metabelian, supersoluble, monomial, A-group
Aliases: C32⋊4D27, C33.8D9, C3⋊(C27⋊S3), C27⋊(C3⋊S3), (C3×C27)⋊11S3, C9.3(C9⋊S3), (C32×C27)⋊5C2, (C3×C9).11D9, C9.(C33⋊C2), (C32×C9).28S3, C32.19(C9⋊S3), C3.2(C32⋊4D9), (C3×C9).22(C3⋊S3), SmallGroup(486,184)
Series: Derived ►Chief ►Lower central ►Upper central
| C32×C27 — C32⋊4D27 |
Generators and relations for C32⋊4D27
G = < a,b,c,d | a3=b3=c27=d2=1, ab=ba, ac=ca, dad=a-1, bc=cb, dbd=b-1, dcd=c-1 >
Subgroups: 2200 in 144 conjugacy classes, 73 normal (7 characteristic)
C1, C2, C3, C3, S3, C9, C9, C32, D9, C3⋊S3, C27, C3×C9, C33, D27, C9⋊S3, C33⋊C2, C3×C27, C32×C9, C27⋊S3, C32⋊4D9, C32×C27, C32⋊4D27
Quotients: C1, C2, S3, D9, C3⋊S3, D27, C9⋊S3, C33⋊C2, C27⋊S3, C32⋊4D9, C32⋊4D27
►On 243 points
Generators in S243
(1 106 81)(2 107 55)(3 108 56)(4 82 57)(5 83 58)(6 84 59)(7 85 60)(8 86 61)(9 87 62)(10 88 63)(11 89 64)(12 90 65)(13 91 66)(14 92 67)(15 93 68)(16 94 69)(17 95 70)(18 96 71)(19 97 72)(20 98 73)(21 99 74)(22 100 75)(23 101 76)(24 102 77)(25 103 78)(26 104 79)(27 105 80)(28 143 119)(29 144 120)(30 145 121)(31 146 122)(32 147 123)(33 148 124)(34 149 125)(35 150 126)(36 151 127)(37 152 128)(38 153 129)(39 154 130)(40 155 131)(41 156 132)(42 157 133)(43 158 134)(44 159 135)(45 160 109)(46 161 110)(47 162 111)(48 136 112)(49 137 113)(50 138 114)(51 139 115)(52 140 116)(53 141 117)(54 142 118)(163 216 243)(164 190 217)(165 191 218)(166 192 219)(167 193 220)(168 194 221)(169 195 222)(170 196 223)(171 197 224)(172 198 225)(173 199 226)(174 200 227)(175 201 228)(176 202 229)(177 203 230)(178 204 231)(179 205 232)(180 206 233)(181 207 234)(182 208 235)(183 209 236)(184 210 237)(185 211 238)(186 212 239)(187 213 240)(188 214 241)(189 215 242)
(1 144 178)(2 145 179)(3 146 180)(4 147 181)(5 148 182)(6 149 183)(7 150 184)(8 151 185)(9 152 186)(10 153 187)(11 154 188)(12 155 189)(13 156 163)(14 157 164)(15 158 165)(16 159 166)(17 160 167)(18 161 168)(19 162 169)(20 136 170)(21 137 171)(22 138 172)(23 139 173)(24 140 174)(25 141 175)(26 142 176)(27 143 177)(28 230 80)(29 231 81)(30 232 55)(31 233 56)(32 234 57)(33 235 58)(34 236 59)(35 237 60)(36 238 61)(37 239 62)(38 240 63)(39 241 64)(40 242 65)(41 243 66)(42 217 67)(43 218 68)(44 219 69)(45 220 70)(46 221 71)(47 222 72)(48 223 73)(49 224 74)(50 225 75)(51 226 76)(52 227 77)(53 228 78)(54 229 79)(82 123 207)(83 124 208)(84 125 209)(85 126 210)(86 127 211)(87 128 212)(88 129 213)(89 130 214)(90 131 215)(91 132 216)(92 133 190)(93 134 191)(94 135 192)(95 109 193)(96 110 194)(97 111 195)(98 112 196)(99 113 197)(100 114 198)(101 115 199)(102 116 200)(103 117 201)(104 118 202)(105 119 203)(106 120 204)(107 121 205)(108 122 206)
(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)
(2 27)(3 26)(4 25)(5 24)(6 23)(7 22)(8 21)(9 20)(10 19)(11 18)(12 17)(13 16)(14 15)(28 205)(29 204)(30 203)(31 202)(32 201)(33 200)(34 199)(35 198)(36 197)(37 196)(38 195)(39 194)(40 193)(41 192)(42 191)(43 190)(44 216)(45 215)(46 214)(47 213)(48 212)(49 211)(50 210)(51 209)(52 208)(53 207)(54 206)(55 105)(56 104)(57 103)(58 102)(59 101)(60 100)(61 99)(62 98)(63 97)(64 96)(65 95)(66 94)(67 93)(68 92)(69 91)(70 90)(71 89)(72 88)(73 87)(74 86)(75 85)(76 84)(77 83)(78 82)(79 108)(80 107)(81 106)(109 242)(110 241)(111 240)(112 239)(113 238)(114 237)(115 236)(116 235)(117 234)(118 233)(119 232)(120 231)(121 230)(122 229)(123 228)(124 227)(125 226)(126 225)(127 224)(128 223)(129 222)(130 221)(131 220)(132 219)(133 218)(134 217)(135 243)(136 186)(137 185)(138 184)(139 183)(140 182)(141 181)(142 180)(143 179)(144 178)(145 177)(146 176)(147 175)(148 174)(149 173)(150 172)(151 171)(152 170)(153 169)(154 168)(155 167)(156 166)(157 165)(158 164)(159 163)(160 189)(161 188)(162 187)
G:=sub<Sym(243)| (1,106,81)(2,107,55)(3,108,56)(4,82,57)(5,83,58)(6,84,59)(7,85,60)(8,86,61)(9,87,62)(10,88,63)(11,89,64)(12,90,65)(13,91,66)(14,92,67)(15,93,68)(16,94,69)(17,95,70)(18,96,71)(19,97,72)(20,98,73)(21,99,74)(22,100,75)(23,101,76)(24,102,77)(25,103,78)(26,104,79)(27,105,80)(28,143,119)(29,144,120)(30,145,121)(31,146,122)(32,147,123)(33,148,124)(34,149,125)(35,150,126)(36,151,127)(37,152,128)(38,153,129)(39,154,130)(40,155,131)(41,156,132)(42,157,133)(43,158,134)(44,159,135)(45,160,109)(46,161,110)(47,162,111)(48,136,112)(49,137,113)(50,138,114)(51,139,115)(52,140,116)(53,141,117)(54,142,118)(163,216,243)(164,190,217)(165,191,218)(166,192,219)(167,193,220)(168,194,221)(169,195,222)(170,196,223)(171,197,224)(172,198,225)(173,199,226)(174,200,227)(175,201,228)(176,202,229)(177,203,230)(178,204,231)(179,205,232)(180,206,233)(181,207,234)(182,208,235)(183,209,236)(184,210,237)(185,211,238)(186,212,239)(187,213,240)(188,214,241)(189,215,242), (1,144,178)(2,145,179)(3,146,180)(4,147,181)(5,148,182)(6,149,183)(7,150,184)(8,151,185)(9,152,186)(10,153,187)(11,154,188)(12,155,189)(13,156,163)(14,157,164)(15,158,165)(16,159,166)(17,160,167)(18,161,168)(19,162,169)(20,136,170)(21,137,171)(22,138,172)(23,139,173)(24,140,174)(25,141,175)(26,142,176)(27,143,177)(28,230,80)(29,231,81)(30,232,55)(31,233,56)(32,234,57)(33,235,58)(34,236,59)(35,237,60)(36,238,61)(37,239,62)(38,240,63)(39,241,64)(40,242,65)(41,243,66)(42,217,67)(43,218,68)(44,219,69)(45,220,70)(46,221,71)(47,222,72)(48,223,73)(49,224,74)(50,225,75)(51,226,76)(52,227,77)(53,228,78)(54,229,79)(82,123,207)(83,124,208)(84,125,209)(85,126,210)(86,127,211)(87,128,212)(88,129,213)(89,130,214)(90,131,215)(91,132,216)(92,133,190)(93,134,191)(94,135,192)(95,109,193)(96,110,194)(97,111,195)(98,112,196)(99,113,197)(100,114,198)(101,115,199)(102,116,200)(103,117,201)(104,118,202)(105,119,203)(106,120,204)(107,121,205)(108,122,206), (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), (2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(28,205)(29,204)(30,203)(31,202)(32,201)(33,200)(34,199)(35,198)(36,197)(37,196)(38,195)(39,194)(40,193)(41,192)(42,191)(43,190)(44,216)(45,215)(46,214)(47,213)(48,212)(49,211)(50,210)(51,209)(52,208)(53,207)(54,206)(55,105)(56,104)(57,103)(58,102)(59,101)(60,100)(61,99)(62,98)(63,97)(64,96)(65,95)(66,94)(67,93)(68,92)(69,91)(70,90)(71,89)(72,88)(73,87)(74,86)(75,85)(76,84)(77,83)(78,82)(79,108)(80,107)(81,106)(109,242)(110,241)(111,240)(112,239)(113,238)(114,237)(115,236)(116,235)(117,234)(118,233)(119,232)(120,231)(121,230)(122,229)(123,228)(124,227)(125,226)(126,225)(127,224)(128,223)(129,222)(130,221)(131,220)(132,219)(133,218)(134,217)(135,243)(136,186)(137,185)(138,184)(139,183)(140,182)(141,181)(142,180)(143,179)(144,178)(145,177)(146,176)(147,175)(148,174)(149,173)(150,172)(151,171)(152,170)(153,169)(154,168)(155,167)(156,166)(157,165)(158,164)(159,163)(160,189)(161,188)(162,187)>;
G:=Group( (1,106,81)(2,107,55)(3,108,56)(4,82,57)(5,83,58)(6,84,59)(7,85,60)(8,86,61)(9,87,62)(10,88,63)(11,89,64)(12,90,65)(13,91,66)(14,92,67)(15,93,68)(16,94,69)(17,95,70)(18,96,71)(19,97,72)(20,98,73)(21,99,74)(22,100,75)(23,101,76)(24,102,77)(25,103,78)(26,104,79)(27,105,80)(28,143,119)(29,144,120)(30,145,121)(31,146,122)(32,147,123)(33,148,124)(34,149,125)(35,150,126)(36,151,127)(37,152,128)(38,153,129)(39,154,130)(40,155,131)(41,156,132)(42,157,133)(43,158,134)(44,159,135)(45,160,109)(46,161,110)(47,162,111)(48,136,112)(49,137,113)(50,138,114)(51,139,115)(52,140,116)(53,141,117)(54,142,118)(163,216,243)(164,190,217)(165,191,218)(166,192,219)(167,193,220)(168,194,221)(169,195,222)(170,196,223)(171,197,224)(172,198,225)(173,199,226)(174,200,227)(175,201,228)(176,202,229)(177,203,230)(178,204,231)(179,205,232)(180,206,233)(181,207,234)(182,208,235)(183,209,236)(184,210,237)(185,211,238)(186,212,239)(187,213,240)(188,214,241)(189,215,242), (1,144,178)(2,145,179)(3,146,180)(4,147,181)(5,148,182)(6,149,183)(7,150,184)(8,151,185)(9,152,186)(10,153,187)(11,154,188)(12,155,189)(13,156,163)(14,157,164)(15,158,165)(16,159,166)(17,160,167)(18,161,168)(19,162,169)(20,136,170)(21,137,171)(22,138,172)(23,139,173)(24,140,174)(25,141,175)(26,142,176)(27,143,177)(28,230,80)(29,231,81)(30,232,55)(31,233,56)(32,234,57)(33,235,58)(34,236,59)(35,237,60)(36,238,61)(37,239,62)(38,240,63)(39,241,64)(40,242,65)(41,243,66)(42,217,67)(43,218,68)(44,219,69)(45,220,70)(46,221,71)(47,222,72)(48,223,73)(49,224,74)(50,225,75)(51,226,76)(52,227,77)(53,228,78)(54,229,79)(82,123,207)(83,124,208)(84,125,209)(85,126,210)(86,127,211)(87,128,212)(88,129,213)(89,130,214)(90,131,215)(91,132,216)(92,133,190)(93,134,191)(94,135,192)(95,109,193)(96,110,194)(97,111,195)(98,112,196)(99,113,197)(100,114,198)(101,115,199)(102,116,200)(103,117,201)(104,118,202)(105,119,203)(106,120,204)(107,121,205)(108,122,206), (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), (2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(28,205)(29,204)(30,203)(31,202)(32,201)(33,200)(34,199)(35,198)(36,197)(37,196)(38,195)(39,194)(40,193)(41,192)(42,191)(43,190)(44,216)(45,215)(46,214)(47,213)(48,212)(49,211)(50,210)(51,209)(52,208)(53,207)(54,206)(55,105)(56,104)(57,103)(58,102)(59,101)(60,100)(61,99)(62,98)(63,97)(64,96)(65,95)(66,94)(67,93)(68,92)(69,91)(70,90)(71,89)(72,88)(73,87)(74,86)(75,85)(76,84)(77,83)(78,82)(79,108)(80,107)(81,106)(109,242)(110,241)(111,240)(112,239)(113,238)(114,237)(115,236)(116,235)(117,234)(118,233)(119,232)(120,231)(121,230)(122,229)(123,228)(124,227)(125,226)(126,225)(127,224)(128,223)(129,222)(130,221)(131,220)(132,219)(133,218)(134,217)(135,243)(136,186)(137,185)(138,184)(139,183)(140,182)(141,181)(142,180)(143,179)(144,178)(145,177)(146,176)(147,175)(148,174)(149,173)(150,172)(151,171)(152,170)(153,169)(154,168)(155,167)(156,166)(157,165)(158,164)(159,163)(160,189)(161,188)(162,187) );
G=PermutationGroup([[(1,106,81),(2,107,55),(3,108,56),(4,82,57),(5,83,58),(6,84,59),(7,85,60),(8,86,61),(9,87,62),(10,88,63),(11,89,64),(12,90,65),(13,91,66),(14,92,67),(15,93,68),(16,94,69),(17,95,70),(18,96,71),(19,97,72),(20,98,73),(21,99,74),(22,100,75),(23,101,76),(24,102,77),(25,103,78),(26,104,79),(27,105,80),(28,143,119),(29,144,120),(30,145,121),(31,146,122),(32,147,123),(33,148,124),(34,149,125),(35,150,126),(36,151,127),(37,152,128),(38,153,129),(39,154,130),(40,155,131),(41,156,132),(42,157,133),(43,158,134),(44,159,135),(45,160,109),(46,161,110),(47,162,111),(48,136,112),(49,137,113),(50,138,114),(51,139,115),(52,140,116),(53,141,117),(54,142,118),(163,216,243),(164,190,217),(165,191,218),(166,192,219),(167,193,220),(168,194,221),(169,195,222),(170,196,223),(171,197,224),(172,198,225),(173,199,226),(174,200,227),(175,201,228),(176,202,229),(177,203,230),(178,204,231),(179,205,232),(180,206,233),(181,207,234),(182,208,235),(183,209,236),(184,210,237),(185,211,238),(186,212,239),(187,213,240),(188,214,241),(189,215,242)], [(1,144,178),(2,145,179),(3,146,180),(4,147,181),(5,148,182),(6,149,183),(7,150,184),(8,151,185),(9,152,186),(10,153,187),(11,154,188),(12,155,189),(13,156,163),(14,157,164),(15,158,165),(16,159,166),(17,160,167),(18,161,168),(19,162,169),(20,136,170),(21,137,171),(22,138,172),(23,139,173),(24,140,174),(25,141,175),(26,142,176),(27,143,177),(28,230,80),(29,231,81),(30,232,55),(31,233,56),(32,234,57),(33,235,58),(34,236,59),(35,237,60),(36,238,61),(37,239,62),(38,240,63),(39,241,64),(40,242,65),(41,243,66),(42,217,67),(43,218,68),(44,219,69),(45,220,70),(46,221,71),(47,222,72),(48,223,73),(49,224,74),(50,225,75),(51,226,76),(52,227,77),(53,228,78),(54,229,79),(82,123,207),(83,124,208),(84,125,209),(85,126,210),(86,127,211),(87,128,212),(88,129,213),(89,130,214),(90,131,215),(91,132,216),(92,133,190),(93,134,191),(94,135,192),(95,109,193),(96,110,194),(97,111,195),(98,112,196),(99,113,197),(100,114,198),(101,115,199),(102,116,200),(103,117,201),(104,118,202),(105,119,203),(106,120,204),(107,121,205),(108,122,206)], [(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)], [(2,27),(3,26),(4,25),(5,24),(6,23),(7,22),(8,21),(9,20),(10,19),(11,18),(12,17),(13,16),(14,15),(28,205),(29,204),(30,203),(31,202),(32,201),(33,200),(34,199),(35,198),(36,197),(37,196),(38,195),(39,194),(40,193),(41,192),(42,191),(43,190),(44,216),(45,215),(46,214),(47,213),(48,212),(49,211),(50,210),(51,209),(52,208),(53,207),(54,206),(55,105),(56,104),(57,103),(58,102),(59,101),(60,100),(61,99),(62,98),(63,97),(64,96),(65,95),(66,94),(67,93),(68,92),(69,91),(70,90),(71,89),(72,88),(73,87),(74,86),(75,85),(76,84),(77,83),(78,82),(79,108),(80,107),(81,106),(109,242),(110,241),(111,240),(112,239),(113,238),(114,237),(115,236),(116,235),(117,234),(118,233),(119,232),(120,231),(121,230),(122,229),(123,228),(124,227),(125,226),(126,225),(127,224),(128,223),(129,222),(130,221),(131,220),(132,219),(133,218),(134,217),(135,243),(136,186),(137,185),(138,184),(139,183),(140,182),(141,181),(142,180),(143,179),(144,178),(145,177),(146,176),(147,175),(148,174),(149,173),(150,172),(151,171),(152,170),(153,169),(154,168),(155,167),(156,166),(157,165),(158,164),(159,163),(160,189),(161,188),(162,187)]])
123 conjugacy classes
| class | 1 | 2 | 3A | ··· | 3M | 9A | ··· | 9AA | 27A | ··· | 27CC |
| order | 1 | 2 | 3 | ··· | 3 | 9 | ··· | 9 | 27 | ··· | 27 |
| size | 1 | 243 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
123 irreducible representations
| dim | 1 | 1 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + |
| image | C1 | C2 | S3 | S3 | D9 | D9 | D27 |
| kernel | C32⋊4D27 | C32×C27 | C3×C27 | C32×C9 | C3×C9 | C33 | C32 |
| # reps | 1 | 1 | 12 | 1 | 24 | 3 | 81 |
Matrix representation of C32⋊4D27 ►in GL6(𝔽109)
| 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 | 108 | 1 |
| 0 | 0 | 0 | 0 | 108 | 0 |
| 108 | 108 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 108 | 108 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 108 |
| 0 | 0 | 0 | 0 | 1 | 108 |
| 27 | 59 | 0 | 0 | 0 | 0 |
| 50 | 77 | 0 | 0 | 0 | 0 |
| 0 | 0 | 58 | 87 | 0 | 0 |
| 0 | 0 | 22 | 80 | 0 | 0 |
| 0 | 0 | 0 | 0 | 102 | 99 |
| 0 | 0 | 0 | 0 | 10 | 92 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 108 | 108 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 10 | 0 | 0 |
| 0 | 0 | 102 | 92 | 0 | 0 |
| 0 | 0 | 0 | 0 | 59 | 82 |
| 0 | 0 | 0 | 0 | 32 | 50 |
G:=sub<GL(6,GF(109))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,108,108,0,0,0,0,1,0],[108,1,0,0,0,0,108,0,0,0,0,0,0,0,108,1,0,0,0,0,108,0,0,0,0,0,0,0,0,1,0,0,0,0,108,108],[27,50,0,0,0,0,59,77,0,0,0,0,0,0,58,22,0,0,0,0,87,80,0,0,0,0,0,0,102,10,0,0,0,0,99,92],[1,108,0,0,0,0,0,108,0,0,0,0,0,0,17,102,0,0,0,0,10,92,0,0,0,0,0,0,59,32,0,0,0,0,82,50] >;
C32⋊4D27 in GAP, Magma, Sage, TeX
C_3^2\rtimes_4D_{27} % in TeX
G:=Group("C3^2:4D27"); // GroupNames label
G:=SmallGroup(486,184);
// by ID
G=gap.SmallGroup(486,184);
# by ID
G:=PCGroup([6,-2,-3,-3,-3,-3,-3,697,1627,218,867,8104,208,11669]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^3=c^27=d^2=1,a*b=b*a,a*c=c*a,d*a*d=a^-1,b*c=c*b,d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations