direct product, metabelian, soluble, monomial, A-group
Aliases: C13×C3.A4, C22⋊C117, C39.2A4, (C2×C26)⋊1C9, C3.(A4×C13), (C2×C6).C39, (C2×C78).1C3, SmallGroup(468,13)
Series: Derived ►Chief ►Lower central ►Upper central
| C22 — C13×C3.A4 |
Generators and relations for C13×C3.A4
G = < a,b,c,d,e | a13=b3=c2=d2=1, e3=b, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, ece-1=cd=dc, ede-1=c >
Smallest permutation representation of C13×C3.A4
►On 234 points
Generators in S234
(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)
(1 101 189)(2 102 190)(3 103 191)(4 104 192)(5 92 193)(6 93 194)(7 94 195)(8 95 183)(9 96 184)(10 97 185)(11 98 186)(12 99 187)(13 100 188)(14 171 132)(15 172 133)(16 173 134)(17 174 135)(18 175 136)(19 176 137)(20 177 138)(21 178 139)(22 179 140)(23 180 141)(24 181 142)(25 182 143)(26 170 131)(27 48 86)(28 49 87)(29 50 88)(30 51 89)(31 52 90)(32 40 91)(33 41 79)(34 42 80)(35 43 81)(36 44 82)(37 45 83)(38 46 84)(39 47 85)(53 129 199)(54 130 200)(55 118 201)(56 119 202)(57 120 203)(58 121 204)(59 122 205)(60 123 206)(61 124 207)(62 125 208)(63 126 196)(64 127 197)(65 128 198)(66 151 232)(67 152 233)(68 153 234)(69 154 222)(70 155 223)(71 156 224)(72 144 225)(73 145 226)(74 146 227)(75 147 228)(76 148 229)(77 149 230)(78 150 231)(105 162 209)(106 163 210)(107 164 211)(108 165 212)(109 166 213)(110 167 214)(111 168 215)(112 169 216)(113 157 217)(114 158 218)(115 159 219)(116 160 220)(117 161 221)
(1 88)(2 89)(3 90)(4 91)(5 79)(6 80)(7 81)(8 82)(9 83)(10 84)(11 85)(12 86)(13 87)(27 99)(28 100)(29 101)(30 102)(31 103)(32 104)(33 92)(34 93)(35 94)(36 95)(37 96)(38 97)(39 98)(40 192)(41 193)(42 194)(43 195)(44 183)(45 184)(46 185)(47 186)(48 187)(49 188)(50 189)(51 190)(52 191)(66 116)(67 117)(68 105)(69 106)(70 107)(71 108)(72 109)(73 110)(74 111)(75 112)(76 113)(77 114)(78 115)(144 166)(145 167)(146 168)(147 169)(148 157)(149 158)(150 159)(151 160)(152 161)(153 162)(154 163)(155 164)(156 165)(209 234)(210 222)(211 223)(212 224)(213 225)(214 226)(215 227)(216 228)(217 229)(218 230)(219 231)(220 232)(221 233)
(1 88)(2 89)(3 90)(4 91)(5 79)(6 80)(7 81)(8 82)(9 83)(10 84)(11 85)(12 86)(13 87)(14 125)(15 126)(16 127)(17 128)(18 129)(19 130)(20 118)(21 119)(22 120)(23 121)(24 122)(25 123)(26 124)(27 99)(28 100)(29 101)(30 102)(31 103)(32 104)(33 92)(34 93)(35 94)(36 95)(37 96)(38 97)(39 98)(40 192)(41 193)(42 194)(43 195)(44 183)(45 184)(46 185)(47 186)(48 187)(49 188)(50 189)(51 190)(52 191)(53 136)(54 137)(55 138)(56 139)(57 140)(58 141)(59 142)(60 143)(61 131)(62 132)(63 133)(64 134)(65 135)(170 207)(171 208)(172 196)(173 197)(174 198)(175 199)(176 200)(177 201)(178 202)(179 203)(180 204)(181 205)(182 206)
(1 172 112 101 133 169 189 15 216)(2 173 113 102 134 157 190 16 217)(3 174 114 103 135 158 191 17 218)(4 175 115 104 136 159 192 18 219)(5 176 116 92 137 160 193 19 220)(6 177 117 93 138 161 194 20 221)(7 178 105 94 139 162 195 21 209)(8 179 106 95 140 163 183 22 210)(9 180 107 96 141 164 184 23 211)(10 181 108 97 142 165 185 24 212)(11 182 109 98 143 166 186 25 213)(12 170 110 99 131 167 187 26 214)(13 171 111 100 132 168 188 14 215)(27 61 145 48 124 226 86 207 73)(28 62 146 49 125 227 87 208 74)(29 63 147 50 126 228 88 196 75)(30 64 148 51 127 229 89 197 76)(31 65 149 52 128 230 90 198 77)(32 53 150 40 129 231 91 199 78)(33 54 151 41 130 232 79 200 66)(34 55 152 42 118 233 80 201 67)(35 56 153 43 119 234 81 202 68)(36 57 154 44 120 222 82 203 69)(37 58 155 45 121 223 83 204 70)(38 59 156 46 122 224 84 205 71)(39 60 144 47 123 225 85 206 72)
G:=sub<Sym(234)| (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), (1,101,189)(2,102,190)(3,103,191)(4,104,192)(5,92,193)(6,93,194)(7,94,195)(8,95,183)(9,96,184)(10,97,185)(11,98,186)(12,99,187)(13,100,188)(14,171,132)(15,172,133)(16,173,134)(17,174,135)(18,175,136)(19,176,137)(20,177,138)(21,178,139)(22,179,140)(23,180,141)(24,181,142)(25,182,143)(26,170,131)(27,48,86)(28,49,87)(29,50,88)(30,51,89)(31,52,90)(32,40,91)(33,41,79)(34,42,80)(35,43,81)(36,44,82)(37,45,83)(38,46,84)(39,47,85)(53,129,199)(54,130,200)(55,118,201)(56,119,202)(57,120,203)(58,121,204)(59,122,205)(60,123,206)(61,124,207)(62,125,208)(63,126,196)(64,127,197)(65,128,198)(66,151,232)(67,152,233)(68,153,234)(69,154,222)(70,155,223)(71,156,224)(72,144,225)(73,145,226)(74,146,227)(75,147,228)(76,148,229)(77,149,230)(78,150,231)(105,162,209)(106,163,210)(107,164,211)(108,165,212)(109,166,213)(110,167,214)(111,168,215)(112,169,216)(113,157,217)(114,158,218)(115,159,219)(116,160,220)(117,161,221), (1,88)(2,89)(3,90)(4,91)(5,79)(6,80)(7,81)(8,82)(9,83)(10,84)(11,85)(12,86)(13,87)(27,99)(28,100)(29,101)(30,102)(31,103)(32,104)(33,92)(34,93)(35,94)(36,95)(37,96)(38,97)(39,98)(40,192)(41,193)(42,194)(43,195)(44,183)(45,184)(46,185)(47,186)(48,187)(49,188)(50,189)(51,190)(52,191)(66,116)(67,117)(68,105)(69,106)(70,107)(71,108)(72,109)(73,110)(74,111)(75,112)(76,113)(77,114)(78,115)(144,166)(145,167)(146,168)(147,169)(148,157)(149,158)(150,159)(151,160)(152,161)(153,162)(154,163)(155,164)(156,165)(209,234)(210,222)(211,223)(212,224)(213,225)(214,226)(215,227)(216,228)(217,229)(218,230)(219,231)(220,232)(221,233), (1,88)(2,89)(3,90)(4,91)(5,79)(6,80)(7,81)(8,82)(9,83)(10,84)(11,85)(12,86)(13,87)(14,125)(15,126)(16,127)(17,128)(18,129)(19,130)(20,118)(21,119)(22,120)(23,121)(24,122)(25,123)(26,124)(27,99)(28,100)(29,101)(30,102)(31,103)(32,104)(33,92)(34,93)(35,94)(36,95)(37,96)(38,97)(39,98)(40,192)(41,193)(42,194)(43,195)(44,183)(45,184)(46,185)(47,186)(48,187)(49,188)(50,189)(51,190)(52,191)(53,136)(54,137)(55,138)(56,139)(57,140)(58,141)(59,142)(60,143)(61,131)(62,132)(63,133)(64,134)(65,135)(170,207)(171,208)(172,196)(173,197)(174,198)(175,199)(176,200)(177,201)(178,202)(179,203)(180,204)(181,205)(182,206), (1,172,112,101,133,169,189,15,216)(2,173,113,102,134,157,190,16,217)(3,174,114,103,135,158,191,17,218)(4,175,115,104,136,159,192,18,219)(5,176,116,92,137,160,193,19,220)(6,177,117,93,138,161,194,20,221)(7,178,105,94,139,162,195,21,209)(8,179,106,95,140,163,183,22,210)(9,180,107,96,141,164,184,23,211)(10,181,108,97,142,165,185,24,212)(11,182,109,98,143,166,186,25,213)(12,170,110,99,131,167,187,26,214)(13,171,111,100,132,168,188,14,215)(27,61,145,48,124,226,86,207,73)(28,62,146,49,125,227,87,208,74)(29,63,147,50,126,228,88,196,75)(30,64,148,51,127,229,89,197,76)(31,65,149,52,128,230,90,198,77)(32,53,150,40,129,231,91,199,78)(33,54,151,41,130,232,79,200,66)(34,55,152,42,118,233,80,201,67)(35,56,153,43,119,234,81,202,68)(36,57,154,44,120,222,82,203,69)(37,58,155,45,121,223,83,204,70)(38,59,156,46,122,224,84,205,71)(39,60,144,47,123,225,85,206,72)>;
G:=Group( (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), (1,101,189)(2,102,190)(3,103,191)(4,104,192)(5,92,193)(6,93,194)(7,94,195)(8,95,183)(9,96,184)(10,97,185)(11,98,186)(12,99,187)(13,100,188)(14,171,132)(15,172,133)(16,173,134)(17,174,135)(18,175,136)(19,176,137)(20,177,138)(21,178,139)(22,179,140)(23,180,141)(24,181,142)(25,182,143)(26,170,131)(27,48,86)(28,49,87)(29,50,88)(30,51,89)(31,52,90)(32,40,91)(33,41,79)(34,42,80)(35,43,81)(36,44,82)(37,45,83)(38,46,84)(39,47,85)(53,129,199)(54,130,200)(55,118,201)(56,119,202)(57,120,203)(58,121,204)(59,122,205)(60,123,206)(61,124,207)(62,125,208)(63,126,196)(64,127,197)(65,128,198)(66,151,232)(67,152,233)(68,153,234)(69,154,222)(70,155,223)(71,156,224)(72,144,225)(73,145,226)(74,146,227)(75,147,228)(76,148,229)(77,149,230)(78,150,231)(105,162,209)(106,163,210)(107,164,211)(108,165,212)(109,166,213)(110,167,214)(111,168,215)(112,169,216)(113,157,217)(114,158,218)(115,159,219)(116,160,220)(117,161,221), (1,88)(2,89)(3,90)(4,91)(5,79)(6,80)(7,81)(8,82)(9,83)(10,84)(11,85)(12,86)(13,87)(27,99)(28,100)(29,101)(30,102)(31,103)(32,104)(33,92)(34,93)(35,94)(36,95)(37,96)(38,97)(39,98)(40,192)(41,193)(42,194)(43,195)(44,183)(45,184)(46,185)(47,186)(48,187)(49,188)(50,189)(51,190)(52,191)(66,116)(67,117)(68,105)(69,106)(70,107)(71,108)(72,109)(73,110)(74,111)(75,112)(76,113)(77,114)(78,115)(144,166)(145,167)(146,168)(147,169)(148,157)(149,158)(150,159)(151,160)(152,161)(153,162)(154,163)(155,164)(156,165)(209,234)(210,222)(211,223)(212,224)(213,225)(214,226)(215,227)(216,228)(217,229)(218,230)(219,231)(220,232)(221,233), (1,88)(2,89)(3,90)(4,91)(5,79)(6,80)(7,81)(8,82)(9,83)(10,84)(11,85)(12,86)(13,87)(14,125)(15,126)(16,127)(17,128)(18,129)(19,130)(20,118)(21,119)(22,120)(23,121)(24,122)(25,123)(26,124)(27,99)(28,100)(29,101)(30,102)(31,103)(32,104)(33,92)(34,93)(35,94)(36,95)(37,96)(38,97)(39,98)(40,192)(41,193)(42,194)(43,195)(44,183)(45,184)(46,185)(47,186)(48,187)(49,188)(50,189)(51,190)(52,191)(53,136)(54,137)(55,138)(56,139)(57,140)(58,141)(59,142)(60,143)(61,131)(62,132)(63,133)(64,134)(65,135)(170,207)(171,208)(172,196)(173,197)(174,198)(175,199)(176,200)(177,201)(178,202)(179,203)(180,204)(181,205)(182,206), (1,172,112,101,133,169,189,15,216)(2,173,113,102,134,157,190,16,217)(3,174,114,103,135,158,191,17,218)(4,175,115,104,136,159,192,18,219)(5,176,116,92,137,160,193,19,220)(6,177,117,93,138,161,194,20,221)(7,178,105,94,139,162,195,21,209)(8,179,106,95,140,163,183,22,210)(9,180,107,96,141,164,184,23,211)(10,181,108,97,142,165,185,24,212)(11,182,109,98,143,166,186,25,213)(12,170,110,99,131,167,187,26,214)(13,171,111,100,132,168,188,14,215)(27,61,145,48,124,226,86,207,73)(28,62,146,49,125,227,87,208,74)(29,63,147,50,126,228,88,196,75)(30,64,148,51,127,229,89,197,76)(31,65,149,52,128,230,90,198,77)(32,53,150,40,129,231,91,199,78)(33,54,151,41,130,232,79,200,66)(34,55,152,42,118,233,80,201,67)(35,56,153,43,119,234,81,202,68)(36,57,154,44,120,222,82,203,69)(37,58,155,45,121,223,83,204,70)(38,59,156,46,122,224,84,205,71)(39,60,144,47,123,225,85,206,72) );
G=PermutationGroup([[(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)], [(1,101,189),(2,102,190),(3,103,191),(4,104,192),(5,92,193),(6,93,194),(7,94,195),(8,95,183),(9,96,184),(10,97,185),(11,98,186),(12,99,187),(13,100,188),(14,171,132),(15,172,133),(16,173,134),(17,174,135),(18,175,136),(19,176,137),(20,177,138),(21,178,139),(22,179,140),(23,180,141),(24,181,142),(25,182,143),(26,170,131),(27,48,86),(28,49,87),(29,50,88),(30,51,89),(31,52,90),(32,40,91),(33,41,79),(34,42,80),(35,43,81),(36,44,82),(37,45,83),(38,46,84),(39,47,85),(53,129,199),(54,130,200),(55,118,201),(56,119,202),(57,120,203),(58,121,204),(59,122,205),(60,123,206),(61,124,207),(62,125,208),(63,126,196),(64,127,197),(65,128,198),(66,151,232),(67,152,233),(68,153,234),(69,154,222),(70,155,223),(71,156,224),(72,144,225),(73,145,226),(74,146,227),(75,147,228),(76,148,229),(77,149,230),(78,150,231),(105,162,209),(106,163,210),(107,164,211),(108,165,212),(109,166,213),(110,167,214),(111,168,215),(112,169,216),(113,157,217),(114,158,218),(115,159,219),(116,160,220),(117,161,221)], [(1,88),(2,89),(3,90),(4,91),(5,79),(6,80),(7,81),(8,82),(9,83),(10,84),(11,85),(12,86),(13,87),(27,99),(28,100),(29,101),(30,102),(31,103),(32,104),(33,92),(34,93),(35,94),(36,95),(37,96),(38,97),(39,98),(40,192),(41,193),(42,194),(43,195),(44,183),(45,184),(46,185),(47,186),(48,187),(49,188),(50,189),(51,190),(52,191),(66,116),(67,117),(68,105),(69,106),(70,107),(71,108),(72,109),(73,110),(74,111),(75,112),(76,113),(77,114),(78,115),(144,166),(145,167),(146,168),(147,169),(148,157),(149,158),(150,159),(151,160),(152,161),(153,162),(154,163),(155,164),(156,165),(209,234),(210,222),(211,223),(212,224),(213,225),(214,226),(215,227),(216,228),(217,229),(218,230),(219,231),(220,232),(221,233)], [(1,88),(2,89),(3,90),(4,91),(5,79),(6,80),(7,81),(8,82),(9,83),(10,84),(11,85),(12,86),(13,87),(14,125),(15,126),(16,127),(17,128),(18,129),(19,130),(20,118),(21,119),(22,120),(23,121),(24,122),(25,123),(26,124),(27,99),(28,100),(29,101),(30,102),(31,103),(32,104),(33,92),(34,93),(35,94),(36,95),(37,96),(38,97),(39,98),(40,192),(41,193),(42,194),(43,195),(44,183),(45,184),(46,185),(47,186),(48,187),(49,188),(50,189),(51,190),(52,191),(53,136),(54,137),(55,138),(56,139),(57,140),(58,141),(59,142),(60,143),(61,131),(62,132),(63,133),(64,134),(65,135),(170,207),(171,208),(172,196),(173,197),(174,198),(175,199),(176,200),(177,201),(178,202),(179,203),(180,204),(181,205),(182,206)], [(1,172,112,101,133,169,189,15,216),(2,173,113,102,134,157,190,16,217),(3,174,114,103,135,158,191,17,218),(4,175,115,104,136,159,192,18,219),(5,176,116,92,137,160,193,19,220),(6,177,117,93,138,161,194,20,221),(7,178,105,94,139,162,195,21,209),(8,179,106,95,140,163,183,22,210),(9,180,107,96,141,164,184,23,211),(10,181,108,97,142,165,185,24,212),(11,182,109,98,143,166,186,25,213),(12,170,110,99,131,167,187,26,214),(13,171,111,100,132,168,188,14,215),(27,61,145,48,124,226,86,207,73),(28,62,146,49,125,227,87,208,74),(29,63,147,50,126,228,88,196,75),(30,64,148,51,127,229,89,197,76),(31,65,149,52,128,230,90,198,77),(32,53,150,40,129,231,91,199,78),(33,54,151,41,130,232,79,200,66),(34,55,152,42,118,233,80,201,67),(35,56,153,43,119,234,81,202,68),(36,57,154,44,120,222,82,203,69),(37,58,155,45,121,223,83,204,70),(38,59,156,46,122,224,84,205,71),(39,60,144,47,123,225,85,206,72)]])
156 conjugacy classes
| class | 1 | 2 | 3A | 3B | 6A | 6B | 9A | ··· | 9F | 13A | ··· | 13L | 26A | ··· | 26L | 39A | ··· | 39X | 78A | ··· | 78X | 117A | ··· | 117BT |
| order | 1 | 2 | 3 | 3 | 6 | 6 | 9 | ··· | 9 | 13 | ··· | 13 | 26 | ··· | 26 | 39 | ··· | 39 | 78 | ··· | 78 | 117 | ··· | 117 |
| size | 1 | 3 | 1 | 1 | 3 | 3 | 4 | ··· | 4 | 1 | ··· | 1 | 3 | ··· | 3 | 1 | ··· | 1 | 3 | ··· | 3 | 4 | ··· | 4 |
156 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 3 | 3 | 3 |
| type | + | + | ||||||||
| image | C1 | C3 | C9 | C13 | C39 | C117 | A4 | C3.A4 | A4×C13 | C13×C3.A4 |
| kernel | C13×C3.A4 | C2×C78 | C2×C26 | C3.A4 | C2×C6 | C22 | C39 | C13 | C3 | C1 |
| # reps | 1 | 2 | 6 | 12 | 24 | 72 | 1 | 2 | 12 | 24 |
Matrix representation of C13×C3.A4 ►in GL4(𝔽937) generated by
| 721 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 322 | 0 | 0 |
| 0 | 0 | 322 | 0 |
| 0 | 0 | 0 | 322 |
| 1 | 0 | 0 | 0 |
| 0 | 936 | 0 | 0 |
| 0 | 0 | 936 | 0 |
| 0 | 638 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 936 | 0 | 0 |
| 0 | 661 | 1 | 0 |
| 0 | 0 | 0 | 936 |
| 1 | 0 | 0 | 0 |
| 0 | 276 | 935 | 0 |
| 0 | 927 | 661 | 1 |
| 0 | 810 | 638 | 0 |
G:=sub<GL(4,GF(937))| [721,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,322,0,0,0,0,322,0,0,0,0,322],[1,0,0,0,0,936,0,638,0,0,936,0,0,0,0,1],[1,0,0,0,0,936,661,0,0,0,1,0,0,0,0,936],[1,0,0,0,0,276,927,810,0,935,661,638,0,0,1,0] >;
C13×C3.A4 in GAP, Magma, Sage, TeX
C_{13}\times C_3.A_4 % in TeX
G:=Group("C13xC3.A4"); // GroupNames label
G:=SmallGroup(468,13);
// by ID
G=gap.SmallGroup(468,13);
# by ID
G:=PCGroup([5,-3,-13,-3,-2,2,195,4683,8779]);
// Polycyclic
G:=Group<a,b,c,d,e|a^13=b^3=c^2=d^2=1,e^3=b,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,e*c*e^-1=c*d=d*c,e*d*e^-1=c>;
// generators/relations
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