direct product, metacyclic, supersoluble, monomial, A-group
Aliases: C22×C7⋊C9, C14⋊2C18, C42.7C6, (C2×C14)⋊3C9, C7⋊2(C2×C18), C21.2(C2×C6), (C2×C42).3C3, C6.3(C2×C7⋊C3), C3.(C22×C7⋊C3), (C2×C6).2(C7⋊C3), SmallGroup(252,9)
Series: Derived ►Chief ►Lower central ►Upper central
| C7 — C22×C7⋊C9 |
Generators and relations for C22×C7⋊C9
G = < a,b,c,d | a2=b2=c7=d9=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c4 >
Smallest permutation representation of C22×C7⋊C9
►Regular action on 252 points
Generators in S252
(1 201)(2 202)(3 203)(4 204)(5 205)(6 206)(7 207)(8 199)(9 200)(10 144)(11 136)(12 137)(13 138)(14 139)(15 140)(16 141)(17 142)(18 143)(19 172)(20 173)(21 174)(22 175)(23 176)(24 177)(25 178)(26 179)(27 180)(28 148)(29 149)(30 150)(31 151)(32 152)(33 153)(34 145)(35 146)(36 147)(37 127)(38 128)(39 129)(40 130)(41 131)(42 132)(43 133)(44 134)(45 135)(46 157)(47 158)(48 159)(49 160)(50 161)(51 162)(52 154)(53 155)(54 156)(55 166)(56 167)(57 168)(58 169)(59 170)(60 171)(61 163)(62 164)(63 165)(64 184)(65 185)(66 186)(67 187)(68 188)(69 189)(70 181)(71 182)(72 183)(73 190)(74 191)(75 192)(76 193)(77 194)(78 195)(79 196)(80 197)(81 198)(82 208)(83 209)(84 210)(85 211)(86 212)(87 213)(88 214)(89 215)(90 216)(91 217)(92 218)(93 219)(94 220)(95 221)(96 222)(97 223)(98 224)(99 225)(100 226)(101 227)(102 228)(103 229)(104 230)(105 231)(106 232)(107 233)(108 234)(109 235)(110 236)(111 237)(112 238)(113 239)(114 240)(115 241)(116 242)(117 243)(118 244)(119 245)(120 246)(121 247)(122 248)(123 249)(124 250)(125 251)(126 252)
(1 138)(2 139)(3 140)(4 141)(5 142)(6 143)(7 144)(8 136)(9 137)(10 207)(11 199)(12 200)(13 201)(14 202)(15 203)(16 204)(17 205)(18 206)(19 235)(20 236)(21 237)(22 238)(23 239)(24 240)(25 241)(26 242)(27 243)(28 211)(29 212)(30 213)(31 214)(32 215)(33 216)(34 208)(35 209)(36 210)(37 190)(38 191)(39 192)(40 193)(41 194)(42 195)(43 196)(44 197)(45 198)(46 220)(47 221)(48 222)(49 223)(50 224)(51 225)(52 217)(53 218)(54 219)(55 229)(56 230)(57 231)(58 232)(59 233)(60 234)(61 226)(62 227)(63 228)(64 121)(65 122)(66 123)(67 124)(68 125)(69 126)(70 118)(71 119)(72 120)(73 127)(74 128)(75 129)(76 130)(77 131)(78 132)(79 133)(80 134)(81 135)(82 145)(83 146)(84 147)(85 148)(86 149)(87 150)(88 151)(89 152)(90 153)(91 154)(92 155)(93 156)(94 157)(95 158)(96 159)(97 160)(98 161)(99 162)(100 163)(101 164)(102 165)(103 166)(104 167)(105 168)(106 169)(107 170)(108 171)(109 172)(110 173)(111 174)(112 175)(113 176)(114 177)(115 178)(116 179)(117 180)(181 244)(182 245)(183 246)(184 247)(185 248)(186 249)(187 250)(188 251)(189 252)
(1 72 91 76 89 113 104)(2 90 64 114 92 105 77)(3 93 82 106 65 78 115)(4 66 94 79 83 116 107)(5 84 67 117 95 108 80)(6 96 85 100 68 81 109)(7 69 97 73 86 110 101)(8 87 70 111 98 102 74)(9 99 88 103 71 75 112)(10 252 49 37 29 20 62)(11 30 244 21 50 63 38)(12 51 31 55 245 39 22)(13 246 52 40 32 23 56)(14 33 247 24 53 57 41)(15 54 34 58 248 42 25)(16 249 46 43 35 26 59)(17 36 250 27 47 60 44)(18 48 28 61 251 45 19)(118 174 161 165 128 136 150)(119 129 175 137 162 151 166)(120 154 130 152 176 167 138)(121 177 155 168 131 139 153)(122 132 178 140 156 145 169)(123 157 133 146 179 170 141)(124 180 158 171 134 142 147)(125 135 172 143 159 148 163)(126 160 127 149 173 164 144)(181 237 224 228 191 199 213)(182 192 238 200 225 214 229)(183 217 193 215 239 230 201)(184 240 218 231 194 202 216)(185 195 241 203 219 208 232)(186 220 196 209 242 233 204)(187 243 221 234 197 205 210)(188 198 235 206 222 211 226)(189 223 190 212 236 227 207)
(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)
G:=sub<Sym(252)| (1,201)(2,202)(3,203)(4,204)(5,205)(6,206)(7,207)(8,199)(9,200)(10,144)(11,136)(12,137)(13,138)(14,139)(15,140)(16,141)(17,142)(18,143)(19,172)(20,173)(21,174)(22,175)(23,176)(24,177)(25,178)(26,179)(27,180)(28,148)(29,149)(30,150)(31,151)(32,152)(33,153)(34,145)(35,146)(36,147)(37,127)(38,128)(39,129)(40,130)(41,131)(42,132)(43,133)(44,134)(45,135)(46,157)(47,158)(48,159)(49,160)(50,161)(51,162)(52,154)(53,155)(54,156)(55,166)(56,167)(57,168)(58,169)(59,170)(60,171)(61,163)(62,164)(63,165)(64,184)(65,185)(66,186)(67,187)(68,188)(69,189)(70,181)(71,182)(72,183)(73,190)(74,191)(75,192)(76,193)(77,194)(78,195)(79,196)(80,197)(81,198)(82,208)(83,209)(84,210)(85,211)(86,212)(87,213)(88,214)(89,215)(90,216)(91,217)(92,218)(93,219)(94,220)(95,221)(96,222)(97,223)(98,224)(99,225)(100,226)(101,227)(102,228)(103,229)(104,230)(105,231)(106,232)(107,233)(108,234)(109,235)(110,236)(111,237)(112,238)(113,239)(114,240)(115,241)(116,242)(117,243)(118,244)(119,245)(120,246)(121,247)(122,248)(123,249)(124,250)(125,251)(126,252), (1,138)(2,139)(3,140)(4,141)(5,142)(6,143)(7,144)(8,136)(9,137)(10,207)(11,199)(12,200)(13,201)(14,202)(15,203)(16,204)(17,205)(18,206)(19,235)(20,236)(21,237)(22,238)(23,239)(24,240)(25,241)(26,242)(27,243)(28,211)(29,212)(30,213)(31,214)(32,215)(33,216)(34,208)(35,209)(36,210)(37,190)(38,191)(39,192)(40,193)(41,194)(42,195)(43,196)(44,197)(45,198)(46,220)(47,221)(48,222)(49,223)(50,224)(51,225)(52,217)(53,218)(54,219)(55,229)(56,230)(57,231)(58,232)(59,233)(60,234)(61,226)(62,227)(63,228)(64,121)(65,122)(66,123)(67,124)(68,125)(69,126)(70,118)(71,119)(72,120)(73,127)(74,128)(75,129)(76,130)(77,131)(78,132)(79,133)(80,134)(81,135)(82,145)(83,146)(84,147)(85,148)(86,149)(87,150)(88,151)(89,152)(90,153)(91,154)(92,155)(93,156)(94,157)(95,158)(96,159)(97,160)(98,161)(99,162)(100,163)(101,164)(102,165)(103,166)(104,167)(105,168)(106,169)(107,170)(108,171)(109,172)(110,173)(111,174)(112,175)(113,176)(114,177)(115,178)(116,179)(117,180)(181,244)(182,245)(183,246)(184,247)(185,248)(186,249)(187,250)(188,251)(189,252), (1,72,91,76,89,113,104)(2,90,64,114,92,105,77)(3,93,82,106,65,78,115)(4,66,94,79,83,116,107)(5,84,67,117,95,108,80)(6,96,85,100,68,81,109)(7,69,97,73,86,110,101)(8,87,70,111,98,102,74)(9,99,88,103,71,75,112)(10,252,49,37,29,20,62)(11,30,244,21,50,63,38)(12,51,31,55,245,39,22)(13,246,52,40,32,23,56)(14,33,247,24,53,57,41)(15,54,34,58,248,42,25)(16,249,46,43,35,26,59)(17,36,250,27,47,60,44)(18,48,28,61,251,45,19)(118,174,161,165,128,136,150)(119,129,175,137,162,151,166)(120,154,130,152,176,167,138)(121,177,155,168,131,139,153)(122,132,178,140,156,145,169)(123,157,133,146,179,170,141)(124,180,158,171,134,142,147)(125,135,172,143,159,148,163)(126,160,127,149,173,164,144)(181,237,224,228,191,199,213)(182,192,238,200,225,214,229)(183,217,193,215,239,230,201)(184,240,218,231,194,202,216)(185,195,241,203,219,208,232)(186,220,196,209,242,233,204)(187,243,221,234,197,205,210)(188,198,235,206,222,211,226)(189,223,190,212,236,227,207), (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)>;
G:=Group( (1,201)(2,202)(3,203)(4,204)(5,205)(6,206)(7,207)(8,199)(9,200)(10,144)(11,136)(12,137)(13,138)(14,139)(15,140)(16,141)(17,142)(18,143)(19,172)(20,173)(21,174)(22,175)(23,176)(24,177)(25,178)(26,179)(27,180)(28,148)(29,149)(30,150)(31,151)(32,152)(33,153)(34,145)(35,146)(36,147)(37,127)(38,128)(39,129)(40,130)(41,131)(42,132)(43,133)(44,134)(45,135)(46,157)(47,158)(48,159)(49,160)(50,161)(51,162)(52,154)(53,155)(54,156)(55,166)(56,167)(57,168)(58,169)(59,170)(60,171)(61,163)(62,164)(63,165)(64,184)(65,185)(66,186)(67,187)(68,188)(69,189)(70,181)(71,182)(72,183)(73,190)(74,191)(75,192)(76,193)(77,194)(78,195)(79,196)(80,197)(81,198)(82,208)(83,209)(84,210)(85,211)(86,212)(87,213)(88,214)(89,215)(90,216)(91,217)(92,218)(93,219)(94,220)(95,221)(96,222)(97,223)(98,224)(99,225)(100,226)(101,227)(102,228)(103,229)(104,230)(105,231)(106,232)(107,233)(108,234)(109,235)(110,236)(111,237)(112,238)(113,239)(114,240)(115,241)(116,242)(117,243)(118,244)(119,245)(120,246)(121,247)(122,248)(123,249)(124,250)(125,251)(126,252), (1,138)(2,139)(3,140)(4,141)(5,142)(6,143)(7,144)(8,136)(9,137)(10,207)(11,199)(12,200)(13,201)(14,202)(15,203)(16,204)(17,205)(18,206)(19,235)(20,236)(21,237)(22,238)(23,239)(24,240)(25,241)(26,242)(27,243)(28,211)(29,212)(30,213)(31,214)(32,215)(33,216)(34,208)(35,209)(36,210)(37,190)(38,191)(39,192)(40,193)(41,194)(42,195)(43,196)(44,197)(45,198)(46,220)(47,221)(48,222)(49,223)(50,224)(51,225)(52,217)(53,218)(54,219)(55,229)(56,230)(57,231)(58,232)(59,233)(60,234)(61,226)(62,227)(63,228)(64,121)(65,122)(66,123)(67,124)(68,125)(69,126)(70,118)(71,119)(72,120)(73,127)(74,128)(75,129)(76,130)(77,131)(78,132)(79,133)(80,134)(81,135)(82,145)(83,146)(84,147)(85,148)(86,149)(87,150)(88,151)(89,152)(90,153)(91,154)(92,155)(93,156)(94,157)(95,158)(96,159)(97,160)(98,161)(99,162)(100,163)(101,164)(102,165)(103,166)(104,167)(105,168)(106,169)(107,170)(108,171)(109,172)(110,173)(111,174)(112,175)(113,176)(114,177)(115,178)(116,179)(117,180)(181,244)(182,245)(183,246)(184,247)(185,248)(186,249)(187,250)(188,251)(189,252), (1,72,91,76,89,113,104)(2,90,64,114,92,105,77)(3,93,82,106,65,78,115)(4,66,94,79,83,116,107)(5,84,67,117,95,108,80)(6,96,85,100,68,81,109)(7,69,97,73,86,110,101)(8,87,70,111,98,102,74)(9,99,88,103,71,75,112)(10,252,49,37,29,20,62)(11,30,244,21,50,63,38)(12,51,31,55,245,39,22)(13,246,52,40,32,23,56)(14,33,247,24,53,57,41)(15,54,34,58,248,42,25)(16,249,46,43,35,26,59)(17,36,250,27,47,60,44)(18,48,28,61,251,45,19)(118,174,161,165,128,136,150)(119,129,175,137,162,151,166)(120,154,130,152,176,167,138)(121,177,155,168,131,139,153)(122,132,178,140,156,145,169)(123,157,133,146,179,170,141)(124,180,158,171,134,142,147)(125,135,172,143,159,148,163)(126,160,127,149,173,164,144)(181,237,224,228,191,199,213)(182,192,238,200,225,214,229)(183,217,193,215,239,230,201)(184,240,218,231,194,202,216)(185,195,241,203,219,208,232)(186,220,196,209,242,233,204)(187,243,221,234,197,205,210)(188,198,235,206,222,211,226)(189,223,190,212,236,227,207), (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) );
G=PermutationGroup([[(1,201),(2,202),(3,203),(4,204),(5,205),(6,206),(7,207),(8,199),(9,200),(10,144),(11,136),(12,137),(13,138),(14,139),(15,140),(16,141),(17,142),(18,143),(19,172),(20,173),(21,174),(22,175),(23,176),(24,177),(25,178),(26,179),(27,180),(28,148),(29,149),(30,150),(31,151),(32,152),(33,153),(34,145),(35,146),(36,147),(37,127),(38,128),(39,129),(40,130),(41,131),(42,132),(43,133),(44,134),(45,135),(46,157),(47,158),(48,159),(49,160),(50,161),(51,162),(52,154),(53,155),(54,156),(55,166),(56,167),(57,168),(58,169),(59,170),(60,171),(61,163),(62,164),(63,165),(64,184),(65,185),(66,186),(67,187),(68,188),(69,189),(70,181),(71,182),(72,183),(73,190),(74,191),(75,192),(76,193),(77,194),(78,195),(79,196),(80,197),(81,198),(82,208),(83,209),(84,210),(85,211),(86,212),(87,213),(88,214),(89,215),(90,216),(91,217),(92,218),(93,219),(94,220),(95,221),(96,222),(97,223),(98,224),(99,225),(100,226),(101,227),(102,228),(103,229),(104,230),(105,231),(106,232),(107,233),(108,234),(109,235),(110,236),(111,237),(112,238),(113,239),(114,240),(115,241),(116,242),(117,243),(118,244),(119,245),(120,246),(121,247),(122,248),(123,249),(124,250),(125,251),(126,252)], [(1,138),(2,139),(3,140),(4,141),(5,142),(6,143),(7,144),(8,136),(9,137),(10,207),(11,199),(12,200),(13,201),(14,202),(15,203),(16,204),(17,205),(18,206),(19,235),(20,236),(21,237),(22,238),(23,239),(24,240),(25,241),(26,242),(27,243),(28,211),(29,212),(30,213),(31,214),(32,215),(33,216),(34,208),(35,209),(36,210),(37,190),(38,191),(39,192),(40,193),(41,194),(42,195),(43,196),(44,197),(45,198),(46,220),(47,221),(48,222),(49,223),(50,224),(51,225),(52,217),(53,218),(54,219),(55,229),(56,230),(57,231),(58,232),(59,233),(60,234),(61,226),(62,227),(63,228),(64,121),(65,122),(66,123),(67,124),(68,125),(69,126),(70,118),(71,119),(72,120),(73,127),(74,128),(75,129),(76,130),(77,131),(78,132),(79,133),(80,134),(81,135),(82,145),(83,146),(84,147),(85,148),(86,149),(87,150),(88,151),(89,152),(90,153),(91,154),(92,155),(93,156),(94,157),(95,158),(96,159),(97,160),(98,161),(99,162),(100,163),(101,164),(102,165),(103,166),(104,167),(105,168),(106,169),(107,170),(108,171),(109,172),(110,173),(111,174),(112,175),(113,176),(114,177),(115,178),(116,179),(117,180),(181,244),(182,245),(183,246),(184,247),(185,248),(186,249),(187,250),(188,251),(189,252)], [(1,72,91,76,89,113,104),(2,90,64,114,92,105,77),(3,93,82,106,65,78,115),(4,66,94,79,83,116,107),(5,84,67,117,95,108,80),(6,96,85,100,68,81,109),(7,69,97,73,86,110,101),(8,87,70,111,98,102,74),(9,99,88,103,71,75,112),(10,252,49,37,29,20,62),(11,30,244,21,50,63,38),(12,51,31,55,245,39,22),(13,246,52,40,32,23,56),(14,33,247,24,53,57,41),(15,54,34,58,248,42,25),(16,249,46,43,35,26,59),(17,36,250,27,47,60,44),(18,48,28,61,251,45,19),(118,174,161,165,128,136,150),(119,129,175,137,162,151,166),(120,154,130,152,176,167,138),(121,177,155,168,131,139,153),(122,132,178,140,156,145,169),(123,157,133,146,179,170,141),(124,180,158,171,134,142,147),(125,135,172,143,159,148,163),(126,160,127,149,173,164,144),(181,237,224,228,191,199,213),(182,192,238,200,225,214,229),(183,217,193,215,239,230,201),(184,240,218,231,194,202,216),(185,195,241,203,219,208,232),(186,220,196,209,242,233,204),(187,243,221,234,197,205,210),(188,198,235,206,222,211,226),(189,223,190,212,236,227,207)], [(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)]])
60 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 6A | ··· | 6F | 7A | 7B | 9A | ··· | 9F | 14A | ··· | 14F | 18A | ··· | 18R | 21A | 21B | 21C | 21D | 42A | ··· | 42L |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 6 | ··· | 6 | 7 | 7 | 9 | ··· | 9 | 14 | ··· | 14 | 18 | ··· | 18 | 21 | 21 | 21 | 21 | 42 | ··· | 42 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 3 | 3 | 7 | ··· | 7 | 3 | ··· | 3 | 7 | ··· | 7 | 3 | 3 | 3 | 3 | 3 | ··· | 3 |
60 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 3 | 3 | 3 |
| type | + | + | ||||||||
| image | C1 | C2 | C3 | C6 | C9 | C18 | C7⋊C3 | C2×C7⋊C3 | C7⋊C9 | C2×C7⋊C9 |
| kernel | C22×C7⋊C9 | C2×C7⋊C9 | C2×C42 | C42 | C2×C14 | C14 | C2×C6 | C6 | C22 | C2 |
| # reps | 1 | 3 | 2 | 6 | 6 | 18 | 2 | 6 | 4 | 12 |
Matrix representation of C22×C7⋊C9 ►in GL6(𝔽127)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 126 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 126 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 126 | 104 | 1 |
| 0 | 0 | 0 | 0 | 104 | 1 |
| 0 | 0 | 0 | 126 | 105 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 37 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 17 | 115 | 35 |
| 0 | 0 | 0 | 13 | 70 | 9 |
| 0 | 0 | 0 | 92 | 122 | 40 |
G:=sub<GL(6,GF(127))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,126,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[126,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,126,0,126,0,0,0,104,104,105,0,0,0,1,1,1],[1,0,0,0,0,0,0,37,0,0,0,0,0,0,1,0,0,0,0,0,0,17,13,92,0,0,0,115,70,122,0,0,0,35,9,40] >;
C22×C7⋊C9 in GAP, Magma, Sage, TeX
C_2^2\times C_7\rtimes C_9
% in TeX
G:=Group("C2^2xC7:C9"); // GroupNames label
G:=SmallGroup(252,9);
// by ID
G=gap.SmallGroup(252,9);
# by ID
G:=PCGroup([5,-2,-2,-3,-3,-7,57,464]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^2=c^7=d^9=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^4>;
// generators/relations
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