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## G = C7×C8⋊2D4order 448 = 26·7

### Direct product of C7 and C8⋊2D4

direct product, metabelian, nilpotent (class 3), monomial, 2-elementary

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C4 — C7×C8⋊2D4
 Chief series C1 — C2 — C22 — C2×C4 — C2×C28 — D4×C14 — C14×D8 — C7×C8⋊2D4
 Lower central C1 — C2 — C2×C4 — C7×C8⋊2D4
 Upper central C1 — C2×C14 — C22×C28 — C7×C8⋊2D4

Generators and relations for C7×C82D4
G = < a,b,c,d | a7=b8=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=b3, dbd=b-1, dcd=c-1 >

Subgroups: 282 in 130 conjugacy classes, 54 normal (30 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C8, C8, C2×C4, C2×C4, D4, C23, C23, C14, C14, C14, C22⋊C4, C4⋊C4, C2×C8, M4(2), D8, C22×C4, C2×D4, C2×D4, C28, C28, C2×C14, C2×C14, D4⋊C4, C4.Q8, C4⋊D4, C2×M4(2), C2×D8, C56, C56, C2×C28, C2×C28, C7×D4, C22×C14, C22×C14, C82D4, C7×C22⋊C4, C7×C4⋊C4, C2×C56, C7×M4(2), C7×D8, C22×C28, D4×C14, D4×C14, C7×D4⋊C4, C7×C4.Q8, C7×C4⋊D4, C14×M4(2), C14×D8, C7×C82D4
Quotients: C1, C2, C22, C7, D4, C23, C14, C2×D4, C4○D4, C2×C14, C4⋊D4, C8⋊C22, C7×D4, C22×C14, C82D4, D4×C14, C7×C4○D4, C7×C4⋊D4, C7×C8⋊C22, C7×C82D4

Smallest permutation representation of C7×C82D4
On 224 points
Generators in S224
(1 17 66 13 85 29 77)(2 18 67 14 86 30 78)(3 19 68 15 87 31 79)(4 20 69 16 88 32 80)(5 21 70 9 81 25 73)(6 22 71 10 82 26 74)(7 23 72 11 83 27 75)(8 24 65 12 84 28 76)(33 117 105 49 97 41 89)(34 118 106 50 98 42 90)(35 119 107 51 99 43 91)(36 120 108 52 100 44 92)(37 113 109 53 101 45 93)(38 114 110 54 102 46 94)(39 115 111 55 103 47 95)(40 116 112 56 104 48 96)(57 220 168 212 160 204 152)(58 221 161 213 153 205 145)(59 222 162 214 154 206 146)(60 223 163 215 155 207 147)(61 224 164 216 156 208 148)(62 217 165 209 157 201 149)(63 218 166 210 158 202 150)(64 219 167 211 159 203 151)(121 174 197 137 189 129 181)(122 175 198 138 190 130 182)(123 176 199 139 191 131 183)(124 169 200 140 192 132 184)(125 170 193 141 185 133 177)(126 171 194 142 186 134 178)(127 172 195 143 187 135 179)(128 173 196 144 188 136 180)
(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)
(1 145 35 123)(2 148 36 126)(3 151 37 121)(4 146 38 124)(5 149 39 127)(6 152 40 122)(7 147 33 125)(8 150 34 128)(9 165 55 143)(10 168 56 138)(11 163 49 141)(12 166 50 144)(13 161 51 139)(14 164 52 142)(15 167 53 137)(16 162 54 140)(17 58 119 176)(18 61 120 171)(19 64 113 174)(20 59 114 169)(21 62 115 172)(22 57 116 175)(23 60 117 170)(24 63 118 173)(25 157 47 135)(26 160 48 130)(27 155 41 133)(28 158 42 136)(29 153 43 131)(30 156 44 134)(31 159 45 129)(32 154 46 132)(65 218 106 196)(66 221 107 199)(67 224 108 194)(68 219 109 197)(69 222 110 200)(70 217 111 195)(71 220 112 198)(72 223 105 193)(73 201 95 179)(74 204 96 182)(75 207 89 177)(76 202 90 180)(77 205 91 183)(78 208 92 178)(79 203 93 181)(80 206 94 184)(81 209 103 187)(82 212 104 190)(83 215 97 185)(84 210 98 188)(85 213 99 191)(86 216 100 186)(87 211 101 189)(88 214 102 192)
(1 123)(2 122)(3 121)(4 128)(5 127)(6 126)(7 125)(8 124)(9 143)(10 142)(11 141)(12 140)(13 139)(14 138)(15 137)(16 144)(17 176)(18 175)(19 174)(20 173)(21 172)(22 171)(23 170)(24 169)(25 135)(26 134)(27 133)(28 132)(29 131)(30 130)(31 129)(32 136)(33 147)(34 146)(35 145)(36 152)(37 151)(38 150)(39 149)(40 148)(41 155)(42 154)(43 153)(44 160)(45 159)(46 158)(47 157)(48 156)(49 163)(50 162)(51 161)(52 168)(53 167)(54 166)(55 165)(56 164)(57 120)(58 119)(59 118)(60 117)(61 116)(62 115)(63 114)(64 113)(65 200)(66 199)(67 198)(68 197)(69 196)(70 195)(71 194)(72 193)(73 179)(74 178)(75 177)(76 184)(77 183)(78 182)(79 181)(80 180)(81 187)(82 186)(83 185)(84 192)(85 191)(86 190)(87 189)(88 188)(89 207)(90 206)(91 205)(92 204)(93 203)(94 202)(95 201)(96 208)(97 215)(98 214)(99 213)(100 212)(101 211)(102 210)(103 209)(104 216)(105 223)(106 222)(107 221)(108 220)(109 219)(110 218)(111 217)(112 224)

G:=sub<Sym(224)| (1,17,66,13,85,29,77)(2,18,67,14,86,30,78)(3,19,68,15,87,31,79)(4,20,69,16,88,32,80)(5,21,70,9,81,25,73)(6,22,71,10,82,26,74)(7,23,72,11,83,27,75)(8,24,65,12,84,28,76)(33,117,105,49,97,41,89)(34,118,106,50,98,42,90)(35,119,107,51,99,43,91)(36,120,108,52,100,44,92)(37,113,109,53,101,45,93)(38,114,110,54,102,46,94)(39,115,111,55,103,47,95)(40,116,112,56,104,48,96)(57,220,168,212,160,204,152)(58,221,161,213,153,205,145)(59,222,162,214,154,206,146)(60,223,163,215,155,207,147)(61,224,164,216,156,208,148)(62,217,165,209,157,201,149)(63,218,166,210,158,202,150)(64,219,167,211,159,203,151)(121,174,197,137,189,129,181)(122,175,198,138,190,130,182)(123,176,199,139,191,131,183)(124,169,200,140,192,132,184)(125,170,193,141,185,133,177)(126,171,194,142,186,134,178)(127,172,195,143,187,135,179)(128,173,196,144,188,136,180), (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), (1,145,35,123)(2,148,36,126)(3,151,37,121)(4,146,38,124)(5,149,39,127)(6,152,40,122)(7,147,33,125)(8,150,34,128)(9,165,55,143)(10,168,56,138)(11,163,49,141)(12,166,50,144)(13,161,51,139)(14,164,52,142)(15,167,53,137)(16,162,54,140)(17,58,119,176)(18,61,120,171)(19,64,113,174)(20,59,114,169)(21,62,115,172)(22,57,116,175)(23,60,117,170)(24,63,118,173)(25,157,47,135)(26,160,48,130)(27,155,41,133)(28,158,42,136)(29,153,43,131)(30,156,44,134)(31,159,45,129)(32,154,46,132)(65,218,106,196)(66,221,107,199)(67,224,108,194)(68,219,109,197)(69,222,110,200)(70,217,111,195)(71,220,112,198)(72,223,105,193)(73,201,95,179)(74,204,96,182)(75,207,89,177)(76,202,90,180)(77,205,91,183)(78,208,92,178)(79,203,93,181)(80,206,94,184)(81,209,103,187)(82,212,104,190)(83,215,97,185)(84,210,98,188)(85,213,99,191)(86,216,100,186)(87,211,101,189)(88,214,102,192), (1,123)(2,122)(3,121)(4,128)(5,127)(6,126)(7,125)(8,124)(9,143)(10,142)(11,141)(12,140)(13,139)(14,138)(15,137)(16,144)(17,176)(18,175)(19,174)(20,173)(21,172)(22,171)(23,170)(24,169)(25,135)(26,134)(27,133)(28,132)(29,131)(30,130)(31,129)(32,136)(33,147)(34,146)(35,145)(36,152)(37,151)(38,150)(39,149)(40,148)(41,155)(42,154)(43,153)(44,160)(45,159)(46,158)(47,157)(48,156)(49,163)(50,162)(51,161)(52,168)(53,167)(54,166)(55,165)(56,164)(57,120)(58,119)(59,118)(60,117)(61,116)(62,115)(63,114)(64,113)(65,200)(66,199)(67,198)(68,197)(69,196)(70,195)(71,194)(72,193)(73,179)(74,178)(75,177)(76,184)(77,183)(78,182)(79,181)(80,180)(81,187)(82,186)(83,185)(84,192)(85,191)(86,190)(87,189)(88,188)(89,207)(90,206)(91,205)(92,204)(93,203)(94,202)(95,201)(96,208)(97,215)(98,214)(99,213)(100,212)(101,211)(102,210)(103,209)(104,216)(105,223)(106,222)(107,221)(108,220)(109,219)(110,218)(111,217)(112,224)>;

G:=Group( (1,17,66,13,85,29,77)(2,18,67,14,86,30,78)(3,19,68,15,87,31,79)(4,20,69,16,88,32,80)(5,21,70,9,81,25,73)(6,22,71,10,82,26,74)(7,23,72,11,83,27,75)(8,24,65,12,84,28,76)(33,117,105,49,97,41,89)(34,118,106,50,98,42,90)(35,119,107,51,99,43,91)(36,120,108,52,100,44,92)(37,113,109,53,101,45,93)(38,114,110,54,102,46,94)(39,115,111,55,103,47,95)(40,116,112,56,104,48,96)(57,220,168,212,160,204,152)(58,221,161,213,153,205,145)(59,222,162,214,154,206,146)(60,223,163,215,155,207,147)(61,224,164,216,156,208,148)(62,217,165,209,157,201,149)(63,218,166,210,158,202,150)(64,219,167,211,159,203,151)(121,174,197,137,189,129,181)(122,175,198,138,190,130,182)(123,176,199,139,191,131,183)(124,169,200,140,192,132,184)(125,170,193,141,185,133,177)(126,171,194,142,186,134,178)(127,172,195,143,187,135,179)(128,173,196,144,188,136,180), (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), (1,145,35,123)(2,148,36,126)(3,151,37,121)(4,146,38,124)(5,149,39,127)(6,152,40,122)(7,147,33,125)(8,150,34,128)(9,165,55,143)(10,168,56,138)(11,163,49,141)(12,166,50,144)(13,161,51,139)(14,164,52,142)(15,167,53,137)(16,162,54,140)(17,58,119,176)(18,61,120,171)(19,64,113,174)(20,59,114,169)(21,62,115,172)(22,57,116,175)(23,60,117,170)(24,63,118,173)(25,157,47,135)(26,160,48,130)(27,155,41,133)(28,158,42,136)(29,153,43,131)(30,156,44,134)(31,159,45,129)(32,154,46,132)(65,218,106,196)(66,221,107,199)(67,224,108,194)(68,219,109,197)(69,222,110,200)(70,217,111,195)(71,220,112,198)(72,223,105,193)(73,201,95,179)(74,204,96,182)(75,207,89,177)(76,202,90,180)(77,205,91,183)(78,208,92,178)(79,203,93,181)(80,206,94,184)(81,209,103,187)(82,212,104,190)(83,215,97,185)(84,210,98,188)(85,213,99,191)(86,216,100,186)(87,211,101,189)(88,214,102,192), (1,123)(2,122)(3,121)(4,128)(5,127)(6,126)(7,125)(8,124)(9,143)(10,142)(11,141)(12,140)(13,139)(14,138)(15,137)(16,144)(17,176)(18,175)(19,174)(20,173)(21,172)(22,171)(23,170)(24,169)(25,135)(26,134)(27,133)(28,132)(29,131)(30,130)(31,129)(32,136)(33,147)(34,146)(35,145)(36,152)(37,151)(38,150)(39,149)(40,148)(41,155)(42,154)(43,153)(44,160)(45,159)(46,158)(47,157)(48,156)(49,163)(50,162)(51,161)(52,168)(53,167)(54,166)(55,165)(56,164)(57,120)(58,119)(59,118)(60,117)(61,116)(62,115)(63,114)(64,113)(65,200)(66,199)(67,198)(68,197)(69,196)(70,195)(71,194)(72,193)(73,179)(74,178)(75,177)(76,184)(77,183)(78,182)(79,181)(80,180)(81,187)(82,186)(83,185)(84,192)(85,191)(86,190)(87,189)(88,188)(89,207)(90,206)(91,205)(92,204)(93,203)(94,202)(95,201)(96,208)(97,215)(98,214)(99,213)(100,212)(101,211)(102,210)(103,209)(104,216)(105,223)(106,222)(107,221)(108,220)(109,219)(110,218)(111,217)(112,224) );

G=PermutationGroup([[(1,17,66,13,85,29,77),(2,18,67,14,86,30,78),(3,19,68,15,87,31,79),(4,20,69,16,88,32,80),(5,21,70,9,81,25,73),(6,22,71,10,82,26,74),(7,23,72,11,83,27,75),(8,24,65,12,84,28,76),(33,117,105,49,97,41,89),(34,118,106,50,98,42,90),(35,119,107,51,99,43,91),(36,120,108,52,100,44,92),(37,113,109,53,101,45,93),(38,114,110,54,102,46,94),(39,115,111,55,103,47,95),(40,116,112,56,104,48,96),(57,220,168,212,160,204,152),(58,221,161,213,153,205,145),(59,222,162,214,154,206,146),(60,223,163,215,155,207,147),(61,224,164,216,156,208,148),(62,217,165,209,157,201,149),(63,218,166,210,158,202,150),(64,219,167,211,159,203,151),(121,174,197,137,189,129,181),(122,175,198,138,190,130,182),(123,176,199,139,191,131,183),(124,169,200,140,192,132,184),(125,170,193,141,185,133,177),(126,171,194,142,186,134,178),(127,172,195,143,187,135,179),(128,173,196,144,188,136,180)], [(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)], [(1,145,35,123),(2,148,36,126),(3,151,37,121),(4,146,38,124),(5,149,39,127),(6,152,40,122),(7,147,33,125),(8,150,34,128),(9,165,55,143),(10,168,56,138),(11,163,49,141),(12,166,50,144),(13,161,51,139),(14,164,52,142),(15,167,53,137),(16,162,54,140),(17,58,119,176),(18,61,120,171),(19,64,113,174),(20,59,114,169),(21,62,115,172),(22,57,116,175),(23,60,117,170),(24,63,118,173),(25,157,47,135),(26,160,48,130),(27,155,41,133),(28,158,42,136),(29,153,43,131),(30,156,44,134),(31,159,45,129),(32,154,46,132),(65,218,106,196),(66,221,107,199),(67,224,108,194),(68,219,109,197),(69,222,110,200),(70,217,111,195),(71,220,112,198),(72,223,105,193),(73,201,95,179),(74,204,96,182),(75,207,89,177),(76,202,90,180),(77,205,91,183),(78,208,92,178),(79,203,93,181),(80,206,94,184),(81,209,103,187),(82,212,104,190),(83,215,97,185),(84,210,98,188),(85,213,99,191),(86,216,100,186),(87,211,101,189),(88,214,102,192)], [(1,123),(2,122),(3,121),(4,128),(5,127),(6,126),(7,125),(8,124),(9,143),(10,142),(11,141),(12,140),(13,139),(14,138),(15,137),(16,144),(17,176),(18,175),(19,174),(20,173),(21,172),(22,171),(23,170),(24,169),(25,135),(26,134),(27,133),(28,132),(29,131),(30,130),(31,129),(32,136),(33,147),(34,146),(35,145),(36,152),(37,151),(38,150),(39,149),(40,148),(41,155),(42,154),(43,153),(44,160),(45,159),(46,158),(47,157),(48,156),(49,163),(50,162),(51,161),(52,168),(53,167),(54,166),(55,165),(56,164),(57,120),(58,119),(59,118),(60,117),(61,116),(62,115),(63,114),(64,113),(65,200),(66,199),(67,198),(68,197),(69,196),(70,195),(71,194),(72,193),(73,179),(74,178),(75,177),(76,184),(77,183),(78,182),(79,181),(80,180),(81,187),(82,186),(83,185),(84,192),(85,191),(86,190),(87,189),(88,188),(89,207),(90,206),(91,205),(92,204),(93,203),(94,202),(95,201),(96,208),(97,215),(98,214),(99,213),(100,212),(101,211),(102,210),(103,209),(104,216),(105,223),(106,222),(107,221),(108,220),(109,219),(110,218),(111,217),(112,224)]])

112 conjugacy classes

 class 1 2A 2B 2C 2D 2E 2F 4A 4B 4C 4D 4E 7A ··· 7F 8A 8B 8C 8D 14A ··· 14R 14S ··· 14X 14Y ··· 14AJ 28A ··· 28L 28M ··· 28R 28S ··· 28AD 56A ··· 56X order 1 2 2 2 2 2 2 4 4 4 4 4 7 ··· 7 8 8 8 8 14 ··· 14 14 ··· 14 14 ··· 14 28 ··· 28 28 ··· 28 28 ··· 28 56 ··· 56 size 1 1 1 1 4 8 8 2 2 4 8 8 1 ··· 1 4 4 4 4 1 ··· 1 4 ··· 4 8 ··· 8 2 ··· 2 4 ··· 4 8 ··· 8 4 ··· 4

112 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 4 4 type + + + + + + + + + + image C1 C2 C2 C2 C2 C2 C7 C14 C14 C14 C14 C14 D4 D4 D4 C4○D4 C7×D4 C7×D4 C7×D4 C7×C4○D4 C8⋊C22 C7×C8⋊C22 kernel C7×C8⋊2D4 C7×D4⋊C4 C7×C4.Q8 C7×C4⋊D4 C14×M4(2) C14×D8 C8⋊2D4 D4⋊C4 C4.Q8 C4⋊D4 C2×M4(2) C2×D8 C56 C2×C28 C22×C14 C28 C8 C2×C4 C23 C4 C14 C2 # reps 1 2 1 2 1 1 6 12 6 12 6 6 2 1 1 2 12 6 6 12 2 12

Matrix representation of C7×C82D4 in GL6(𝔽113)

 1 0 0 0 0 0 0 1 0 0 0 0 0 0 16 0 0 0 0 0 0 16 0 0 0 0 0 0 16 0 0 0 0 0 0 16
,
 112 0 0 0 0 0 0 112 0 0 0 0 0 0 0 0 1 0 0 0 97 18 112 111 0 0 0 112 0 0 0 0 25 106 96 95
,
 79 109 0 0 0 0 35 34 0 0 0 0 0 0 46 33 103 34 0 0 20 34 69 59 0 0 27 17 0 0 0 0 16 47 23 33
,
 79 109 0 0 0 0 91 34 0 0 0 0 0 0 46 33 103 34 0 0 20 34 69 59 0 0 86 96 0 0 0 0 60 37 23 33

G:=sub<GL(6,GF(113))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,16,0,0,0,0,0,0,16,0,0,0,0,0,0,16,0,0,0,0,0,0,16],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,0,97,0,25,0,0,0,18,112,106,0,0,1,112,0,96,0,0,0,111,0,95],[79,35,0,0,0,0,109,34,0,0,0,0,0,0,46,20,27,16,0,0,33,34,17,47,0,0,103,69,0,23,0,0,34,59,0,33],[79,91,0,0,0,0,109,34,0,0,0,0,0,0,46,20,86,60,0,0,33,34,96,37,0,0,103,69,0,23,0,0,34,59,0,33] >;

C7×C82D4 in GAP, Magma, Sage, TeX

C_7\times C_8\rtimes_2D_4
% in TeX

G:=Group("C7xC8:2D4");
// GroupNames label

G:=SmallGroup(448,877);
// by ID

G=gap.SmallGroup(448,877);
# by ID

G:=PCGroup([7,-2,-2,-2,-7,-2,-2,-2,813,1968,2438,2403,9804,172]);
// Polycyclic

G:=Group<a,b,c,d|a^7=b^8=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^3,d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations

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