metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×C14).40D8, C14.49(C2×D8), C4⋊C4.227D14, C28⋊7D4.9C2, (C2×C28).283D4, C14.D8⋊25C2, C4.86(C4○D28), C28.55D4⋊4C2, C28.Q8⋊25C2, C22.9(D4⋊D7), (C22×C4).94D14, C7⋊4(C22.D8), C28.174(C4○D4), (C2×C28).320C23, (C2×D28).90C22, (C22×C14).185D4, C23.77(C7⋊D4), C2.6(C28.C23), C14.84(C8.C22), C4⋊Dic7.130C22, (C22×C28).135C22, C2.8(C23.23D14), C14.58(C22.D4), (C2×C4⋊C4)⋊3D7, (C14×C4⋊C4)⋊3C2, C2.5(C2×D4⋊D7), (C2×C7⋊C8).81C22, (C2×C14).440(C2×D4), (C2×C4).31(C7⋊D4), (C7×C4⋊C4).258C22, (C2×C4).420(C22×D7), C22.130(C2×C7⋊D4), SmallGroup(448,501)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×C14).40D8
G = < a,b,c,d | a14=b2=c8=1, d2=a7, ab=ba, cac-1=a-1, ad=da, cbc-1=a7b, bd=db, dcd-1=c-1 >
Subgroups: 580 in 114 conjugacy classes, 43 normal (25 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C22×C4, C22×C4, C2×D4, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C14, C22⋊C8, D4⋊C4, C2.D8, C2×C4⋊C4, C4⋊D4, C7⋊C8, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C22×D7, C22×C14, C22.D8, C2×C7⋊C8, C4⋊Dic7, D14⋊C4, C7×C4⋊C4, C7×C4⋊C4, C2×D28, C2×C7⋊D4, C22×C28, C22×C28, C28.Q8, C14.D8, C28.55D4, C28⋊7D4, C14×C4⋊C4, (C2×C14).40D8
Quotients: C1, C2, C22, D4, C23, D7, D8, C2×D4, C4○D4, D14, C22.D4, C2×D8, C8.C22, C7⋊D4, C22×D7, C22.D8, D4⋊D7, C4○D28, C2×C7⋊D4, C23.23D14, C2×D4⋊D7, C28.C23, (C2×C14).40D8
►On 224 points
Generators in S224
(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)
(1 114)(2 115)(3 116)(4 117)(5 118)(6 119)(7 120)(8 121)(9 122)(10 123)(11 124)(12 125)(13 126)(14 113)(15 146)(16 147)(17 148)(18 149)(19 150)(20 151)(21 152)(22 153)(23 154)(24 141)(25 142)(26 143)(27 144)(28 145)(29 63)(30 64)(31 65)(32 66)(33 67)(34 68)(35 69)(36 70)(37 57)(38 58)(39 59)(40 60)(41 61)(42 62)(43 83)(44 84)(45 71)(46 72)(47 73)(48 74)(49 75)(50 76)(51 77)(52 78)(53 79)(54 80)(55 81)(56 82)(85 127)(86 128)(87 129)(88 130)(89 131)(90 132)(91 133)(92 134)(93 135)(94 136)(95 137)(96 138)(97 139)(98 140)(99 210)(100 197)(101 198)(102 199)(103 200)(104 201)(105 202)(106 203)(107 204)(108 205)(109 206)(110 207)(111 208)(112 209)(155 186)(156 187)(157 188)(158 189)(159 190)(160 191)(161 192)(162 193)(163 194)(164 195)(165 196)(166 183)(167 184)(168 185)(169 211)(170 212)(171 213)(172 214)(173 215)(174 216)(175 217)(176 218)(177 219)(178 220)(179 221)(180 222)(181 223)(182 224)
(1 192 131 75 114 168 89 56)(2 191 132 74 115 167 90 55)(3 190 133 73 116 166 91 54)(4 189 134 72 117 165 92 53)(5 188 135 71 118 164 93 52)(6 187 136 84 119 163 94 51)(7 186 137 83 120 162 95 50)(8 185 138 82 121 161 96 49)(9 184 139 81 122 160 97 48)(10 183 140 80 123 159 98 47)(11 196 127 79 124 158 85 46)(12 195 128 78 125 157 86 45)(13 194 129 77 126 156 87 44)(14 193 130 76 113 155 88 43)(15 112 34 213 146 202 68 178)(16 111 35 212 147 201 69 177)(17 110 36 211 148 200 70 176)(18 109 37 224 149 199 57 175)(19 108 38 223 150 198 58 174)(20 107 39 222 151 197 59 173)(21 106 40 221 152 210 60 172)(22 105 41 220 153 209 61 171)(23 104 42 219 154 208 62 170)(24 103 29 218 141 207 63 169)(25 102 30 217 142 206 64 182)(26 101 31 216 143 205 65 181)(27 100 32 215 144 204 66 180)(28 99 33 214 145 203 67 179)
(1 19 8 26)(2 20 9 27)(3 21 10 28)(4 22 11 15)(5 23 12 16)(6 24 13 17)(7 25 14 18)(29 87 36 94)(30 88 37 95)(31 89 38 96)(32 90 39 97)(33 91 40 98)(34 92 41 85)(35 93 42 86)(43 109 50 102)(44 110 51 103)(45 111 52 104)(46 112 53 105)(47 99 54 106)(48 100 55 107)(49 101 56 108)(57 137 64 130)(58 138 65 131)(59 139 66 132)(60 140 67 133)(61 127 68 134)(62 128 69 135)(63 129 70 136)(71 208 78 201)(72 209 79 202)(73 210 80 203)(74 197 81 204)(75 198 82 205)(76 199 83 206)(77 200 84 207)(113 149 120 142)(114 150 121 143)(115 151 122 144)(116 152 123 145)(117 153 124 146)(118 154 125 147)(119 141 126 148)(155 224 162 217)(156 211 163 218)(157 212 164 219)(158 213 165 220)(159 214 166 221)(160 215 167 222)(161 216 168 223)(169 194 176 187)(170 195 177 188)(171 196 178 189)(172 183 179 190)(173 184 180 191)(174 185 181 192)(175 186 182 193)
G:=sub<Sym(224)| (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), (1,114)(2,115)(3,116)(4,117)(5,118)(6,119)(7,120)(8,121)(9,122)(10,123)(11,124)(12,125)(13,126)(14,113)(15,146)(16,147)(17,148)(18,149)(19,150)(20,151)(21,152)(22,153)(23,154)(24,141)(25,142)(26,143)(27,144)(28,145)(29,63)(30,64)(31,65)(32,66)(33,67)(34,68)(35,69)(36,70)(37,57)(38,58)(39,59)(40,60)(41,61)(42,62)(43,83)(44,84)(45,71)(46,72)(47,73)(48,74)(49,75)(50,76)(51,77)(52,78)(53,79)(54,80)(55,81)(56,82)(85,127)(86,128)(87,129)(88,130)(89,131)(90,132)(91,133)(92,134)(93,135)(94,136)(95,137)(96,138)(97,139)(98,140)(99,210)(100,197)(101,198)(102,199)(103,200)(104,201)(105,202)(106,203)(107,204)(108,205)(109,206)(110,207)(111,208)(112,209)(155,186)(156,187)(157,188)(158,189)(159,190)(160,191)(161,192)(162,193)(163,194)(164,195)(165,196)(166,183)(167,184)(168,185)(169,211)(170,212)(171,213)(172,214)(173,215)(174,216)(175,217)(176,218)(177,219)(178,220)(179,221)(180,222)(181,223)(182,224), (1,192,131,75,114,168,89,56)(2,191,132,74,115,167,90,55)(3,190,133,73,116,166,91,54)(4,189,134,72,117,165,92,53)(5,188,135,71,118,164,93,52)(6,187,136,84,119,163,94,51)(7,186,137,83,120,162,95,50)(8,185,138,82,121,161,96,49)(9,184,139,81,122,160,97,48)(10,183,140,80,123,159,98,47)(11,196,127,79,124,158,85,46)(12,195,128,78,125,157,86,45)(13,194,129,77,126,156,87,44)(14,193,130,76,113,155,88,43)(15,112,34,213,146,202,68,178)(16,111,35,212,147,201,69,177)(17,110,36,211,148,200,70,176)(18,109,37,224,149,199,57,175)(19,108,38,223,150,198,58,174)(20,107,39,222,151,197,59,173)(21,106,40,221,152,210,60,172)(22,105,41,220,153,209,61,171)(23,104,42,219,154,208,62,170)(24,103,29,218,141,207,63,169)(25,102,30,217,142,206,64,182)(26,101,31,216,143,205,65,181)(27,100,32,215,144,204,66,180)(28,99,33,214,145,203,67,179), (1,19,8,26)(2,20,9,27)(3,21,10,28)(4,22,11,15)(5,23,12,16)(6,24,13,17)(7,25,14,18)(29,87,36,94)(30,88,37,95)(31,89,38,96)(32,90,39,97)(33,91,40,98)(34,92,41,85)(35,93,42,86)(43,109,50,102)(44,110,51,103)(45,111,52,104)(46,112,53,105)(47,99,54,106)(48,100,55,107)(49,101,56,108)(57,137,64,130)(58,138,65,131)(59,139,66,132)(60,140,67,133)(61,127,68,134)(62,128,69,135)(63,129,70,136)(71,208,78,201)(72,209,79,202)(73,210,80,203)(74,197,81,204)(75,198,82,205)(76,199,83,206)(77,200,84,207)(113,149,120,142)(114,150,121,143)(115,151,122,144)(116,152,123,145)(117,153,124,146)(118,154,125,147)(119,141,126,148)(155,224,162,217)(156,211,163,218)(157,212,164,219)(158,213,165,220)(159,214,166,221)(160,215,167,222)(161,216,168,223)(169,194,176,187)(170,195,177,188)(171,196,178,189)(172,183,179,190)(173,184,180,191)(174,185,181,192)(175,186,182,193)>;
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), (1,114)(2,115)(3,116)(4,117)(5,118)(6,119)(7,120)(8,121)(9,122)(10,123)(11,124)(12,125)(13,126)(14,113)(15,146)(16,147)(17,148)(18,149)(19,150)(20,151)(21,152)(22,153)(23,154)(24,141)(25,142)(26,143)(27,144)(28,145)(29,63)(30,64)(31,65)(32,66)(33,67)(34,68)(35,69)(36,70)(37,57)(38,58)(39,59)(40,60)(41,61)(42,62)(43,83)(44,84)(45,71)(46,72)(47,73)(48,74)(49,75)(50,76)(51,77)(52,78)(53,79)(54,80)(55,81)(56,82)(85,127)(86,128)(87,129)(88,130)(89,131)(90,132)(91,133)(92,134)(93,135)(94,136)(95,137)(96,138)(97,139)(98,140)(99,210)(100,197)(101,198)(102,199)(103,200)(104,201)(105,202)(106,203)(107,204)(108,205)(109,206)(110,207)(111,208)(112,209)(155,186)(156,187)(157,188)(158,189)(159,190)(160,191)(161,192)(162,193)(163,194)(164,195)(165,196)(166,183)(167,184)(168,185)(169,211)(170,212)(171,213)(172,214)(173,215)(174,216)(175,217)(176,218)(177,219)(178,220)(179,221)(180,222)(181,223)(182,224), (1,192,131,75,114,168,89,56)(2,191,132,74,115,167,90,55)(3,190,133,73,116,166,91,54)(4,189,134,72,117,165,92,53)(5,188,135,71,118,164,93,52)(6,187,136,84,119,163,94,51)(7,186,137,83,120,162,95,50)(8,185,138,82,121,161,96,49)(9,184,139,81,122,160,97,48)(10,183,140,80,123,159,98,47)(11,196,127,79,124,158,85,46)(12,195,128,78,125,157,86,45)(13,194,129,77,126,156,87,44)(14,193,130,76,113,155,88,43)(15,112,34,213,146,202,68,178)(16,111,35,212,147,201,69,177)(17,110,36,211,148,200,70,176)(18,109,37,224,149,199,57,175)(19,108,38,223,150,198,58,174)(20,107,39,222,151,197,59,173)(21,106,40,221,152,210,60,172)(22,105,41,220,153,209,61,171)(23,104,42,219,154,208,62,170)(24,103,29,218,141,207,63,169)(25,102,30,217,142,206,64,182)(26,101,31,216,143,205,65,181)(27,100,32,215,144,204,66,180)(28,99,33,214,145,203,67,179), (1,19,8,26)(2,20,9,27)(3,21,10,28)(4,22,11,15)(5,23,12,16)(6,24,13,17)(7,25,14,18)(29,87,36,94)(30,88,37,95)(31,89,38,96)(32,90,39,97)(33,91,40,98)(34,92,41,85)(35,93,42,86)(43,109,50,102)(44,110,51,103)(45,111,52,104)(46,112,53,105)(47,99,54,106)(48,100,55,107)(49,101,56,108)(57,137,64,130)(58,138,65,131)(59,139,66,132)(60,140,67,133)(61,127,68,134)(62,128,69,135)(63,129,70,136)(71,208,78,201)(72,209,79,202)(73,210,80,203)(74,197,81,204)(75,198,82,205)(76,199,83,206)(77,200,84,207)(113,149,120,142)(114,150,121,143)(115,151,122,144)(116,152,123,145)(117,153,124,146)(118,154,125,147)(119,141,126,148)(155,224,162,217)(156,211,163,218)(157,212,164,219)(158,213,165,220)(159,214,166,221)(160,215,167,222)(161,216,168,223)(169,194,176,187)(170,195,177,188)(171,196,178,189)(172,183,179,190)(173,184,180,191)(174,185,181,192)(175,186,182,193) );
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)], [(1,114),(2,115),(3,116),(4,117),(5,118),(6,119),(7,120),(8,121),(9,122),(10,123),(11,124),(12,125),(13,126),(14,113),(15,146),(16,147),(17,148),(18,149),(19,150),(20,151),(21,152),(22,153),(23,154),(24,141),(25,142),(26,143),(27,144),(28,145),(29,63),(30,64),(31,65),(32,66),(33,67),(34,68),(35,69),(36,70),(37,57),(38,58),(39,59),(40,60),(41,61),(42,62),(43,83),(44,84),(45,71),(46,72),(47,73),(48,74),(49,75),(50,76),(51,77),(52,78),(53,79),(54,80),(55,81),(56,82),(85,127),(86,128),(87,129),(88,130),(89,131),(90,132),(91,133),(92,134),(93,135),(94,136),(95,137),(96,138),(97,139),(98,140),(99,210),(100,197),(101,198),(102,199),(103,200),(104,201),(105,202),(106,203),(107,204),(108,205),(109,206),(110,207),(111,208),(112,209),(155,186),(156,187),(157,188),(158,189),(159,190),(160,191),(161,192),(162,193),(163,194),(164,195),(165,196),(166,183),(167,184),(168,185),(169,211),(170,212),(171,213),(172,214),(173,215),(174,216),(175,217),(176,218),(177,219),(178,220),(179,221),(180,222),(181,223),(182,224)], [(1,192,131,75,114,168,89,56),(2,191,132,74,115,167,90,55),(3,190,133,73,116,166,91,54),(4,189,134,72,117,165,92,53),(5,188,135,71,118,164,93,52),(6,187,136,84,119,163,94,51),(7,186,137,83,120,162,95,50),(8,185,138,82,121,161,96,49),(9,184,139,81,122,160,97,48),(10,183,140,80,123,159,98,47),(11,196,127,79,124,158,85,46),(12,195,128,78,125,157,86,45),(13,194,129,77,126,156,87,44),(14,193,130,76,113,155,88,43),(15,112,34,213,146,202,68,178),(16,111,35,212,147,201,69,177),(17,110,36,211,148,200,70,176),(18,109,37,224,149,199,57,175),(19,108,38,223,150,198,58,174),(20,107,39,222,151,197,59,173),(21,106,40,221,152,210,60,172),(22,105,41,220,153,209,61,171),(23,104,42,219,154,208,62,170),(24,103,29,218,141,207,63,169),(25,102,30,217,142,206,64,182),(26,101,31,216,143,205,65,181),(27,100,32,215,144,204,66,180),(28,99,33,214,145,203,67,179)], [(1,19,8,26),(2,20,9,27),(3,21,10,28),(4,22,11,15),(5,23,12,16),(6,24,13,17),(7,25,14,18),(29,87,36,94),(30,88,37,95),(31,89,38,96),(32,90,39,97),(33,91,40,98),(34,92,41,85),(35,93,42,86),(43,109,50,102),(44,110,51,103),(45,111,52,104),(46,112,53,105),(47,99,54,106),(48,100,55,107),(49,101,56,108),(57,137,64,130),(58,138,65,131),(59,139,66,132),(60,140,67,133),(61,127,68,134),(62,128,69,135),(63,129,70,136),(71,208,78,201),(72,209,79,202),(73,210,80,203),(74,197,81,204),(75,198,82,205),(76,199,83,206),(77,200,84,207),(113,149,120,142),(114,150,121,143),(115,151,122,144),(116,152,123,145),(117,153,124,146),(118,154,125,147),(119,141,126,148),(155,224,162,217),(156,211,163,218),(157,212,164,219),(158,213,165,220),(159,214,166,221),(160,215,167,222),(161,216,168,223),(169,194,176,187),(170,195,177,188),(171,196,178,189),(172,183,179,190),(173,184,180,191),(174,185,181,192),(175,186,182,193)]])
79 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | ··· | 4G | 4H | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 56 | 2 | 2 | 4 | ··· | 4 | 56 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 |
79 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | + | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | C4○D4 | D8 | D14 | D14 | C7⋊D4 | C7⋊D4 | C4○D28 | C8.C22 | D4⋊D7 | C28.C23 |
| kernel | (C2×C14).40D8 | C28.Q8 | C14.D8 | C28.55D4 | C28⋊7D4 | C14×C4⋊C4 | C2×C28 | C22×C14 | C2×C4⋊C4 | C28 | C2×C14 | C4⋊C4 | C22×C4 | C2×C4 | C23 | C4 | C14 | C22 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 4 | 6 | 3 | 6 | 6 | 24 | 1 | 6 | 6 |
Matrix representation of (C2×C14).40D8 ►in GL4(𝔽113) generated by
| 83 | 0 | 0 | 0 |
| 56 | 64 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 107 | 112 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 90 | 30 | 0 | 0 |
| 5 | 23 | 0 | 0 |
| 0 | 0 | 82 | 82 |
| 0 | 0 | 31 | 82 |
| 98 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 3 | 61 |
| 0 | 0 | 61 | 110 |
G:=sub<GL(4,GF(113))| [83,56,0,0,0,64,0,0,0,0,1,0,0,0,0,1],[1,107,0,0,0,112,0,0,0,0,112,0,0,0,0,112],[90,5,0,0,30,23,0,0,0,0,82,31,0,0,82,82],[98,0,0,0,0,98,0,0,0,0,3,61,0,0,61,110] >;
(C2×C14).40D8 in GAP, Magma, Sage, TeX
(C_2\times C_{14})._{40}D_8 % in TeX
G:=Group("(C2xC14).40D8"); // GroupNames label
G:=SmallGroup(448,501);
// by ID
G=gap.SmallGroup(448,501);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,254,100,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^2=c^8=1,d^2=a^7,a*b=b*a,c*a*c^-1=a^-1,a*d=d*a,c*b*c^-1=a^7*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations