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G = C23×C34order 272 = 24·17

Abelian group of type [2,2,2,34]

direct product, abelian, monomial, 2-elementary

Aliases: C23×C34, SmallGroup(272,54)

Series: Derived Chief Lower central Upper central

C1 — C23×C34
C1C17C34C2×C34C22×C34 — C23×C34
C1 — C23×C34
C1 — C23×C34

Generators and relations for C23×C34
 G = < a,b,c,d | a2=b2=c2=d34=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, cd=dc >

Subgroups: 134, all normal (4 characteristic)
C1, C2 [×15], C22 [×35], C23 [×15], C24, C17, C34 [×15], C2×C34 [×35], C22×C34 [×15], C23×C34
Quotients: C1, C2 [×15], C22 [×35], C23 [×15], C24, C17, C34 [×15], C2×C34 [×35], C22×C34 [×15], C23×C34

Smallest permutation representation of C23×C34
Regular action on 272 points
Generators in S272
(1 156)(2 157)(3 158)(4 159)(5 160)(6 161)(7 162)(8 163)(9 164)(10 165)(11 166)(12 167)(13 168)(14 169)(15 170)(16 137)(17 138)(18 139)(19 140)(20 141)(21 142)(22 143)(23 144)(24 145)(25 146)(26 147)(27 148)(28 149)(29 150)(30 151)(31 152)(32 153)(33 154)(34 155)(35 201)(36 202)(37 203)(38 204)(39 171)(40 172)(41 173)(42 174)(43 175)(44 176)(45 177)(46 178)(47 179)(48 180)(49 181)(50 182)(51 183)(52 184)(53 185)(54 186)(55 187)(56 188)(57 189)(58 190)(59 191)(60 192)(61 193)(62 194)(63 195)(64 196)(65 197)(66 198)(67 199)(68 200)(69 217)(70 218)(71 219)(72 220)(73 221)(74 222)(75 223)(76 224)(77 225)(78 226)(79 227)(80 228)(81 229)(82 230)(83 231)(84 232)(85 233)(86 234)(87 235)(88 236)(89 237)(90 238)(91 205)(92 206)(93 207)(94 208)(95 209)(96 210)(97 211)(98 212)(99 213)(100 214)(101 215)(102 216)(103 240)(104 241)(105 242)(106 243)(107 244)(108 245)(109 246)(110 247)(111 248)(112 249)(113 250)(114 251)(115 252)(116 253)(117 254)(118 255)(119 256)(120 257)(121 258)(122 259)(123 260)(124 261)(125 262)(126 263)(127 264)(128 265)(129 266)(130 267)(131 268)(132 269)(133 270)(134 271)(135 272)(136 239)
(1 91)(2 92)(3 93)(4 94)(5 95)(6 96)(7 97)(8 98)(9 99)(10 100)(11 101)(12 102)(13 69)(14 70)(15 71)(16 72)(17 73)(18 74)(19 75)(20 76)(21 77)(22 78)(23 79)(24 80)(25 81)(26 82)(27 83)(28 84)(29 85)(30 86)(31 87)(32 88)(33 89)(34 90)(35 133)(36 134)(37 135)(38 136)(39 103)(40 104)(41 105)(42 106)(43 107)(44 108)(45 109)(46 110)(47 111)(48 112)(49 113)(50 114)(51 115)(52 116)(53 117)(54 118)(55 119)(56 120)(57 121)(58 122)(59 123)(60 124)(61 125)(62 126)(63 127)(64 128)(65 129)(66 130)(67 131)(68 132)(137 220)(138 221)(139 222)(140 223)(141 224)(142 225)(143 226)(144 227)(145 228)(146 229)(147 230)(148 231)(149 232)(150 233)(151 234)(152 235)(153 236)(154 237)(155 238)(156 205)(157 206)(158 207)(159 208)(160 209)(161 210)(162 211)(163 212)(164 213)(165 214)(166 215)(167 216)(168 217)(169 218)(170 219)(171 240)(172 241)(173 242)(174 243)(175 244)(176 245)(177 246)(178 247)(179 248)(180 249)(181 250)(182 251)(183 252)(184 253)(185 254)(186 255)(187 256)(188 257)(189 258)(190 259)(191 260)(192 261)(193 262)(194 263)(195 264)(196 265)(197 266)(198 267)(199 268)(200 269)(201 270)(202 271)(203 272)(204 239)
(1 66)(2 67)(3 68)(4 35)(5 36)(6 37)(7 38)(8 39)(9 40)(10 41)(11 42)(12 43)(13 44)(14 45)(15 46)(16 47)(17 48)(18 49)(19 50)(20 51)(21 52)(22 53)(23 54)(24 55)(25 56)(26 57)(27 58)(28 59)(29 60)(30 61)(31 62)(32 63)(33 64)(34 65)(69 108)(70 109)(71 110)(72 111)(73 112)(74 113)(75 114)(76 115)(77 116)(78 117)(79 118)(80 119)(81 120)(82 121)(83 122)(84 123)(85 124)(86 125)(87 126)(88 127)(89 128)(90 129)(91 130)(92 131)(93 132)(94 133)(95 134)(96 135)(97 136)(98 103)(99 104)(100 105)(101 106)(102 107)(137 179)(138 180)(139 181)(140 182)(141 183)(142 184)(143 185)(144 186)(145 187)(146 188)(147 189)(148 190)(149 191)(150 192)(151 193)(152 194)(153 195)(154 196)(155 197)(156 198)(157 199)(158 200)(159 201)(160 202)(161 203)(162 204)(163 171)(164 172)(165 173)(166 174)(167 175)(168 176)(169 177)(170 178)(205 267)(206 268)(207 269)(208 270)(209 271)(210 272)(211 239)(212 240)(213 241)(214 242)(215 243)(216 244)(217 245)(218 246)(219 247)(220 248)(221 249)(222 250)(223 251)(224 252)(225 253)(226 254)(227 255)(228 256)(229 257)(230 258)(231 259)(232 260)(233 261)(234 262)(235 263)(236 264)(237 265)(238 266)
(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)

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

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

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

272 conjugacy classes

class 1 2A···2O17A···17P34A···34IF
order12···217···1734···34
size11···11···11···1

272 irreducible representations

dim1111
type++
imageC1C2C17C34
kernelC23×C34C22×C34C24C23
# reps11516240

Matrix representation of C23×C34 in GL4(𝔽103) generated by

1000
0100
001020
0001
,
1000
0100
001020
000102
,
102000
0100
0010
000102
,
22000
09000
00790
0008
G:=sub<GL(4,GF(103))| [1,0,0,0,0,1,0,0,0,0,102,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,102,0,0,0,0,102],[102,0,0,0,0,1,0,0,0,0,1,0,0,0,0,102],[22,0,0,0,0,90,0,0,0,0,79,0,0,0,0,8] >;

C23×C34 in GAP, Magma, Sage, TeX

C_2^3\times C_{34}
% in TeX

G:=Group("C2^3xC34");
// GroupNames label

G:=SmallGroup(272,54);
// by ID

G=gap.SmallGroup(272,54);
# by ID

G:=PCGroup([5,-2,-2,-2,-2,-17]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^2=c^2=d^34=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,c*d=d*c>;
// generators/relations

׿
×
𝔽