metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: SD16⋊1Dic7, C56⋊9(C2×C4), C56⋊C4⋊4C2, C8⋊3(C2×Dic7), (C7×SD16)⋊1C4, (Q8×Dic7)⋊5C2, Q8⋊2(C2×Dic7), C56⋊1C4⋊26C2, C14.96(C4×D4), (C2×C8).88D14, D4.2(C2×Dic7), (D4×Dic7).9C2, (C2×SD16).1D7, C2.13(D4×Dic7), (C2×D4).144D14, C28.98(C4○D4), Q8⋊Dic7⋊26C2, C7⋊7(SD16⋊C4), C2.7(D56⋊C2), C28.74(C22×C4), (C2×Q8).114D14, (C14×SD16).1C2, C22.117(D4×D7), C4.31(D4⋊2D7), C4.4(C22×Dic7), C14.76(C8⋊C22), (C2×C56).113C22, (C2×C28).441C23, (C2×Dic7).183D4, D4⋊Dic7.15C2, C2.7(SD16⋊D7), (D4×C14).90C22, (Q8×C14).71C22, C14.46(C8.C22), C4⋊Dic7.171C22, (C4×Dic7).48C22, (C7×Q8)⋊7(C2×C4), (C7×D4).9(C2×C4), (C2×C14).353(C2×D4), (C2×C7⋊C8).153C22, (C2×C4).530(C22×D7), SmallGroup(448,698)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for SD16⋊Dic7
G = < a,b,c,d | a8=b2=c14=1, d2=c7, bab=a3, ac=ca, dad-1=a5, bc=cb, bd=db, dcd-1=c-1 >
Subgroups: 484 in 120 conjugacy classes, 57 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C8, C2×C4, C2×C4, D4, D4, Q8, Q8, C23, C14, C14, C42, C22⋊C4, C4⋊C4, C2×C8, C2×C8, SD16, C22×C4, C2×D4, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C8⋊C4, D4⋊C4, Q8⋊C4, C2.D8, C4×D4, C4×Q8, C2×SD16, C7⋊C8, C56, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×D4, C7×D4, C7×Q8, C7×Q8, C22×C14, SD16⋊C4, C2×C7⋊C8, C4×Dic7, C4×Dic7, C4⋊Dic7, C4⋊Dic7, C23.D7, C2×C56, C7×SD16, C22×Dic7, D4×C14, Q8×C14, C56⋊C4, C56⋊1C4, D4⋊Dic7, Q8⋊Dic7, D4×Dic7, Q8×Dic7, C14×SD16, SD16⋊Dic7
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22×C4, C2×D4, C4○D4, Dic7, D14, C4×D4, C8⋊C22, C8.C22, C2×Dic7, C22×D7, SD16⋊C4, D4×D7, D4⋊2D7, C22×Dic7, D56⋊C2, SD16⋊D7, D4×Dic7, SD16⋊Dic7
►On 224 points
Generators in S224
(1 90 28 203 107 49 35 61)(2 91 15 204 108 50 36 62)(3 92 16 205 109 51 37 63)(4 93 17 206 110 52 38 64)(5 94 18 207 111 53 39 65)(6 95 19 208 112 54 40 66)(7 96 20 209 99 55 41 67)(8 97 21 210 100 56 42 68)(9 98 22 197 101 43 29 69)(10 85 23 198 102 44 30 70)(11 86 24 199 103 45 31 57)(12 87 25 200 104 46 32 58)(13 88 26 201 105 47 33 59)(14 89 27 202 106 48 34 60)(71 177 130 148 164 185 214 119)(72 178 131 149 165 186 215 120)(73 179 132 150 166 187 216 121)(74 180 133 151 167 188 217 122)(75 181 134 152 168 189 218 123)(76 182 135 153 155 190 219 124)(77 169 136 154 156 191 220 125)(78 170 137 141 157 192 221 126)(79 171 138 142 158 193 222 113)(80 172 139 143 159 194 223 114)(81 173 140 144 160 195 224 115)(82 174 127 145 161 196 211 116)(83 175 128 146 162 183 212 117)(84 176 129 147 163 184 213 118)
(15 36)(16 37)(17 38)(18 39)(19 40)(20 41)(21 42)(22 29)(23 30)(24 31)(25 32)(26 33)(27 34)(28 35)(43 69)(44 70)(45 57)(46 58)(47 59)(48 60)(49 61)(50 62)(51 63)(52 64)(53 65)(54 66)(55 67)(56 68)(71 214)(72 215)(73 216)(74 217)(75 218)(76 219)(77 220)(78 221)(79 222)(80 223)(81 224)(82 211)(83 212)(84 213)(85 198)(86 199)(87 200)(88 201)(89 202)(90 203)(91 204)(92 205)(93 206)(94 207)(95 208)(96 209)(97 210)(98 197)(113 142)(114 143)(115 144)(116 145)(117 146)(118 147)(119 148)(120 149)(121 150)(122 151)(123 152)(124 153)(125 154)(126 141)(127 161)(128 162)(129 163)(130 164)(131 165)(132 166)(133 167)(134 168)(135 155)(136 156)(137 157)(138 158)(139 159)(140 160)
(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)
(1 172 8 179)(2 171 9 178)(3 170 10 177)(4 169 11 176)(5 182 12 175)(6 181 13 174)(7 180 14 173)(15 142 22 149)(16 141 23 148)(17 154 24 147)(18 153 25 146)(19 152 26 145)(20 151 27 144)(21 150 28 143)(29 120 36 113)(30 119 37 126)(31 118 38 125)(32 117 39 124)(33 116 40 123)(34 115 41 122)(35 114 42 121)(43 131 50 138)(44 130 51 137)(45 129 52 136)(46 128 53 135)(47 127 54 134)(48 140 55 133)(49 139 56 132)(57 163 64 156)(58 162 65 155)(59 161 66 168)(60 160 67 167)(61 159 68 166)(62 158 69 165)(63 157 70 164)(71 205 78 198)(72 204 79 197)(73 203 80 210)(74 202 81 209)(75 201 82 208)(76 200 83 207)(77 199 84 206)(85 214 92 221)(86 213 93 220)(87 212 94 219)(88 211 95 218)(89 224 96 217)(90 223 97 216)(91 222 98 215)(99 188 106 195)(100 187 107 194)(101 186 108 193)(102 185 109 192)(103 184 110 191)(104 183 111 190)(105 196 112 189)
G:=sub<Sym(224)| (1,90,28,203,107,49,35,61)(2,91,15,204,108,50,36,62)(3,92,16,205,109,51,37,63)(4,93,17,206,110,52,38,64)(5,94,18,207,111,53,39,65)(6,95,19,208,112,54,40,66)(7,96,20,209,99,55,41,67)(8,97,21,210,100,56,42,68)(9,98,22,197,101,43,29,69)(10,85,23,198,102,44,30,70)(11,86,24,199,103,45,31,57)(12,87,25,200,104,46,32,58)(13,88,26,201,105,47,33,59)(14,89,27,202,106,48,34,60)(71,177,130,148,164,185,214,119)(72,178,131,149,165,186,215,120)(73,179,132,150,166,187,216,121)(74,180,133,151,167,188,217,122)(75,181,134,152,168,189,218,123)(76,182,135,153,155,190,219,124)(77,169,136,154,156,191,220,125)(78,170,137,141,157,192,221,126)(79,171,138,142,158,193,222,113)(80,172,139,143,159,194,223,114)(81,173,140,144,160,195,224,115)(82,174,127,145,161,196,211,116)(83,175,128,146,162,183,212,117)(84,176,129,147,163,184,213,118), (15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42)(22,29)(23,30)(24,31)(25,32)(26,33)(27,34)(28,35)(43,69)(44,70)(45,57)(46,58)(47,59)(48,60)(49,61)(50,62)(51,63)(52,64)(53,65)(54,66)(55,67)(56,68)(71,214)(72,215)(73,216)(74,217)(75,218)(76,219)(77,220)(78,221)(79,222)(80,223)(81,224)(82,211)(83,212)(84,213)(85,198)(86,199)(87,200)(88,201)(89,202)(90,203)(91,204)(92,205)(93,206)(94,207)(95,208)(96,209)(97,210)(98,197)(113,142)(114,143)(115,144)(116,145)(117,146)(118,147)(119,148)(120,149)(121,150)(122,151)(123,152)(124,153)(125,154)(126,141)(127,161)(128,162)(129,163)(130,164)(131,165)(132,166)(133,167)(134,168)(135,155)(136,156)(137,157)(138,158)(139,159)(140,160), (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), (1,172,8,179)(2,171,9,178)(3,170,10,177)(4,169,11,176)(5,182,12,175)(6,181,13,174)(7,180,14,173)(15,142,22,149)(16,141,23,148)(17,154,24,147)(18,153,25,146)(19,152,26,145)(20,151,27,144)(21,150,28,143)(29,120,36,113)(30,119,37,126)(31,118,38,125)(32,117,39,124)(33,116,40,123)(34,115,41,122)(35,114,42,121)(43,131,50,138)(44,130,51,137)(45,129,52,136)(46,128,53,135)(47,127,54,134)(48,140,55,133)(49,139,56,132)(57,163,64,156)(58,162,65,155)(59,161,66,168)(60,160,67,167)(61,159,68,166)(62,158,69,165)(63,157,70,164)(71,205,78,198)(72,204,79,197)(73,203,80,210)(74,202,81,209)(75,201,82,208)(76,200,83,207)(77,199,84,206)(85,214,92,221)(86,213,93,220)(87,212,94,219)(88,211,95,218)(89,224,96,217)(90,223,97,216)(91,222,98,215)(99,188,106,195)(100,187,107,194)(101,186,108,193)(102,185,109,192)(103,184,110,191)(104,183,111,190)(105,196,112,189)>;
G:=Group( (1,90,28,203,107,49,35,61)(2,91,15,204,108,50,36,62)(3,92,16,205,109,51,37,63)(4,93,17,206,110,52,38,64)(5,94,18,207,111,53,39,65)(6,95,19,208,112,54,40,66)(7,96,20,209,99,55,41,67)(8,97,21,210,100,56,42,68)(9,98,22,197,101,43,29,69)(10,85,23,198,102,44,30,70)(11,86,24,199,103,45,31,57)(12,87,25,200,104,46,32,58)(13,88,26,201,105,47,33,59)(14,89,27,202,106,48,34,60)(71,177,130,148,164,185,214,119)(72,178,131,149,165,186,215,120)(73,179,132,150,166,187,216,121)(74,180,133,151,167,188,217,122)(75,181,134,152,168,189,218,123)(76,182,135,153,155,190,219,124)(77,169,136,154,156,191,220,125)(78,170,137,141,157,192,221,126)(79,171,138,142,158,193,222,113)(80,172,139,143,159,194,223,114)(81,173,140,144,160,195,224,115)(82,174,127,145,161,196,211,116)(83,175,128,146,162,183,212,117)(84,176,129,147,163,184,213,118), (15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42)(22,29)(23,30)(24,31)(25,32)(26,33)(27,34)(28,35)(43,69)(44,70)(45,57)(46,58)(47,59)(48,60)(49,61)(50,62)(51,63)(52,64)(53,65)(54,66)(55,67)(56,68)(71,214)(72,215)(73,216)(74,217)(75,218)(76,219)(77,220)(78,221)(79,222)(80,223)(81,224)(82,211)(83,212)(84,213)(85,198)(86,199)(87,200)(88,201)(89,202)(90,203)(91,204)(92,205)(93,206)(94,207)(95,208)(96,209)(97,210)(98,197)(113,142)(114,143)(115,144)(116,145)(117,146)(118,147)(119,148)(120,149)(121,150)(122,151)(123,152)(124,153)(125,154)(126,141)(127,161)(128,162)(129,163)(130,164)(131,165)(132,166)(133,167)(134,168)(135,155)(136,156)(137,157)(138,158)(139,159)(140,160), (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), (1,172,8,179)(2,171,9,178)(3,170,10,177)(4,169,11,176)(5,182,12,175)(6,181,13,174)(7,180,14,173)(15,142,22,149)(16,141,23,148)(17,154,24,147)(18,153,25,146)(19,152,26,145)(20,151,27,144)(21,150,28,143)(29,120,36,113)(30,119,37,126)(31,118,38,125)(32,117,39,124)(33,116,40,123)(34,115,41,122)(35,114,42,121)(43,131,50,138)(44,130,51,137)(45,129,52,136)(46,128,53,135)(47,127,54,134)(48,140,55,133)(49,139,56,132)(57,163,64,156)(58,162,65,155)(59,161,66,168)(60,160,67,167)(61,159,68,166)(62,158,69,165)(63,157,70,164)(71,205,78,198)(72,204,79,197)(73,203,80,210)(74,202,81,209)(75,201,82,208)(76,200,83,207)(77,199,84,206)(85,214,92,221)(86,213,93,220)(87,212,94,219)(88,211,95,218)(89,224,96,217)(90,223,97,216)(91,222,98,215)(99,188,106,195)(100,187,107,194)(101,186,108,193)(102,185,109,192)(103,184,110,191)(104,183,111,190)(105,196,112,189) );
G=PermutationGroup([[(1,90,28,203,107,49,35,61),(2,91,15,204,108,50,36,62),(3,92,16,205,109,51,37,63),(4,93,17,206,110,52,38,64),(5,94,18,207,111,53,39,65),(6,95,19,208,112,54,40,66),(7,96,20,209,99,55,41,67),(8,97,21,210,100,56,42,68),(9,98,22,197,101,43,29,69),(10,85,23,198,102,44,30,70),(11,86,24,199,103,45,31,57),(12,87,25,200,104,46,32,58),(13,88,26,201,105,47,33,59),(14,89,27,202,106,48,34,60),(71,177,130,148,164,185,214,119),(72,178,131,149,165,186,215,120),(73,179,132,150,166,187,216,121),(74,180,133,151,167,188,217,122),(75,181,134,152,168,189,218,123),(76,182,135,153,155,190,219,124),(77,169,136,154,156,191,220,125),(78,170,137,141,157,192,221,126),(79,171,138,142,158,193,222,113),(80,172,139,143,159,194,223,114),(81,173,140,144,160,195,224,115),(82,174,127,145,161,196,211,116),(83,175,128,146,162,183,212,117),(84,176,129,147,163,184,213,118)], [(15,36),(16,37),(17,38),(18,39),(19,40),(20,41),(21,42),(22,29),(23,30),(24,31),(25,32),(26,33),(27,34),(28,35),(43,69),(44,70),(45,57),(46,58),(47,59),(48,60),(49,61),(50,62),(51,63),(52,64),(53,65),(54,66),(55,67),(56,68),(71,214),(72,215),(73,216),(74,217),(75,218),(76,219),(77,220),(78,221),(79,222),(80,223),(81,224),(82,211),(83,212),(84,213),(85,198),(86,199),(87,200),(88,201),(89,202),(90,203),(91,204),(92,205),(93,206),(94,207),(95,208),(96,209),(97,210),(98,197),(113,142),(114,143),(115,144),(116,145),(117,146),(118,147),(119,148),(120,149),(121,150),(122,151),(123,152),(124,153),(125,154),(126,141),(127,161),(128,162),(129,163),(130,164),(131,165),(132,166),(133,167),(134,168),(135,155),(136,156),(137,157),(138,158),(139,159),(140,160)], [(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)], [(1,172,8,179),(2,171,9,178),(3,170,10,177),(4,169,11,176),(5,182,12,175),(6,181,13,174),(7,180,14,173),(15,142,22,149),(16,141,23,148),(17,154,24,147),(18,153,25,146),(19,152,26,145),(20,151,27,144),(21,150,28,143),(29,120,36,113),(30,119,37,126),(31,118,38,125),(32,117,39,124),(33,116,40,123),(34,115,41,122),(35,114,42,121),(43,131,50,138),(44,130,51,137),(45,129,52,136),(46,128,53,135),(47,127,54,134),(48,140,55,133),(49,139,56,132),(57,163,64,156),(58,162,65,155),(59,161,66,168),(60,160,67,167),(61,159,68,166),(62,158,69,165),(63,157,70,164),(71,205,78,198),(72,204,79,197),(73,203,80,210),(74,202,81,209),(75,201,82,208),(76,200,83,207),(77,199,84,206),(85,214,92,221),(86,213,93,220),(87,212,94,219),(88,211,95,218),(89,224,96,217),(90,223,97,216),(91,222,98,215),(99,188,106,195),(100,187,107,194),(101,186,108,193),(102,185,109,192),(103,184,110,191),(104,183,111,190),(105,196,112,189)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28F | 28G | ··· | 28L | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 2 | 2 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 4 | 4 | 28 | 28 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | - | + | + | + | - | - | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D7 | C4○D4 | D14 | Dic7 | D14 | D14 | C8⋊C22 | C8.C22 | D4⋊2D7 | D4×D7 | D56⋊C2 | SD16⋊D7 |
| kernel | SD16⋊Dic7 | C56⋊C4 | C56⋊1C4 | D4⋊Dic7 | Q8⋊Dic7 | D4×Dic7 | Q8×Dic7 | C14×SD16 | C7×SD16 | C2×Dic7 | C2×SD16 | C28 | C2×C8 | SD16 | C2×D4 | C2×Q8 | C14 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8 | 2 | 3 | 2 | 3 | 12 | 3 | 3 | 1 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of SD16⋊Dic7 ►in GL6(𝔽113)
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 38 | 70 | 38 | 70 |
| 0 | 0 | 6 | 75 | 6 | 75 |
| 0 | 0 | 75 | 43 | 38 | 70 |
| 0 | 0 | 107 | 38 | 6 | 75 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 1 | 104 | 0 | 0 | 0 | 0 |
| 0 | 0 | 103 | 1 | 0 | 0 |
| 0 | 0 | 13 | 89 | 0 | 0 |
| 0 | 0 | 0 | 0 | 103 | 1 |
| 0 | 0 | 0 | 0 | 13 | 89 |
| 73 | 84 | 0 | 0 | 0 | 0 |
| 63 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 66 | 53 | 0 | 0 |
| 0 | 0 | 82 | 47 | 0 | 0 |
| 0 | 0 | 0 | 0 | 66 | 53 |
| 0 | 0 | 0 | 0 | 82 | 47 |
G:=sub<GL(6,GF(113))| [112,0,0,0,0,0,0,112,0,0,0,0,0,0,38,6,75,107,0,0,70,75,43,38,0,0,38,6,38,6,0,0,70,75,70,75],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[0,1,0,0,0,0,112,104,0,0,0,0,0,0,103,13,0,0,0,0,1,89,0,0,0,0,0,0,103,13,0,0,0,0,1,89],[73,63,0,0,0,0,84,40,0,0,0,0,0,0,66,82,0,0,0,0,53,47,0,0,0,0,0,0,66,82,0,0,0,0,53,47] >;
SD16⋊Dic7 in GAP, Magma, Sage, TeX
{\rm SD}_{16}\rtimes {\rm Dic}_7 % in TeX
G:=Group("SD16:Dic7"); // GroupNames label
G:=SmallGroup(448,698);
// by ID
G=gap.SmallGroup(448,698);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,56,758,219,184,851,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^8=b^2=c^14=1,d^2=c^7,b*a*b=a^3,a*c=c*a,d*a*d^-1=a^5,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations