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G = C2×C152order 304 = 24·19

Abelian group of type [2,152]

direct product, abelian, monomial, 2-elementary

Aliases: C2×C152, SmallGroup(304,22)

Series: Derived Chief Lower central Upper central

C1 — C2×C152
C1C2C4C76C152 — C2×C152
C1 — C2×C152
C1 — C2×C152

Generators and relations for C2×C152
 G = < a,b | a2=b152=1, ab=ba >


Smallest permutation representation of C2×C152
Regular action on 304 points
Generators in S304
(1 192)(2 193)(3 194)(4 195)(5 196)(6 197)(7 198)(8 199)(9 200)(10 201)(11 202)(12 203)(13 204)(14 205)(15 206)(16 207)(17 208)(18 209)(19 210)(20 211)(21 212)(22 213)(23 214)(24 215)(25 216)(26 217)(27 218)(28 219)(29 220)(30 221)(31 222)(32 223)(33 224)(34 225)(35 226)(36 227)(37 228)(38 229)(39 230)(40 231)(41 232)(42 233)(43 234)(44 235)(45 236)(46 237)(47 238)(48 239)(49 240)(50 241)(51 242)(52 243)(53 244)(54 245)(55 246)(56 247)(57 248)(58 249)(59 250)(60 251)(61 252)(62 253)(63 254)(64 255)(65 256)(66 257)(67 258)(68 259)(69 260)(70 261)(71 262)(72 263)(73 264)(74 265)(75 266)(76 267)(77 268)(78 269)(79 270)(80 271)(81 272)(82 273)(83 274)(84 275)(85 276)(86 277)(87 278)(88 279)(89 280)(90 281)(91 282)(92 283)(93 284)(94 285)(95 286)(96 287)(97 288)(98 289)(99 290)(100 291)(101 292)(102 293)(103 294)(104 295)(105 296)(106 297)(107 298)(108 299)(109 300)(110 301)(111 302)(112 303)(113 304)(114 153)(115 154)(116 155)(117 156)(118 157)(119 158)(120 159)(121 160)(122 161)(123 162)(124 163)(125 164)(126 165)(127 166)(128 167)(129 168)(130 169)(131 170)(132 171)(133 172)(134 173)(135 174)(136 175)(137 176)(138 177)(139 178)(140 179)(141 180)(142 181)(143 182)(144 183)(145 184)(146 185)(147 186)(148 187)(149 188)(150 189)(151 190)(152 191)
(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)

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

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

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

304 conjugacy classes

class 1 2A2B2C4A4B4C4D8A···8H19A···19R38A···38BB76A···76BT152A···152EN
order122244448···819···1938···3876···76152···152
size111111111···11···11···11···11···1

304 irreducible representations

dim111111111111
type+++
imageC1C2C2C4C4C8C19C38C38C76C76C152
kernelC2×C152C152C2×C76C76C2×C38C38C2×C8C8C2×C4C4C22C2
# reps1212281836183636144

Matrix representation of C2×C152 in GL2(𝔽457) generated by

4560
01
,
4460
0172
G:=sub<GL(2,GF(457))| [456,0,0,1],[446,0,0,172] >;

C2×C152 in GAP, Magma, Sage, TeX

C_2\times C_{152}
% in TeX

G:=Group("C2xC152");
// GroupNames label

G:=SmallGroup(304,22);
// by ID

G=gap.SmallGroup(304,22);
# by ID

G:=PCGroup([5,-2,-2,-19,-2,-2,380,58]);
// Polycyclic

G:=Group<a,b|a^2=b^152=1,a*b=b*a>;
// generators/relations

Export

Subgroup lattice of C2×C152 in TeX

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