metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D16⋊3D7, D8.1D14, D14.1D8, C16.8D14, Dic56⋊4C2, C56.15C23, C112.6C22, Dic7.12D8, Dic28.2C22, C7⋊C8.12D4, C4.3(D4×D7), (D7×C16)⋊2C2, (C7×D16)⋊3C2, C7⋊2(C4○D16), D8.D7⋊2C2, C2.18(D7×D8), C28.9(C2×D4), D8⋊3D7⋊4C2, (C4×D7).19D4, C14.34(C2×D8), C7⋊C16.5C22, (C7×D8).1C22, C8.21(C22×D7), (C8×D7).10C22, SmallGroup(448,446)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D16⋊3D7
G = < a,b,c,d | a16=b2=c7=d2=1, bab=a-1, ac=ca, ad=da, bc=cb, dbd=a8b, dcd=c-1 >
Subgroups: 496 in 84 conjugacy classes, 31 normal (21 characteristic)
C1, C2, C2, C4, C4, C22, C7, C8, C8, C2×C4, D4, Q8, D7, C14, C14, C16, C16, C2×C8, D8, SD16, Q16, C4○D4, Dic7, Dic7, C28, D14, C2×C14, C2×C16, D16, SD32, Q32, C4○D8, C7⋊C8, C56, Dic14, C4×D7, C2×Dic7, C7⋊D4, C7×D4, C4○D16, C7⋊C16, C112, C8×D7, Dic28, D4.D7, C7×D8, D4⋊2D7, D7×C16, Dic56, D8.D7, C7×D16, D8⋊3D7, D16⋊3D7
Quotients: C1, C2, C22, D4, C23, D7, D8, C2×D4, D14, C2×D8, C22×D7, C4○D16, D4×D7, D7×D8, D16⋊3D7
►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 36)(2 35)(3 34)(4 33)(5 48)(6 47)(7 46)(8 45)(9 44)(10 43)(11 42)(12 41)(13 40)(14 39)(15 38)(16 37)(17 223)(18 222)(19 221)(20 220)(21 219)(22 218)(23 217)(24 216)(25 215)(26 214)(27 213)(28 212)(29 211)(30 210)(31 209)(32 224)(49 106)(50 105)(51 104)(52 103)(53 102)(54 101)(55 100)(56 99)(57 98)(58 97)(59 112)(60 111)(61 110)(62 109)(63 108)(64 107)(65 85)(66 84)(67 83)(68 82)(69 81)(70 96)(71 95)(72 94)(73 93)(74 92)(75 91)(76 90)(77 89)(78 88)(79 87)(80 86)(113 191)(114 190)(115 189)(116 188)(117 187)(118 186)(119 185)(120 184)(121 183)(122 182)(123 181)(124 180)(125 179)(126 178)(127 177)(128 192)(129 201)(130 200)(131 199)(132 198)(133 197)(134 196)(135 195)(136 194)(137 193)(138 208)(139 207)(140 206)(141 205)(142 204)(143 203)(144 202)(145 168)(146 167)(147 166)(148 165)(149 164)(150 163)(151 162)(152 161)(153 176)(154 175)(155 174)(156 173)(157 172)(158 171)(159 170)(160 169)
(1 53 85 193 217 148 114)(2 54 86 194 218 149 115)(3 55 87 195 219 150 116)(4 56 88 196 220 151 117)(5 57 89 197 221 152 118)(6 58 90 198 222 153 119)(7 59 91 199 223 154 120)(8 60 92 200 224 155 121)(9 61 93 201 209 156 122)(10 62 94 202 210 157 123)(11 63 95 203 211 158 124)(12 64 96 204 212 159 125)(13 49 81 205 213 160 126)(14 50 82 206 214 145 127)(15 51 83 207 215 146 128)(16 52 84 208 216 147 113)(17 175 184 46 112 75 131)(18 176 185 47 97 76 132)(19 161 186 48 98 77 133)(20 162 187 33 99 78 134)(21 163 188 34 100 79 135)(22 164 189 35 101 80 136)(23 165 190 36 102 65 137)(24 166 191 37 103 66 138)(25 167 192 38 104 67 139)(26 168 177 39 105 68 140)(27 169 178 40 106 69 141)(28 170 179 41 107 70 142)(29 171 180 42 108 71 143)(30 172 181 43 109 72 144)(31 173 182 44 110 73 129)(32 174 183 45 111 74 130)
(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)(14 127)(15 128)(16 113)(17 67)(18 68)(19 69)(20 70)(21 71)(22 72)(23 73)(24 74)(25 75)(26 76)(27 77)(28 78)(29 79)(30 80)(31 65)(32 66)(33 179)(34 180)(35 181)(36 182)(37 183)(38 184)(39 185)(40 186)(41 187)(42 188)(43 189)(44 190)(45 191)(46 192)(47 177)(48 178)(49 160)(50 145)(51 146)(52 147)(53 148)(54 149)(55 150)(56 151)(57 152)(58 153)(59 154)(60 155)(61 156)(62 157)(63 158)(64 159)(81 213)(82 214)(83 215)(84 216)(85 217)(86 218)(87 219)(88 220)(89 221)(90 222)(91 223)(92 224)(93 209)(94 210)(95 211)(96 212)(97 168)(98 169)(99 170)(100 171)(101 172)(102 173)(103 174)(104 175)(105 176)(106 161)(107 162)(108 163)(109 164)(110 165)(111 166)(112 167)(129 137)(130 138)(131 139)(132 140)(133 141)(134 142)(135 143)(136 144)
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), (1,36)(2,35)(3,34)(4,33)(5,48)(6,47)(7,46)(8,45)(9,44)(10,43)(11,42)(12,41)(13,40)(14,39)(15,38)(16,37)(17,223)(18,222)(19,221)(20,220)(21,219)(22,218)(23,217)(24,216)(25,215)(26,214)(27,213)(28,212)(29,211)(30,210)(31,209)(32,224)(49,106)(50,105)(51,104)(52,103)(53,102)(54,101)(55,100)(56,99)(57,98)(58,97)(59,112)(60,111)(61,110)(62,109)(63,108)(64,107)(65,85)(66,84)(67,83)(68,82)(69,81)(70,96)(71,95)(72,94)(73,93)(74,92)(75,91)(76,90)(77,89)(78,88)(79,87)(80,86)(113,191)(114,190)(115,189)(116,188)(117,187)(118,186)(119,185)(120,184)(121,183)(122,182)(123,181)(124,180)(125,179)(126,178)(127,177)(128,192)(129,201)(130,200)(131,199)(132,198)(133,197)(134,196)(135,195)(136,194)(137,193)(138,208)(139,207)(140,206)(141,205)(142,204)(143,203)(144,202)(145,168)(146,167)(147,166)(148,165)(149,164)(150,163)(151,162)(152,161)(153,176)(154,175)(155,174)(156,173)(157,172)(158,171)(159,170)(160,169), (1,53,85,193,217,148,114)(2,54,86,194,218,149,115)(3,55,87,195,219,150,116)(4,56,88,196,220,151,117)(5,57,89,197,221,152,118)(6,58,90,198,222,153,119)(7,59,91,199,223,154,120)(8,60,92,200,224,155,121)(9,61,93,201,209,156,122)(10,62,94,202,210,157,123)(11,63,95,203,211,158,124)(12,64,96,204,212,159,125)(13,49,81,205,213,160,126)(14,50,82,206,214,145,127)(15,51,83,207,215,146,128)(16,52,84,208,216,147,113)(17,175,184,46,112,75,131)(18,176,185,47,97,76,132)(19,161,186,48,98,77,133)(20,162,187,33,99,78,134)(21,163,188,34,100,79,135)(22,164,189,35,101,80,136)(23,165,190,36,102,65,137)(24,166,191,37,103,66,138)(25,167,192,38,104,67,139)(26,168,177,39,105,68,140)(27,169,178,40,106,69,141)(28,170,179,41,107,70,142)(29,171,180,42,108,71,143)(30,172,181,43,109,72,144)(31,173,182,44,110,73,129)(32,174,183,45,111,74,130), (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)(14,127)(15,128)(16,113)(17,67)(18,68)(19,69)(20,70)(21,71)(22,72)(23,73)(24,74)(25,75)(26,76)(27,77)(28,78)(29,79)(30,80)(31,65)(32,66)(33,179)(34,180)(35,181)(36,182)(37,183)(38,184)(39,185)(40,186)(41,187)(42,188)(43,189)(44,190)(45,191)(46,192)(47,177)(48,178)(49,160)(50,145)(51,146)(52,147)(53,148)(54,149)(55,150)(56,151)(57,152)(58,153)(59,154)(60,155)(61,156)(62,157)(63,158)(64,159)(81,213)(82,214)(83,215)(84,216)(85,217)(86,218)(87,219)(88,220)(89,221)(90,222)(91,223)(92,224)(93,209)(94,210)(95,211)(96,212)(97,168)(98,169)(99,170)(100,171)(101,172)(102,173)(103,174)(104,175)(105,176)(106,161)(107,162)(108,163)(109,164)(110,165)(111,166)(112,167)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)>;
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), (1,36)(2,35)(3,34)(4,33)(5,48)(6,47)(7,46)(8,45)(9,44)(10,43)(11,42)(12,41)(13,40)(14,39)(15,38)(16,37)(17,223)(18,222)(19,221)(20,220)(21,219)(22,218)(23,217)(24,216)(25,215)(26,214)(27,213)(28,212)(29,211)(30,210)(31,209)(32,224)(49,106)(50,105)(51,104)(52,103)(53,102)(54,101)(55,100)(56,99)(57,98)(58,97)(59,112)(60,111)(61,110)(62,109)(63,108)(64,107)(65,85)(66,84)(67,83)(68,82)(69,81)(70,96)(71,95)(72,94)(73,93)(74,92)(75,91)(76,90)(77,89)(78,88)(79,87)(80,86)(113,191)(114,190)(115,189)(116,188)(117,187)(118,186)(119,185)(120,184)(121,183)(122,182)(123,181)(124,180)(125,179)(126,178)(127,177)(128,192)(129,201)(130,200)(131,199)(132,198)(133,197)(134,196)(135,195)(136,194)(137,193)(138,208)(139,207)(140,206)(141,205)(142,204)(143,203)(144,202)(145,168)(146,167)(147,166)(148,165)(149,164)(150,163)(151,162)(152,161)(153,176)(154,175)(155,174)(156,173)(157,172)(158,171)(159,170)(160,169), (1,53,85,193,217,148,114)(2,54,86,194,218,149,115)(3,55,87,195,219,150,116)(4,56,88,196,220,151,117)(5,57,89,197,221,152,118)(6,58,90,198,222,153,119)(7,59,91,199,223,154,120)(8,60,92,200,224,155,121)(9,61,93,201,209,156,122)(10,62,94,202,210,157,123)(11,63,95,203,211,158,124)(12,64,96,204,212,159,125)(13,49,81,205,213,160,126)(14,50,82,206,214,145,127)(15,51,83,207,215,146,128)(16,52,84,208,216,147,113)(17,175,184,46,112,75,131)(18,176,185,47,97,76,132)(19,161,186,48,98,77,133)(20,162,187,33,99,78,134)(21,163,188,34,100,79,135)(22,164,189,35,101,80,136)(23,165,190,36,102,65,137)(24,166,191,37,103,66,138)(25,167,192,38,104,67,139)(26,168,177,39,105,68,140)(27,169,178,40,106,69,141)(28,170,179,41,107,70,142)(29,171,180,42,108,71,143)(30,172,181,43,109,72,144)(31,173,182,44,110,73,129)(32,174,183,45,111,74,130), (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)(14,127)(15,128)(16,113)(17,67)(18,68)(19,69)(20,70)(21,71)(22,72)(23,73)(24,74)(25,75)(26,76)(27,77)(28,78)(29,79)(30,80)(31,65)(32,66)(33,179)(34,180)(35,181)(36,182)(37,183)(38,184)(39,185)(40,186)(41,187)(42,188)(43,189)(44,190)(45,191)(46,192)(47,177)(48,178)(49,160)(50,145)(51,146)(52,147)(53,148)(54,149)(55,150)(56,151)(57,152)(58,153)(59,154)(60,155)(61,156)(62,157)(63,158)(64,159)(81,213)(82,214)(83,215)(84,216)(85,217)(86,218)(87,219)(88,220)(89,221)(90,222)(91,223)(92,224)(93,209)(94,210)(95,211)(96,212)(97,168)(98,169)(99,170)(100,171)(101,172)(102,173)(103,174)(104,175)(105,176)(106,161)(107,162)(108,163)(109,164)(110,165)(111,166)(112,167)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144) );
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)], [(1,36),(2,35),(3,34),(4,33),(5,48),(6,47),(7,46),(8,45),(9,44),(10,43),(11,42),(12,41),(13,40),(14,39),(15,38),(16,37),(17,223),(18,222),(19,221),(20,220),(21,219),(22,218),(23,217),(24,216),(25,215),(26,214),(27,213),(28,212),(29,211),(30,210),(31,209),(32,224),(49,106),(50,105),(51,104),(52,103),(53,102),(54,101),(55,100),(56,99),(57,98),(58,97),(59,112),(60,111),(61,110),(62,109),(63,108),(64,107),(65,85),(66,84),(67,83),(68,82),(69,81),(70,96),(71,95),(72,94),(73,93),(74,92),(75,91),(76,90),(77,89),(78,88),(79,87),(80,86),(113,191),(114,190),(115,189),(116,188),(117,187),(118,186),(119,185),(120,184),(121,183),(122,182),(123,181),(124,180),(125,179),(126,178),(127,177),(128,192),(129,201),(130,200),(131,199),(132,198),(133,197),(134,196),(135,195),(136,194),(137,193),(138,208),(139,207),(140,206),(141,205),(142,204),(143,203),(144,202),(145,168),(146,167),(147,166),(148,165),(149,164),(150,163),(151,162),(152,161),(153,176),(154,175),(155,174),(156,173),(157,172),(158,171),(159,170),(160,169)], [(1,53,85,193,217,148,114),(2,54,86,194,218,149,115),(3,55,87,195,219,150,116),(4,56,88,196,220,151,117),(5,57,89,197,221,152,118),(6,58,90,198,222,153,119),(7,59,91,199,223,154,120),(8,60,92,200,224,155,121),(9,61,93,201,209,156,122),(10,62,94,202,210,157,123),(11,63,95,203,211,158,124),(12,64,96,204,212,159,125),(13,49,81,205,213,160,126),(14,50,82,206,214,145,127),(15,51,83,207,215,146,128),(16,52,84,208,216,147,113),(17,175,184,46,112,75,131),(18,176,185,47,97,76,132),(19,161,186,48,98,77,133),(20,162,187,33,99,78,134),(21,163,188,34,100,79,135),(22,164,189,35,101,80,136),(23,165,190,36,102,65,137),(24,166,191,37,103,66,138),(25,167,192,38,104,67,139),(26,168,177,39,105,68,140),(27,169,178,40,106,69,141),(28,170,179,41,107,70,142),(29,171,180,42,108,71,143),(30,172,181,43,109,72,144),(31,173,182,44,110,73,129),(32,174,183,45,111,74,130)], [(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),(14,127),(15,128),(16,113),(17,67),(18,68),(19,69),(20,70),(21,71),(22,72),(23,73),(24,74),(25,75),(26,76),(27,77),(28,78),(29,79),(30,80),(31,65),(32,66),(33,179),(34,180),(35,181),(36,182),(37,183),(38,184),(39,185),(40,186),(41,187),(42,188),(43,189),(44,190),(45,191),(46,192),(47,177),(48,178),(49,160),(50,145),(51,146),(52,147),(53,148),(54,149),(55,150),(56,151),(57,152),(58,153),(59,154),(60,155),(61,156),(62,157),(63,158),(64,159),(81,213),(82,214),(83,215),(84,216),(85,217),(86,218),(87,219),(88,220),(89,221),(90,222),(91,223),(92,224),(93,209),(94,210),(95,211),(96,212),(97,168),(98,169),(99,170),(100,171),(101,172),(102,173),(103,174),(104,175),(105,176),(106,161),(107,162),(108,163),(109,164),(110,165),(111,166),(112,167),(129,137),(130,138),(131,139),(132,140),(133,141),(134,142),(135,143),(136,144)]])
55 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | 14B | 14C | 14D | ··· | 14I | 16A | 16B | 16C | 16D | 16E | 16F | 16G | 16H | 28A | 28B | 28C | 56A | ··· | 56F | 112A | ··· | 112L |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | 14 | 14 | 14 | ··· | 14 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 28 | 28 | 28 | 56 | ··· | 56 | 112 | ··· | 112 |
| size | 1 | 1 | 8 | 8 | 14 | 2 | 7 | 7 | 56 | 56 | 2 | 2 | 2 | 2 | 2 | 14 | 14 | 2 | 2 | 2 | 16 | ··· | 16 | 2 | 2 | 2 | 2 | 14 | 14 | 14 | 14 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 |
55 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | D8 | D8 | D14 | D14 | C4○D16 | D4×D7 | D7×D8 | D16⋊3D7 |
| kernel | D16⋊3D7 | D7×C16 | Dic56 | D8.D7 | C7×D16 | D8⋊3D7 | C7⋊C8 | C4×D7 | D16 | Dic7 | D14 | C16 | D8 | C7 | C4 | C2 | C1 |
| # reps | 1 | 1 | 1 | 2 | 1 | 2 | 1 | 1 | 3 | 2 | 2 | 3 | 6 | 8 | 3 | 6 | 12 |
Matrix representation of D16⋊3D7 ►in GL4(𝔽113) generated by
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 35 | 0 |
| 0 | 0 | 60 | 42 |
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 71 | 29 |
| 0 | 0 | 60 | 42 |
| 0 | 1 | 0 | 0 |
| 112 | 24 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 112 | 112 |
G:=sub<GL(4,GF(113))| [112,0,0,0,0,112,0,0,0,0,35,60,0,0,0,42],[112,0,0,0,0,112,0,0,0,0,71,60,0,0,29,42],[0,112,0,0,1,24,0,0,0,0,1,0,0,0,0,1],[0,1,0,0,1,0,0,0,0,0,1,112,0,0,0,112] >;
D16⋊3D7 in GAP, Magma, Sage, TeX
D_{16}\rtimes_3D_7 % in TeX
G:=Group("D16:3D7"); // GroupNames label
G:=SmallGroup(448,446);
// by ID
G=gap.SmallGroup(448,446);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,758,135,346,185,192,851,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^16=b^2=c^7=d^2=1,b*a*b=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d=a^8*b,d*c*d=c^-1>;
// generators/relations