direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C7⋊D16, D8⋊7D14, C14⋊2D16, C56.20D4, C28.20D8, D56⋊13C22, C56.23C23, C7⋊3(C2×D16), (C2×D8)⋊1D7, (C14×D8)⋊4C2, C7⋊C16⋊7C22, (C2×D56)⋊17C2, C4.8(D4⋊D7), (C2×C14).41D8, C14.62(C2×D8), (C7×D8)⋊7C22, C28.159(C2×D4), (C2×C8).233D14, (C2×C28).179D4, C8.13(C7⋊D4), C8.29(C22×D7), (C2×C56).85C22, C22.21(D4⋊D7), (C2×C7⋊C16)⋊6C2, C4.1(C2×C7⋊D4), C2.17(C2×D4⋊D7), (C2×C4).142(C7⋊D4), SmallGroup(448,680)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C7⋊D16
G = < a,b,c,d | a2=b7=c16=d2=1, ab=ba, ac=ca, ad=da, cbc-1=dbd=b-1, dcd=c-1 >
Subgroups: 676 in 98 conjugacy classes, 39 normal (23 characteristic)
C1, C2, C2, C2, C4, C22, C22, C7, C8, C2×C4, D4, C23, D7, C14, C14, C14, C16, C2×C8, D8, D8, C2×D4, C28, D14, C2×C14, C2×C14, C2×C16, D16, C2×D8, C2×D8, C56, D28, C2×C28, C7×D4, C22×D7, C22×C14, C2×D16, C7⋊C16, D56, D56, C2×C56, C7×D8, C7×D8, C2×D28, D4×C14, C2×C7⋊C16, C7⋊D16, C2×D56, C14×D8, C2×C7⋊D16
Quotients: C1, C2, C22, D4, C23, D7, D8, C2×D4, D14, D16, C2×D8, C7⋊D4, C22×D7, C2×D16, D4⋊D7, C2×C7⋊D4, C7⋊D16, C2×D4⋊D7, C2×C7⋊D16
►On 224 points
Generators in S224
(1 45)(2 46)(3 47)(4 48)(5 33)(6 34)(7 35)(8 36)(9 37)(10 38)(11 39)(12 40)(13 41)(14 42)(15 43)(16 44)(17 145)(18 146)(19 147)(20 148)(21 149)(22 150)(23 151)(24 152)(25 153)(26 154)(27 155)(28 156)(29 157)(30 158)(31 159)(32 160)(49 187)(50 188)(51 189)(52 190)(53 191)(54 192)(55 177)(56 178)(57 179)(58 180)(59 181)(60 182)(61 183)(62 184)(63 185)(64 186)(65 216)(66 217)(67 218)(68 219)(69 220)(70 221)(71 222)(72 223)(73 224)(74 209)(75 210)(76 211)(77 212)(78 213)(79 214)(80 215)(81 127)(82 128)(83 113)(84 114)(85 115)(86 116)(87 117)(88 118)(89 119)(90 120)(91 121)(92 122)(93 123)(94 124)(95 125)(96 126)(97 132)(98 133)(99 134)(100 135)(101 136)(102 137)(103 138)(104 139)(105 140)(106 141)(107 142)(108 143)(109 144)(110 129)(111 130)(112 131)(161 197)(162 198)(163 199)(164 200)(165 201)(166 202)(167 203)(168 204)(169 205)(170 206)(171 207)(172 208)(173 193)(174 194)(175 195)(176 196)
(1 129 25 182 162 217 120)(2 121 218 163 183 26 130)(3 131 27 184 164 219 122)(4 123 220 165 185 28 132)(5 133 29 186 166 221 124)(6 125 222 167 187 30 134)(7 135 31 188 168 223 126)(8 127 224 169 189 32 136)(9 137 17 190 170 209 128)(10 113 210 171 191 18 138)(11 139 19 192 172 211 114)(12 115 212 173 177 20 140)(13 141 21 178 174 213 116)(14 117 214 175 179 22 142)(15 143 23 180 176 215 118)(16 119 216 161 181 24 144)(33 98 157 64 202 70 94)(34 95 71 203 49 158 99)(35 100 159 50 204 72 96)(36 81 73 205 51 160 101)(37 102 145 52 206 74 82)(38 83 75 207 53 146 103)(39 104 147 54 208 76 84)(40 85 77 193 55 148 105)(41 106 149 56 194 78 86)(42 87 79 195 57 150 107)(43 108 151 58 196 80 88)(44 89 65 197 59 152 109)(45 110 153 60 198 66 90)(46 91 67 199 61 154 111)(47 112 155 62 200 68 92)(48 93 69 201 63 156 97)
(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)
(2 16)(3 15)(4 14)(5 13)(6 12)(7 11)(8 10)(17 209)(18 224)(19 223)(20 222)(21 221)(22 220)(23 219)(24 218)(25 217)(26 216)(27 215)(28 214)(29 213)(30 212)(31 211)(32 210)(33 41)(34 40)(35 39)(36 38)(42 48)(43 47)(44 46)(49 193)(50 208)(51 207)(52 206)(53 205)(54 204)(55 203)(56 202)(57 201)(58 200)(59 199)(60 198)(61 197)(62 196)(63 195)(64 194)(65 154)(66 153)(67 152)(68 151)(69 150)(70 149)(71 148)(72 147)(73 146)(74 145)(75 160)(76 159)(77 158)(78 157)(79 156)(80 155)(81 103)(82 102)(83 101)(84 100)(85 99)(86 98)(87 97)(88 112)(89 111)(90 110)(91 109)(92 108)(93 107)(94 106)(95 105)(96 104)(113 136)(114 135)(115 134)(116 133)(117 132)(118 131)(119 130)(120 129)(121 144)(122 143)(123 142)(124 141)(125 140)(126 139)(127 138)(128 137)(161 183)(162 182)(163 181)(164 180)(165 179)(166 178)(167 177)(168 192)(169 191)(170 190)(171 189)(172 188)(173 187)(174 186)(175 185)(176 184)
G:=sub<Sym(224)| (1,45)(2,46)(3,47)(4,48)(5,33)(6,34)(7,35)(8,36)(9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,43)(16,44)(17,145)(18,146)(19,147)(20,148)(21,149)(22,150)(23,151)(24,152)(25,153)(26,154)(27,155)(28,156)(29,157)(30,158)(31,159)(32,160)(49,187)(50,188)(51,189)(52,190)(53,191)(54,192)(55,177)(56,178)(57,179)(58,180)(59,181)(60,182)(61,183)(62,184)(63,185)(64,186)(65,216)(66,217)(67,218)(68,219)(69,220)(70,221)(71,222)(72,223)(73,224)(74,209)(75,210)(76,211)(77,212)(78,213)(79,214)(80,215)(81,127)(82,128)(83,113)(84,114)(85,115)(86,116)(87,117)(88,118)(89,119)(90,120)(91,121)(92,122)(93,123)(94,124)(95,125)(96,126)(97,132)(98,133)(99,134)(100,135)(101,136)(102,137)(103,138)(104,139)(105,140)(106,141)(107,142)(108,143)(109,144)(110,129)(111,130)(112,131)(161,197)(162,198)(163,199)(164,200)(165,201)(166,202)(167,203)(168,204)(169,205)(170,206)(171,207)(172,208)(173,193)(174,194)(175,195)(176,196), (1,129,25,182,162,217,120)(2,121,218,163,183,26,130)(3,131,27,184,164,219,122)(4,123,220,165,185,28,132)(5,133,29,186,166,221,124)(6,125,222,167,187,30,134)(7,135,31,188,168,223,126)(8,127,224,169,189,32,136)(9,137,17,190,170,209,128)(10,113,210,171,191,18,138)(11,139,19,192,172,211,114)(12,115,212,173,177,20,140)(13,141,21,178,174,213,116)(14,117,214,175,179,22,142)(15,143,23,180,176,215,118)(16,119,216,161,181,24,144)(33,98,157,64,202,70,94)(34,95,71,203,49,158,99)(35,100,159,50,204,72,96)(36,81,73,205,51,160,101)(37,102,145,52,206,74,82)(38,83,75,207,53,146,103)(39,104,147,54,208,76,84)(40,85,77,193,55,148,105)(41,106,149,56,194,78,86)(42,87,79,195,57,150,107)(43,108,151,58,196,80,88)(44,89,65,197,59,152,109)(45,110,153,60,198,66,90)(46,91,67,199,61,154,111)(47,112,155,62,200,68,92)(48,93,69,201,63,156,97), (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), (2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)(17,209)(18,224)(19,223)(20,222)(21,221)(22,220)(23,219)(24,218)(25,217)(26,216)(27,215)(28,214)(29,213)(30,212)(31,211)(32,210)(33,41)(34,40)(35,39)(36,38)(42,48)(43,47)(44,46)(49,193)(50,208)(51,207)(52,206)(53,205)(54,204)(55,203)(56,202)(57,201)(58,200)(59,199)(60,198)(61,197)(62,196)(63,195)(64,194)(65,154)(66,153)(67,152)(68,151)(69,150)(70,149)(71,148)(72,147)(73,146)(74,145)(75,160)(76,159)(77,158)(78,157)(79,156)(80,155)(81,103)(82,102)(83,101)(84,100)(85,99)(86,98)(87,97)(88,112)(89,111)(90,110)(91,109)(92,108)(93,107)(94,106)(95,105)(96,104)(113,136)(114,135)(115,134)(116,133)(117,132)(118,131)(119,130)(120,129)(121,144)(122,143)(123,142)(124,141)(125,140)(126,139)(127,138)(128,137)(161,183)(162,182)(163,181)(164,180)(165,179)(166,178)(167,177)(168,192)(169,191)(170,190)(171,189)(172,188)(173,187)(174,186)(175,185)(176,184)>;
G:=Group( (1,45)(2,46)(3,47)(4,48)(5,33)(6,34)(7,35)(8,36)(9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,43)(16,44)(17,145)(18,146)(19,147)(20,148)(21,149)(22,150)(23,151)(24,152)(25,153)(26,154)(27,155)(28,156)(29,157)(30,158)(31,159)(32,160)(49,187)(50,188)(51,189)(52,190)(53,191)(54,192)(55,177)(56,178)(57,179)(58,180)(59,181)(60,182)(61,183)(62,184)(63,185)(64,186)(65,216)(66,217)(67,218)(68,219)(69,220)(70,221)(71,222)(72,223)(73,224)(74,209)(75,210)(76,211)(77,212)(78,213)(79,214)(80,215)(81,127)(82,128)(83,113)(84,114)(85,115)(86,116)(87,117)(88,118)(89,119)(90,120)(91,121)(92,122)(93,123)(94,124)(95,125)(96,126)(97,132)(98,133)(99,134)(100,135)(101,136)(102,137)(103,138)(104,139)(105,140)(106,141)(107,142)(108,143)(109,144)(110,129)(111,130)(112,131)(161,197)(162,198)(163,199)(164,200)(165,201)(166,202)(167,203)(168,204)(169,205)(170,206)(171,207)(172,208)(173,193)(174,194)(175,195)(176,196), (1,129,25,182,162,217,120)(2,121,218,163,183,26,130)(3,131,27,184,164,219,122)(4,123,220,165,185,28,132)(5,133,29,186,166,221,124)(6,125,222,167,187,30,134)(7,135,31,188,168,223,126)(8,127,224,169,189,32,136)(9,137,17,190,170,209,128)(10,113,210,171,191,18,138)(11,139,19,192,172,211,114)(12,115,212,173,177,20,140)(13,141,21,178,174,213,116)(14,117,214,175,179,22,142)(15,143,23,180,176,215,118)(16,119,216,161,181,24,144)(33,98,157,64,202,70,94)(34,95,71,203,49,158,99)(35,100,159,50,204,72,96)(36,81,73,205,51,160,101)(37,102,145,52,206,74,82)(38,83,75,207,53,146,103)(39,104,147,54,208,76,84)(40,85,77,193,55,148,105)(41,106,149,56,194,78,86)(42,87,79,195,57,150,107)(43,108,151,58,196,80,88)(44,89,65,197,59,152,109)(45,110,153,60,198,66,90)(46,91,67,199,61,154,111)(47,112,155,62,200,68,92)(48,93,69,201,63,156,97), (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), (2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)(17,209)(18,224)(19,223)(20,222)(21,221)(22,220)(23,219)(24,218)(25,217)(26,216)(27,215)(28,214)(29,213)(30,212)(31,211)(32,210)(33,41)(34,40)(35,39)(36,38)(42,48)(43,47)(44,46)(49,193)(50,208)(51,207)(52,206)(53,205)(54,204)(55,203)(56,202)(57,201)(58,200)(59,199)(60,198)(61,197)(62,196)(63,195)(64,194)(65,154)(66,153)(67,152)(68,151)(69,150)(70,149)(71,148)(72,147)(73,146)(74,145)(75,160)(76,159)(77,158)(78,157)(79,156)(80,155)(81,103)(82,102)(83,101)(84,100)(85,99)(86,98)(87,97)(88,112)(89,111)(90,110)(91,109)(92,108)(93,107)(94,106)(95,105)(96,104)(113,136)(114,135)(115,134)(116,133)(117,132)(118,131)(119,130)(120,129)(121,144)(122,143)(123,142)(124,141)(125,140)(126,139)(127,138)(128,137)(161,183)(162,182)(163,181)(164,180)(165,179)(166,178)(167,177)(168,192)(169,191)(170,190)(171,189)(172,188)(173,187)(174,186)(175,185)(176,184) );
G=PermutationGroup([[(1,45),(2,46),(3,47),(4,48),(5,33),(6,34),(7,35),(8,36),(9,37),(10,38),(11,39),(12,40),(13,41),(14,42),(15,43),(16,44),(17,145),(18,146),(19,147),(20,148),(21,149),(22,150),(23,151),(24,152),(25,153),(26,154),(27,155),(28,156),(29,157),(30,158),(31,159),(32,160),(49,187),(50,188),(51,189),(52,190),(53,191),(54,192),(55,177),(56,178),(57,179),(58,180),(59,181),(60,182),(61,183),(62,184),(63,185),(64,186),(65,216),(66,217),(67,218),(68,219),(69,220),(70,221),(71,222),(72,223),(73,224),(74,209),(75,210),(76,211),(77,212),(78,213),(79,214),(80,215),(81,127),(82,128),(83,113),(84,114),(85,115),(86,116),(87,117),(88,118),(89,119),(90,120),(91,121),(92,122),(93,123),(94,124),(95,125),(96,126),(97,132),(98,133),(99,134),(100,135),(101,136),(102,137),(103,138),(104,139),(105,140),(106,141),(107,142),(108,143),(109,144),(110,129),(111,130),(112,131),(161,197),(162,198),(163,199),(164,200),(165,201),(166,202),(167,203),(168,204),(169,205),(170,206),(171,207),(172,208),(173,193),(174,194),(175,195),(176,196)], [(1,129,25,182,162,217,120),(2,121,218,163,183,26,130),(3,131,27,184,164,219,122),(4,123,220,165,185,28,132),(5,133,29,186,166,221,124),(6,125,222,167,187,30,134),(7,135,31,188,168,223,126),(8,127,224,169,189,32,136),(9,137,17,190,170,209,128),(10,113,210,171,191,18,138),(11,139,19,192,172,211,114),(12,115,212,173,177,20,140),(13,141,21,178,174,213,116),(14,117,214,175,179,22,142),(15,143,23,180,176,215,118),(16,119,216,161,181,24,144),(33,98,157,64,202,70,94),(34,95,71,203,49,158,99),(35,100,159,50,204,72,96),(36,81,73,205,51,160,101),(37,102,145,52,206,74,82),(38,83,75,207,53,146,103),(39,104,147,54,208,76,84),(40,85,77,193,55,148,105),(41,106,149,56,194,78,86),(42,87,79,195,57,150,107),(43,108,151,58,196,80,88),(44,89,65,197,59,152,109),(45,110,153,60,198,66,90),(46,91,67,199,61,154,111),(47,112,155,62,200,68,92),(48,93,69,201,63,156,97)], [(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)], [(2,16),(3,15),(4,14),(5,13),(6,12),(7,11),(8,10),(17,209),(18,224),(19,223),(20,222),(21,221),(22,220),(23,219),(24,218),(25,217),(26,216),(27,215),(28,214),(29,213),(30,212),(31,211),(32,210),(33,41),(34,40),(35,39),(36,38),(42,48),(43,47),(44,46),(49,193),(50,208),(51,207),(52,206),(53,205),(54,204),(55,203),(56,202),(57,201),(58,200),(59,199),(60,198),(61,197),(62,196),(63,195),(64,194),(65,154),(66,153),(67,152),(68,151),(69,150),(70,149),(71,148),(72,147),(73,146),(74,145),(75,160),(76,159),(77,158),(78,157),(79,156),(80,155),(81,103),(82,102),(83,101),(84,100),(85,99),(86,98),(87,97),(88,112),(89,111),(90,110),(91,109),(92,108),(93,107),(94,106),(95,105),(96,104),(113,136),(114,135),(115,134),(116,133),(117,132),(118,131),(119,130),(120,129),(121,144),(122,143),(123,142),(124,141),(125,140),(126,139),(127,138),(128,137),(161,183),(162,182),(163,181),(164,180),(165,179),(166,178),(167,177),(168,192),(169,191),(170,190),(171,189),(172,188),(173,187),(174,186),(175,185),(176,184)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14U | 16A | ··· | 16H | 28A | ··· | 28F | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 16 | ··· | 16 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 8 | 8 | 56 | 56 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | ··· | 8 | 14 | ··· | 14 | 4 | ··· | 4 | 4 | ··· | 4 |
64 irreducible representations
| dim | 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 | D4 | D4 | D7 | D8 | D8 | D14 | D14 | D16 | C7⋊D4 | C7⋊D4 | D4⋊D7 | D4⋊D7 | C7⋊D16 |
| kernel | C2×C7⋊D16 | C2×C7⋊C16 | C7⋊D16 | C2×D56 | C14×D8 | C56 | C2×C28 | C2×D8 | C28 | C2×C14 | C2×C8 | D8 | C14 | C8 | C2×C4 | C4 | C22 | C2 |
| # reps | 1 | 1 | 4 | 1 | 1 | 1 | 1 | 3 | 2 | 2 | 3 | 6 | 8 | 6 | 6 | 3 | 3 | 12 |
Matrix representation of C2×C7⋊D16 ►in GL4(𝔽113) generated by
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 9 | 112 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 9 | 112 | 0 | 0 |
| 0 | 0 | 91 | 13 |
| 0 | 0 | 11 | 14 |
| 1 | 0 | 0 | 0 |
| 9 | 112 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 81 | 112 |
G:=sub<GL(4,GF(113))| [112,0,0,0,0,112,0,0,0,0,1,0,0,0,0,1],[9,1,0,0,112,0,0,0,0,0,1,0,0,0,0,1],[1,9,0,0,0,112,0,0,0,0,91,11,0,0,13,14],[1,9,0,0,0,112,0,0,0,0,1,81,0,0,0,112] >;
C2×C7⋊D16 in GAP, Magma, Sage, TeX
C_2\times C_7\rtimes D_{16} % in TeX
G:=Group("C2xC7:D16"); // GroupNames label
G:=SmallGroup(448,680);
// by ID
G=gap.SmallGroup(448,680);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,254,675,185,192,1684,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^7=c^16=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations