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G = C4×C92order 368 = 24·23

Abelian group of type [4,92]

direct product, abelian, monomial, 2-elementary

Aliases: C4×C92, SmallGroup(368,19)

Series: Derived Chief Lower central Upper central

C1 — C4×C92
C1C2C22C2×C46C2×C92 — C4×C92
C1 — C4×C92
C1 — C4×C92

Generators and relations for C4×C92
 G = < a,b | a4=b92=1, ab=ba >


Smallest permutation representation of C4×C92
Regular action on 368 points
Generators in S368
(1 300 132 232)(2 301 133 233)(3 302 134 234)(4 303 135 235)(5 304 136 236)(6 305 137 237)(7 306 138 238)(8 307 139 239)(9 308 140 240)(10 309 141 241)(11 310 142 242)(12 311 143 243)(13 312 144 244)(14 313 145 245)(15 314 146 246)(16 315 147 247)(17 316 148 248)(18 317 149 249)(19 318 150 250)(20 319 151 251)(21 320 152 252)(22 321 153 253)(23 322 154 254)(24 323 155 255)(25 324 156 256)(26 325 157 257)(27 326 158 258)(28 327 159 259)(29 328 160 260)(30 329 161 261)(31 330 162 262)(32 331 163 263)(33 332 164 264)(34 333 165 265)(35 334 166 266)(36 335 167 267)(37 336 168 268)(38 337 169 269)(39 338 170 270)(40 339 171 271)(41 340 172 272)(42 341 173 273)(43 342 174 274)(44 343 175 275)(45 344 176 276)(46 345 177 185)(47 346 178 186)(48 347 179 187)(49 348 180 188)(50 349 181 189)(51 350 182 190)(52 351 183 191)(53 352 184 192)(54 353 93 193)(55 354 94 194)(56 355 95 195)(57 356 96 196)(58 357 97 197)(59 358 98 198)(60 359 99 199)(61 360 100 200)(62 361 101 201)(63 362 102 202)(64 363 103 203)(65 364 104 204)(66 365 105 205)(67 366 106 206)(68 367 107 207)(69 368 108 208)(70 277 109 209)(71 278 110 210)(72 279 111 211)(73 280 112 212)(74 281 113 213)(75 282 114 214)(76 283 115 215)(77 284 116 216)(78 285 117 217)(79 286 118 218)(80 287 119 219)(81 288 120 220)(82 289 121 221)(83 290 122 222)(84 291 123 223)(85 292 124 224)(86 293 125 225)(87 294 126 226)(88 295 127 227)(89 296 128 228)(90 297 129 229)(91 298 130 230)(92 299 131 231)
(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)(277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368)

G:=sub<Sym(368)| (1,300,132,232)(2,301,133,233)(3,302,134,234)(4,303,135,235)(5,304,136,236)(6,305,137,237)(7,306,138,238)(8,307,139,239)(9,308,140,240)(10,309,141,241)(11,310,142,242)(12,311,143,243)(13,312,144,244)(14,313,145,245)(15,314,146,246)(16,315,147,247)(17,316,148,248)(18,317,149,249)(19,318,150,250)(20,319,151,251)(21,320,152,252)(22,321,153,253)(23,322,154,254)(24,323,155,255)(25,324,156,256)(26,325,157,257)(27,326,158,258)(28,327,159,259)(29,328,160,260)(30,329,161,261)(31,330,162,262)(32,331,163,263)(33,332,164,264)(34,333,165,265)(35,334,166,266)(36,335,167,267)(37,336,168,268)(38,337,169,269)(39,338,170,270)(40,339,171,271)(41,340,172,272)(42,341,173,273)(43,342,174,274)(44,343,175,275)(45,344,176,276)(46,345,177,185)(47,346,178,186)(48,347,179,187)(49,348,180,188)(50,349,181,189)(51,350,182,190)(52,351,183,191)(53,352,184,192)(54,353,93,193)(55,354,94,194)(56,355,95,195)(57,356,96,196)(58,357,97,197)(59,358,98,198)(60,359,99,199)(61,360,100,200)(62,361,101,201)(63,362,102,202)(64,363,103,203)(65,364,104,204)(66,365,105,205)(67,366,106,206)(68,367,107,207)(69,368,108,208)(70,277,109,209)(71,278,110,210)(72,279,111,211)(73,280,112,212)(74,281,113,213)(75,282,114,214)(76,283,115,215)(77,284,116,216)(78,285,117,217)(79,286,118,218)(80,287,119,219)(81,288,120,220)(82,289,121,221)(83,290,122,222)(84,291,123,223)(85,292,124,224)(86,293,125,225)(87,294,126,226)(88,295,127,227)(89,296,128,228)(90,297,129,229)(91,298,130,230)(92,299,131,231), (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)(277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368)>;

G:=Group( (1,300,132,232)(2,301,133,233)(3,302,134,234)(4,303,135,235)(5,304,136,236)(6,305,137,237)(7,306,138,238)(8,307,139,239)(9,308,140,240)(10,309,141,241)(11,310,142,242)(12,311,143,243)(13,312,144,244)(14,313,145,245)(15,314,146,246)(16,315,147,247)(17,316,148,248)(18,317,149,249)(19,318,150,250)(20,319,151,251)(21,320,152,252)(22,321,153,253)(23,322,154,254)(24,323,155,255)(25,324,156,256)(26,325,157,257)(27,326,158,258)(28,327,159,259)(29,328,160,260)(30,329,161,261)(31,330,162,262)(32,331,163,263)(33,332,164,264)(34,333,165,265)(35,334,166,266)(36,335,167,267)(37,336,168,268)(38,337,169,269)(39,338,170,270)(40,339,171,271)(41,340,172,272)(42,341,173,273)(43,342,174,274)(44,343,175,275)(45,344,176,276)(46,345,177,185)(47,346,178,186)(48,347,179,187)(49,348,180,188)(50,349,181,189)(51,350,182,190)(52,351,183,191)(53,352,184,192)(54,353,93,193)(55,354,94,194)(56,355,95,195)(57,356,96,196)(58,357,97,197)(59,358,98,198)(60,359,99,199)(61,360,100,200)(62,361,101,201)(63,362,102,202)(64,363,103,203)(65,364,104,204)(66,365,105,205)(67,366,106,206)(68,367,107,207)(69,368,108,208)(70,277,109,209)(71,278,110,210)(72,279,111,211)(73,280,112,212)(74,281,113,213)(75,282,114,214)(76,283,115,215)(77,284,116,216)(78,285,117,217)(79,286,118,218)(80,287,119,219)(81,288,120,220)(82,289,121,221)(83,290,122,222)(84,291,123,223)(85,292,124,224)(86,293,125,225)(87,294,126,226)(88,295,127,227)(89,296,128,228)(90,297,129,229)(91,298,130,230)(92,299,131,231), (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)(277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368) );

G=PermutationGroup([(1,300,132,232),(2,301,133,233),(3,302,134,234),(4,303,135,235),(5,304,136,236),(6,305,137,237),(7,306,138,238),(8,307,139,239),(9,308,140,240),(10,309,141,241),(11,310,142,242),(12,311,143,243),(13,312,144,244),(14,313,145,245),(15,314,146,246),(16,315,147,247),(17,316,148,248),(18,317,149,249),(19,318,150,250),(20,319,151,251),(21,320,152,252),(22,321,153,253),(23,322,154,254),(24,323,155,255),(25,324,156,256),(26,325,157,257),(27,326,158,258),(28,327,159,259),(29,328,160,260),(30,329,161,261),(31,330,162,262),(32,331,163,263),(33,332,164,264),(34,333,165,265),(35,334,166,266),(36,335,167,267),(37,336,168,268),(38,337,169,269),(39,338,170,270),(40,339,171,271),(41,340,172,272),(42,341,173,273),(43,342,174,274),(44,343,175,275),(45,344,176,276),(46,345,177,185),(47,346,178,186),(48,347,179,187),(49,348,180,188),(50,349,181,189),(51,350,182,190),(52,351,183,191),(53,352,184,192),(54,353,93,193),(55,354,94,194),(56,355,95,195),(57,356,96,196),(58,357,97,197),(59,358,98,198),(60,359,99,199),(61,360,100,200),(62,361,101,201),(63,362,102,202),(64,363,103,203),(65,364,104,204),(66,365,105,205),(67,366,106,206),(68,367,107,207),(69,368,108,208),(70,277,109,209),(71,278,110,210),(72,279,111,211),(73,280,112,212),(74,281,113,213),(75,282,114,214),(76,283,115,215),(77,284,116,216),(78,285,117,217),(79,286,118,218),(80,287,119,219),(81,288,120,220),(82,289,121,221),(83,290,122,222),(84,291,123,223),(85,292,124,224),(86,293,125,225),(87,294,126,226),(88,295,127,227),(89,296,128,228),(90,297,129,229),(91,298,130,230),(92,299,131,231)], [(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),(277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368)])

368 conjugacy classes

class 1 2A2B2C4A···4L23A···23V46A···46BN92A···92JD
order12224···423···2346···4692···92
size11111···11···11···11···1

368 irreducible representations

dim111111
type++
imageC1C2C4C23C46C92
kernelC4×C92C2×C92C92C42C2×C4C4
# reps13122266264

Matrix representation of C4×C92 in GL2(𝔽277) generated by

600
060
,
1490
0113
G:=sub<GL(2,GF(277))| [60,0,0,60],[149,0,0,113] >;

C4×C92 in GAP, Magma, Sage, TeX

C_4\times C_{92}
% in TeX

G:=Group("C4xC92");
// GroupNames label

G:=SmallGroup(368,19);
// by ID

G=gap.SmallGroup(368,19);
# by ID

G:=PCGroup([5,-2,-2,-23,-2,-2,460,926]);
// Polycyclic

G:=Group<a,b|a^4=b^92=1,a*b=b*a>;
// generators/relations

Export

Subgroup lattice of C4×C92 in TeX

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