conjugacy classes

class 1 2A2B2C7A···7F13A···13L14A···14R26A···26AJ91A···91BT182A···182HH
order12227···713···1314···1426···2691···91182···182
size11111···11···11···11···11···11···1

364 irreducible representations

dim11111111
type++
imageC1C2C7C13C14C26C91C182
kernelC2×C182C182C2×C26C2×C14C26C14C22C2
# reps13612183672216

Matrix representation of C2×C182 in GL2(𝔽547) generated by

10
0546
,
2260
0454
G:=sub<GL(2,GF(547))| [1,0,0,546],[226,0,0,454] >;

C2×C182 in GAP, Magma, Sage, TeX

C_2\times C_{182}
% in TeX

G:=Group("C2xC182");
// GroupNames label

G:=SmallGroup(364,11);
// by ID

G=gap.SmallGroup(364,11);
# by ID

G:=PCGroup([4,-2,-2,-7,-13]);
// Polycyclic

G:=Group<a,b|a^2=b^182=1,a*b=b*a>;
// generators/relations

Export

Subgroup lattice of C2×C182 in TeX

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