metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4⋊C4.8D14, (C8×Dic7)⋊20C2, D4⋊C4.1D7, (C2×D4).22D14, C28.6(C4○D4), C14.Q16⋊3C2, (C2×C8).200D14, C28.3Q8⋊4C2, C14.38(C4○D8), C4.23(C4○D28), C2.8(D8⋊3D7), (C2×Dic7).87D4, D4⋊Dic7.6C2, C22.170(D4×D7), C28.44D4⋊17C2, C4.49(D4⋊2D7), (C2×C56).181C22, (C2×C28).208C23, C28.17D4.4C2, (D4×C14).29C22, C4⋊Dic7.66C22, C2.9(SD16⋊3D7), C14.25(C4.4D4), C7⋊2(C42.78C22), (C2×Dic14).54C22, (C4×Dic7).223C22, C2.15(Dic7.D4), (C2×C14).221(C2×D4), (C7×C4⋊C4).13C22, (C2×C7⋊C8).210C22, (C7×D4⋊C4).10C2, (C2×C4).315(C22×D7), SmallGroup(448,302)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C8×Dic7)⋊C2
G = < a,b,c,d | a8=b14=d2=1, c2=b7, ab=ba, ac=ca, dad=a-1b7, cbc-1=b-1, bd=db, dcd=a4b7c >
Subgroups: 436 in 96 conjugacy classes, 37 normal (all characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, C14, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, C2×D4, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C4×C8, D4⋊C4, D4⋊C4, Q8⋊C4, C4.4D4, C42.C2, C7⋊C8, C56, Dic14, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×D4, C22×C14, C42.78C22, C2×C7⋊C8, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, C23.D7, C7×C4⋊C4, C2×C56, C2×Dic14, D4×C14, C14.Q16, C8×Dic7, C28.44D4, D4⋊Dic7, C7×D4⋊C4, C28.3Q8, C28.17D4, (C8×Dic7)⋊C2
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4.4D4, C4○D8, C22×D7, C42.78C22, C4○D28, D4×D7, D4⋊2D7, Dic7.D4, D8⋊3D7, SD16⋊3D7, (C8×Dic7)⋊C2
►On 224 points
Generators in S224
(1 30 183 72 49 148 97 118)(2 31 184 73 50 149 98 119)(3 32 185 74 51 150 85 120)(4 33 186 75 52 151 86 121)(5 34 187 76 53 152 87 122)(6 35 188 77 54 153 88 123)(7 36 189 78 55 154 89 124)(8 37 190 79 56 141 90 125)(9 38 191 80 43 142 91 126)(10 39 192 81 44 143 92 113)(11 40 193 82 45 144 93 114)(12 41 194 83 46 145 94 115)(13 42 195 84 47 146 95 116)(14 29 196 71 48 147 96 117)(15 57 205 221 128 178 100 158)(16 58 206 222 129 179 101 159)(17 59 207 223 130 180 102 160)(18 60 208 224 131 181 103 161)(19 61 209 211 132 182 104 162)(20 62 210 212 133 169 105 163)(21 63 197 213 134 170 106 164)(22 64 198 214 135 171 107 165)(23 65 199 215 136 172 108 166)(24 66 200 216 137 173 109 167)(25 67 201 217 138 174 110 168)(26 68 202 218 139 175 111 155)(27 69 203 219 140 176 112 156)(28 70 204 220 127 177 99 157)
(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 65 8 58)(2 64 9 57)(3 63 10 70)(4 62 11 69)(5 61 12 68)(6 60 13 67)(7 59 14 66)(15 119 22 126)(16 118 23 125)(17 117 24 124)(18 116 25 123)(19 115 26 122)(20 114 27 121)(21 113 28 120)(29 200 36 207)(30 199 37 206)(31 198 38 205)(32 197 39 204)(33 210 40 203)(34 209 41 202)(35 208 42 201)(43 178 50 171)(44 177 51 170)(45 176 52 169)(46 175 53 182)(47 174 54 181)(48 173 55 180)(49 172 56 179)(71 137 78 130)(72 136 79 129)(73 135 80 128)(74 134 81 127)(75 133 82 140)(76 132 83 139)(77 131 84 138)(85 164 92 157)(86 163 93 156)(87 162 94 155)(88 161 95 168)(89 160 96 167)(90 159 97 166)(91 158 98 165)(99 150 106 143)(100 149 107 142)(101 148 108 141)(102 147 109 154)(103 146 110 153)(104 145 111 152)(105 144 112 151)(183 215 190 222)(184 214 191 221)(185 213 192 220)(186 212 193 219)(187 211 194 218)(188 224 195 217)(189 223 196 216)
(15 100)(16 101)(17 102)(18 103)(19 104)(20 105)(21 106)(22 107)(23 108)(24 109)(25 110)(26 111)(27 112)(28 99)(29 124)(30 125)(31 126)(32 113)(33 114)(34 115)(35 116)(36 117)(37 118)(38 119)(39 120)(40 121)(41 122)(42 123)(57 171)(58 172)(59 173)(60 174)(61 175)(62 176)(63 177)(64 178)(65 179)(66 180)(67 181)(68 182)(69 169)(70 170)(71 154)(72 141)(73 142)(74 143)(75 144)(76 145)(77 146)(78 147)(79 148)(80 149)(81 150)(82 151)(83 152)(84 153)(85 185)(86 186)(87 187)(88 188)(89 189)(90 190)(91 191)(92 192)(93 193)(94 194)(95 195)(96 196)(97 183)(98 184)(127 204)(128 205)(129 206)(130 207)(131 208)(132 209)(133 210)(134 197)(135 198)(136 199)(137 200)(138 201)(139 202)(140 203)(155 162)(156 163)(157 164)(158 165)(159 166)(160 167)(161 168)(211 218)(212 219)(213 220)(214 221)(215 222)(216 223)(217 224)
G:=sub<Sym(224)| (1,30,183,72,49,148,97,118)(2,31,184,73,50,149,98,119)(3,32,185,74,51,150,85,120)(4,33,186,75,52,151,86,121)(5,34,187,76,53,152,87,122)(6,35,188,77,54,153,88,123)(7,36,189,78,55,154,89,124)(8,37,190,79,56,141,90,125)(9,38,191,80,43,142,91,126)(10,39,192,81,44,143,92,113)(11,40,193,82,45,144,93,114)(12,41,194,83,46,145,94,115)(13,42,195,84,47,146,95,116)(14,29,196,71,48,147,96,117)(15,57,205,221,128,178,100,158)(16,58,206,222,129,179,101,159)(17,59,207,223,130,180,102,160)(18,60,208,224,131,181,103,161)(19,61,209,211,132,182,104,162)(20,62,210,212,133,169,105,163)(21,63,197,213,134,170,106,164)(22,64,198,214,135,171,107,165)(23,65,199,215,136,172,108,166)(24,66,200,216,137,173,109,167)(25,67,201,217,138,174,110,168)(26,68,202,218,139,175,111,155)(27,69,203,219,140,176,112,156)(28,70,204,220,127,177,99,157), (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), (1,65,8,58)(2,64,9,57)(3,63,10,70)(4,62,11,69)(5,61,12,68)(6,60,13,67)(7,59,14,66)(15,119,22,126)(16,118,23,125)(17,117,24,124)(18,116,25,123)(19,115,26,122)(20,114,27,121)(21,113,28,120)(29,200,36,207)(30,199,37,206)(31,198,38,205)(32,197,39,204)(33,210,40,203)(34,209,41,202)(35,208,42,201)(43,178,50,171)(44,177,51,170)(45,176,52,169)(46,175,53,182)(47,174,54,181)(48,173,55,180)(49,172,56,179)(71,137,78,130)(72,136,79,129)(73,135,80,128)(74,134,81,127)(75,133,82,140)(76,132,83,139)(77,131,84,138)(85,164,92,157)(86,163,93,156)(87,162,94,155)(88,161,95,168)(89,160,96,167)(90,159,97,166)(91,158,98,165)(99,150,106,143)(100,149,107,142)(101,148,108,141)(102,147,109,154)(103,146,110,153)(104,145,111,152)(105,144,112,151)(183,215,190,222)(184,214,191,221)(185,213,192,220)(186,212,193,219)(187,211,194,218)(188,224,195,217)(189,223,196,216), (15,100)(16,101)(17,102)(18,103)(19,104)(20,105)(21,106)(22,107)(23,108)(24,109)(25,110)(26,111)(27,112)(28,99)(29,124)(30,125)(31,126)(32,113)(33,114)(34,115)(35,116)(36,117)(37,118)(38,119)(39,120)(40,121)(41,122)(42,123)(57,171)(58,172)(59,173)(60,174)(61,175)(62,176)(63,177)(64,178)(65,179)(66,180)(67,181)(68,182)(69,169)(70,170)(71,154)(72,141)(73,142)(74,143)(75,144)(76,145)(77,146)(78,147)(79,148)(80,149)(81,150)(82,151)(83,152)(84,153)(85,185)(86,186)(87,187)(88,188)(89,189)(90,190)(91,191)(92,192)(93,193)(94,194)(95,195)(96,196)(97,183)(98,184)(127,204)(128,205)(129,206)(130,207)(131,208)(132,209)(133,210)(134,197)(135,198)(136,199)(137,200)(138,201)(139,202)(140,203)(155,162)(156,163)(157,164)(158,165)(159,166)(160,167)(161,168)(211,218)(212,219)(213,220)(214,221)(215,222)(216,223)(217,224)>;
G:=Group( (1,30,183,72,49,148,97,118)(2,31,184,73,50,149,98,119)(3,32,185,74,51,150,85,120)(4,33,186,75,52,151,86,121)(5,34,187,76,53,152,87,122)(6,35,188,77,54,153,88,123)(7,36,189,78,55,154,89,124)(8,37,190,79,56,141,90,125)(9,38,191,80,43,142,91,126)(10,39,192,81,44,143,92,113)(11,40,193,82,45,144,93,114)(12,41,194,83,46,145,94,115)(13,42,195,84,47,146,95,116)(14,29,196,71,48,147,96,117)(15,57,205,221,128,178,100,158)(16,58,206,222,129,179,101,159)(17,59,207,223,130,180,102,160)(18,60,208,224,131,181,103,161)(19,61,209,211,132,182,104,162)(20,62,210,212,133,169,105,163)(21,63,197,213,134,170,106,164)(22,64,198,214,135,171,107,165)(23,65,199,215,136,172,108,166)(24,66,200,216,137,173,109,167)(25,67,201,217,138,174,110,168)(26,68,202,218,139,175,111,155)(27,69,203,219,140,176,112,156)(28,70,204,220,127,177,99,157), (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), (1,65,8,58)(2,64,9,57)(3,63,10,70)(4,62,11,69)(5,61,12,68)(6,60,13,67)(7,59,14,66)(15,119,22,126)(16,118,23,125)(17,117,24,124)(18,116,25,123)(19,115,26,122)(20,114,27,121)(21,113,28,120)(29,200,36,207)(30,199,37,206)(31,198,38,205)(32,197,39,204)(33,210,40,203)(34,209,41,202)(35,208,42,201)(43,178,50,171)(44,177,51,170)(45,176,52,169)(46,175,53,182)(47,174,54,181)(48,173,55,180)(49,172,56,179)(71,137,78,130)(72,136,79,129)(73,135,80,128)(74,134,81,127)(75,133,82,140)(76,132,83,139)(77,131,84,138)(85,164,92,157)(86,163,93,156)(87,162,94,155)(88,161,95,168)(89,160,96,167)(90,159,97,166)(91,158,98,165)(99,150,106,143)(100,149,107,142)(101,148,108,141)(102,147,109,154)(103,146,110,153)(104,145,111,152)(105,144,112,151)(183,215,190,222)(184,214,191,221)(185,213,192,220)(186,212,193,219)(187,211,194,218)(188,224,195,217)(189,223,196,216), (15,100)(16,101)(17,102)(18,103)(19,104)(20,105)(21,106)(22,107)(23,108)(24,109)(25,110)(26,111)(27,112)(28,99)(29,124)(30,125)(31,126)(32,113)(33,114)(34,115)(35,116)(36,117)(37,118)(38,119)(39,120)(40,121)(41,122)(42,123)(57,171)(58,172)(59,173)(60,174)(61,175)(62,176)(63,177)(64,178)(65,179)(66,180)(67,181)(68,182)(69,169)(70,170)(71,154)(72,141)(73,142)(74,143)(75,144)(76,145)(77,146)(78,147)(79,148)(80,149)(81,150)(82,151)(83,152)(84,153)(85,185)(86,186)(87,187)(88,188)(89,189)(90,190)(91,191)(92,192)(93,193)(94,194)(95,195)(96,196)(97,183)(98,184)(127,204)(128,205)(129,206)(130,207)(131,208)(132,209)(133,210)(134,197)(135,198)(136,199)(137,200)(138,201)(139,202)(140,203)(155,162)(156,163)(157,164)(158,165)(159,166)(160,167)(161,168)(211,218)(212,219)(213,220)(214,221)(215,222)(216,223)(217,224) );
G=PermutationGroup([[(1,30,183,72,49,148,97,118),(2,31,184,73,50,149,98,119),(3,32,185,74,51,150,85,120),(4,33,186,75,52,151,86,121),(5,34,187,76,53,152,87,122),(6,35,188,77,54,153,88,123),(7,36,189,78,55,154,89,124),(8,37,190,79,56,141,90,125),(9,38,191,80,43,142,91,126),(10,39,192,81,44,143,92,113),(11,40,193,82,45,144,93,114),(12,41,194,83,46,145,94,115),(13,42,195,84,47,146,95,116),(14,29,196,71,48,147,96,117),(15,57,205,221,128,178,100,158),(16,58,206,222,129,179,101,159),(17,59,207,223,130,180,102,160),(18,60,208,224,131,181,103,161),(19,61,209,211,132,182,104,162),(20,62,210,212,133,169,105,163),(21,63,197,213,134,170,106,164),(22,64,198,214,135,171,107,165),(23,65,199,215,136,172,108,166),(24,66,200,216,137,173,109,167),(25,67,201,217,138,174,110,168),(26,68,202,218,139,175,111,155),(27,69,203,219,140,176,112,156),(28,70,204,220,127,177,99,157)], [(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)], [(1,65,8,58),(2,64,9,57),(3,63,10,70),(4,62,11,69),(5,61,12,68),(6,60,13,67),(7,59,14,66),(15,119,22,126),(16,118,23,125),(17,117,24,124),(18,116,25,123),(19,115,26,122),(20,114,27,121),(21,113,28,120),(29,200,36,207),(30,199,37,206),(31,198,38,205),(32,197,39,204),(33,210,40,203),(34,209,41,202),(35,208,42,201),(43,178,50,171),(44,177,51,170),(45,176,52,169),(46,175,53,182),(47,174,54,181),(48,173,55,180),(49,172,56,179),(71,137,78,130),(72,136,79,129),(73,135,80,128),(74,134,81,127),(75,133,82,140),(76,132,83,139),(77,131,84,138),(85,164,92,157),(86,163,93,156),(87,162,94,155),(88,161,95,168),(89,160,96,167),(90,159,97,166),(91,158,98,165),(99,150,106,143),(100,149,107,142),(101,148,108,141),(102,147,109,154),(103,146,110,153),(104,145,111,152),(105,144,112,151),(183,215,190,222),(184,214,191,221),(185,213,192,220),(186,212,193,219),(187,211,194,218),(188,224,195,217),(189,223,196,216)], [(15,100),(16,101),(17,102),(18,103),(19,104),(20,105),(21,106),(22,107),(23,108),(24,109),(25,110),(26,111),(27,112),(28,99),(29,124),(30,125),(31,126),(32,113),(33,114),(34,115),(35,116),(36,117),(37,118),(38,119),(39,120),(40,121),(41,122),(42,123),(57,171),(58,172),(59,173),(60,174),(61,175),(62,176),(63,177),(64,178),(65,179),(66,180),(67,181),(68,182),(69,169),(70,170),(71,154),(72,141),(73,142),(74,143),(75,144),(76,145),(77,146),(78,147),(79,148),(80,149),(81,150),(82,151),(83,152),(84,153),(85,185),(86,186),(87,187),(88,188),(89,189),(90,190),(91,191),(92,192),(93,193),(94,194),(95,195),(96,196),(97,183),(98,184),(127,204),(128,205),(129,206),(130,207),(131,208),(132,209),(133,210),(134,197),(135,198),(136,199),(137,200),(138,201),(139,202),(140,203),(155,162),(156,163),(157,164),(158,165),(159,166),(160,167),(161,168),(211,218),(212,219),(213,220),(214,221),(215,222),(216,223),(217,224)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28F | 28G | ··· | 28L | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 8 | 2 | 2 | 8 | 14 | 14 | 14 | 14 | 56 | 56 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 14 | 14 | 14 | 14 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | C4○D8 | C4○D28 | D4⋊2D7 | D4×D7 | D8⋊3D7 | SD16⋊3D7 |
| kernel | (C8×Dic7)⋊C2 | C14.Q16 | C8×Dic7 | C28.44D4 | D4⋊Dic7 | C7×D4⋊C4 | C28.3Q8 | C28.17D4 | C2×Dic7 | D4⋊C4 | C28 | C4⋊C4 | C2×C8 | C2×D4 | C14 | C4 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 3 | 4 | 3 | 3 | 3 | 8 | 12 | 3 | 3 | 6 | 6 |
Matrix representation of (C8×Dic7)⋊C2 ►in GL4(𝔽113) generated by
| 0 | 100 | 0 | 0 |
| 26 | 87 | 0 | 0 |
| 0 | 0 | 98 | 0 |
| 0 | 0 | 0 | 98 |
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 64 | 0 |
| 0 | 0 | 50 | 83 |
| 15 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 |
| 0 | 0 | 112 | 29 |
| 0 | 0 | 35 | 1 |
| 1 | 112 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 78 | 112 |
G:=sub<GL(4,GF(113))| [0,26,0,0,100,87,0,0,0,0,98,0,0,0,0,98],[112,0,0,0,0,112,0,0,0,0,64,50,0,0,0,83],[15,0,0,0,0,15,0,0,0,0,112,35,0,0,29,1],[1,0,0,0,112,112,0,0,0,0,1,78,0,0,0,112] >;
(C8×Dic7)⋊C2 in GAP, Magma, Sage, TeX
(C_8\times {\rm Dic}_7)\rtimes C_2 % in TeX
G:=Group("(C8xDic7):C2"); // GroupNames label
G:=SmallGroup(448,302);
// by ID
G=gap.SmallGroup(448,302);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,701,1094,135,100,570,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^8=b^14=d^2=1,c^2=b^7,a*b=b*a,a*c=c*a,d*a*d=a^-1*b^7,c*b*c^-1=b^-1,b*d=d*b,d*c*d=a^4*b^7*c>;
// generators/relations