metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28.11D4, Dic7⋊2SD16, C4.96(D4×D7), Dic7⋊C8⋊14C2, C4⋊C4.156D14, Q8⋊C4⋊14D7, C4.7(C4○D28), C28.128(C2×D4), (C2×C8).126D14, C7⋊1(D4.D4), (C2×Q8).23D14, C2.19(D7×SD16), Dic7⋊Q8⋊2C2, D28⋊C4.3C2, C28.23(C4○D4), C14.Q16⋊13C2, (C2×Dic7).35D4, C14.33(C2×SD16), C22.207(D4×D7), C14.27(C4⋊D4), (C2×C28).258C23, (C2×C56).137C22, (C2×D28).68C22, (Q8×C14).41C22, C2.30(D14⋊D4), C2.19(Q16⋊D7), C14.66(C8.C22), (C4×Dic7).25C22, (C2×Dic14).75C22, (C2×Q8⋊D7).3C2, (C2×C56⋊C2).4C2, (C2×C7⋊C8).48C22, (C7×Q8⋊C4)⋊14C2, (C2×C14).271(C2×D4), (C7×C4⋊C4).59C22, (C2×C4).365(C22×D7), SmallGroup(448,352)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic7⋊SD16
G = < a,b,c,d | a14=c8=d2=1, b2=a7, bab-1=cac-1=dad=a-1, cbc-1=a7b, bd=db, dcd=c3 >
Subgroups: 692 in 120 conjugacy classes, 41 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, SD16, C22×C4, C2×D4, C2×Q8, C2×Q8, Dic7, Dic7, C28, C28, D14, C2×C14, Q8⋊C4, Q8⋊C4, C4⋊C8, C4×D4, C4⋊Q8, C2×SD16, C7⋊C8, C56, Dic14, C4×D7, D28, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, D4.D4, C56⋊C2, C2×C7⋊C8, C4×Dic7, Dic7⋊C4, D14⋊C4, Q8⋊D7, C7×C4⋊C4, C2×C56, C2×Dic14, C2×C4×D7, C2×D28, Q8×C14, C14.Q16, Dic7⋊C8, C7×Q8⋊C4, D28⋊C4, C2×C56⋊C2, C2×Q8⋊D7, Dic7⋊Q8, Dic7⋊SD16
Quotients: C1, C2, C22, D4, C23, D7, SD16, C2×D4, C4○D4, D14, C4⋊D4, C2×SD16, C8.C22, C22×D7, D4.D4, C4○D28, D4×D7, D14⋊D4, D7×SD16, Q16⋊D7, Dic7⋊SD16
►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)
(1 188 8 195)(2 187 9 194)(3 186 10 193)(4 185 11 192)(5 184 12 191)(6 183 13 190)(7 196 14 189)(15 84 22 77)(16 83 23 76)(17 82 24 75)(18 81 25 74)(19 80 26 73)(20 79 27 72)(21 78 28 71)(29 58 36 65)(30 57 37 64)(31 70 38 63)(32 69 39 62)(33 68 40 61)(34 67 41 60)(35 66 42 59)(43 154 50 147)(44 153 51 146)(45 152 52 145)(46 151 53 144)(47 150 54 143)(48 149 55 142)(49 148 56 141)(85 138 92 131)(86 137 93 130)(87 136 94 129)(88 135 95 128)(89 134 96 127)(90 133 97 140)(91 132 98 139)(99 199 106 206)(100 198 107 205)(101 197 108 204)(102 210 109 203)(103 209 110 202)(104 208 111 201)(105 207 112 200)(113 216 120 223)(114 215 121 222)(115 214 122 221)(116 213 123 220)(117 212 124 219)(118 211 125 218)(119 224 126 217)(155 177 162 170)(156 176 163 169)(157 175 164 182)(158 174 165 181)(159 173 166 180)(160 172 167 179)(161 171 168 178)
(1 56 130 35 27 104 180 221)(2 55 131 34 28 103 181 220)(3 54 132 33 15 102 182 219)(4 53 133 32 16 101 169 218)(5 52 134 31 17 100 170 217)(6 51 135 30 18 99 171 216)(7 50 136 29 19 112 172 215)(8 49 137 42 20 111 173 214)(9 48 138 41 21 110 174 213)(10 47 139 40 22 109 175 212)(11 46 140 39 23 108 176 211)(12 45 127 38 24 107 177 224)(13 44 128 37 25 106 178 223)(14 43 129 36 26 105 179 222)(57 74 199 161 120 190 146 88)(58 73 200 160 121 189 147 87)(59 72 201 159 122 188 148 86)(60 71 202 158 123 187 149 85)(61 84 203 157 124 186 150 98)(62 83 204 156 125 185 151 97)(63 82 205 155 126 184 152 96)(64 81 206 168 113 183 153 95)(65 80 207 167 114 196 154 94)(66 79 208 166 115 195 141 93)(67 78 209 165 116 194 142 92)(68 77 210 164 117 193 143 91)(69 76 197 163 118 192 144 90)(70 75 198 162 119 191 145 89)
(1 137)(2 136)(3 135)(4 134)(5 133)(6 132)(7 131)(8 130)(9 129)(10 128)(11 127)(12 140)(13 139)(14 138)(15 171)(16 170)(17 169)(18 182)(19 181)(20 180)(21 179)(22 178)(23 177)(24 176)(25 175)(26 174)(27 173)(28 172)(29 34)(30 33)(31 32)(35 42)(36 41)(37 40)(38 39)(43 110)(44 109)(45 108)(46 107)(47 106)(48 105)(49 104)(50 103)(51 102)(52 101)(53 100)(54 99)(55 112)(56 111)(57 68)(58 67)(59 66)(60 65)(61 64)(62 63)(69 70)(71 167)(72 166)(73 165)(74 164)(75 163)(76 162)(77 161)(78 160)(79 159)(80 158)(81 157)(82 156)(83 155)(84 168)(85 196)(86 195)(87 194)(88 193)(89 192)(90 191)(91 190)(92 189)(93 188)(94 187)(95 186)(96 185)(97 184)(98 183)(113 124)(114 123)(115 122)(116 121)(117 120)(118 119)(125 126)(141 201)(142 200)(143 199)(144 198)(145 197)(146 210)(147 209)(148 208)(149 207)(150 206)(151 205)(152 204)(153 203)(154 202)(211 224)(212 223)(213 222)(214 221)(215 220)(216 219)(217 218)
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), (1,188,8,195)(2,187,9,194)(3,186,10,193)(4,185,11,192)(5,184,12,191)(6,183,13,190)(7,196,14,189)(15,84,22,77)(16,83,23,76)(17,82,24,75)(18,81,25,74)(19,80,26,73)(20,79,27,72)(21,78,28,71)(29,58,36,65)(30,57,37,64)(31,70,38,63)(32,69,39,62)(33,68,40,61)(34,67,41,60)(35,66,42,59)(43,154,50,147)(44,153,51,146)(45,152,52,145)(46,151,53,144)(47,150,54,143)(48,149,55,142)(49,148,56,141)(85,138,92,131)(86,137,93,130)(87,136,94,129)(88,135,95,128)(89,134,96,127)(90,133,97,140)(91,132,98,139)(99,199,106,206)(100,198,107,205)(101,197,108,204)(102,210,109,203)(103,209,110,202)(104,208,111,201)(105,207,112,200)(113,216,120,223)(114,215,121,222)(115,214,122,221)(116,213,123,220)(117,212,124,219)(118,211,125,218)(119,224,126,217)(155,177,162,170)(156,176,163,169)(157,175,164,182)(158,174,165,181)(159,173,166,180)(160,172,167,179)(161,171,168,178), (1,56,130,35,27,104,180,221)(2,55,131,34,28,103,181,220)(3,54,132,33,15,102,182,219)(4,53,133,32,16,101,169,218)(5,52,134,31,17,100,170,217)(6,51,135,30,18,99,171,216)(7,50,136,29,19,112,172,215)(8,49,137,42,20,111,173,214)(9,48,138,41,21,110,174,213)(10,47,139,40,22,109,175,212)(11,46,140,39,23,108,176,211)(12,45,127,38,24,107,177,224)(13,44,128,37,25,106,178,223)(14,43,129,36,26,105,179,222)(57,74,199,161,120,190,146,88)(58,73,200,160,121,189,147,87)(59,72,201,159,122,188,148,86)(60,71,202,158,123,187,149,85)(61,84,203,157,124,186,150,98)(62,83,204,156,125,185,151,97)(63,82,205,155,126,184,152,96)(64,81,206,168,113,183,153,95)(65,80,207,167,114,196,154,94)(66,79,208,166,115,195,141,93)(67,78,209,165,116,194,142,92)(68,77,210,164,117,193,143,91)(69,76,197,163,118,192,144,90)(70,75,198,162,119,191,145,89), (1,137)(2,136)(3,135)(4,134)(5,133)(6,132)(7,131)(8,130)(9,129)(10,128)(11,127)(12,140)(13,139)(14,138)(15,171)(16,170)(17,169)(18,182)(19,181)(20,180)(21,179)(22,178)(23,177)(24,176)(25,175)(26,174)(27,173)(28,172)(29,34)(30,33)(31,32)(35,42)(36,41)(37,40)(38,39)(43,110)(44,109)(45,108)(46,107)(47,106)(48,105)(49,104)(50,103)(51,102)(52,101)(53,100)(54,99)(55,112)(56,111)(57,68)(58,67)(59,66)(60,65)(61,64)(62,63)(69,70)(71,167)(72,166)(73,165)(74,164)(75,163)(76,162)(77,161)(78,160)(79,159)(80,158)(81,157)(82,156)(83,155)(84,168)(85,196)(86,195)(87,194)(88,193)(89,192)(90,191)(91,190)(92,189)(93,188)(94,187)(95,186)(96,185)(97,184)(98,183)(113,124)(114,123)(115,122)(116,121)(117,120)(118,119)(125,126)(141,201)(142,200)(143,199)(144,198)(145,197)(146,210)(147,209)(148,208)(149,207)(150,206)(151,205)(152,204)(153,203)(154,202)(211,224)(212,223)(213,222)(214,221)(215,220)(216,219)(217,218)>;
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), (1,188,8,195)(2,187,9,194)(3,186,10,193)(4,185,11,192)(5,184,12,191)(6,183,13,190)(7,196,14,189)(15,84,22,77)(16,83,23,76)(17,82,24,75)(18,81,25,74)(19,80,26,73)(20,79,27,72)(21,78,28,71)(29,58,36,65)(30,57,37,64)(31,70,38,63)(32,69,39,62)(33,68,40,61)(34,67,41,60)(35,66,42,59)(43,154,50,147)(44,153,51,146)(45,152,52,145)(46,151,53,144)(47,150,54,143)(48,149,55,142)(49,148,56,141)(85,138,92,131)(86,137,93,130)(87,136,94,129)(88,135,95,128)(89,134,96,127)(90,133,97,140)(91,132,98,139)(99,199,106,206)(100,198,107,205)(101,197,108,204)(102,210,109,203)(103,209,110,202)(104,208,111,201)(105,207,112,200)(113,216,120,223)(114,215,121,222)(115,214,122,221)(116,213,123,220)(117,212,124,219)(118,211,125,218)(119,224,126,217)(155,177,162,170)(156,176,163,169)(157,175,164,182)(158,174,165,181)(159,173,166,180)(160,172,167,179)(161,171,168,178), (1,56,130,35,27,104,180,221)(2,55,131,34,28,103,181,220)(3,54,132,33,15,102,182,219)(4,53,133,32,16,101,169,218)(5,52,134,31,17,100,170,217)(6,51,135,30,18,99,171,216)(7,50,136,29,19,112,172,215)(8,49,137,42,20,111,173,214)(9,48,138,41,21,110,174,213)(10,47,139,40,22,109,175,212)(11,46,140,39,23,108,176,211)(12,45,127,38,24,107,177,224)(13,44,128,37,25,106,178,223)(14,43,129,36,26,105,179,222)(57,74,199,161,120,190,146,88)(58,73,200,160,121,189,147,87)(59,72,201,159,122,188,148,86)(60,71,202,158,123,187,149,85)(61,84,203,157,124,186,150,98)(62,83,204,156,125,185,151,97)(63,82,205,155,126,184,152,96)(64,81,206,168,113,183,153,95)(65,80,207,167,114,196,154,94)(66,79,208,166,115,195,141,93)(67,78,209,165,116,194,142,92)(68,77,210,164,117,193,143,91)(69,76,197,163,118,192,144,90)(70,75,198,162,119,191,145,89), (1,137)(2,136)(3,135)(4,134)(5,133)(6,132)(7,131)(8,130)(9,129)(10,128)(11,127)(12,140)(13,139)(14,138)(15,171)(16,170)(17,169)(18,182)(19,181)(20,180)(21,179)(22,178)(23,177)(24,176)(25,175)(26,174)(27,173)(28,172)(29,34)(30,33)(31,32)(35,42)(36,41)(37,40)(38,39)(43,110)(44,109)(45,108)(46,107)(47,106)(48,105)(49,104)(50,103)(51,102)(52,101)(53,100)(54,99)(55,112)(56,111)(57,68)(58,67)(59,66)(60,65)(61,64)(62,63)(69,70)(71,167)(72,166)(73,165)(74,164)(75,163)(76,162)(77,161)(78,160)(79,159)(80,158)(81,157)(82,156)(83,155)(84,168)(85,196)(86,195)(87,194)(88,193)(89,192)(90,191)(91,190)(92,189)(93,188)(94,187)(95,186)(96,185)(97,184)(98,183)(113,124)(114,123)(115,122)(116,121)(117,120)(118,119)(125,126)(141,201)(142,200)(143,199)(144,198)(145,197)(146,210)(147,209)(148,208)(149,207)(150,206)(151,205)(152,204)(153,203)(154,202)(211,224)(212,223)(213,222)(214,221)(215,220)(216,219)(217,218) );
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)], [(1,188,8,195),(2,187,9,194),(3,186,10,193),(4,185,11,192),(5,184,12,191),(6,183,13,190),(7,196,14,189),(15,84,22,77),(16,83,23,76),(17,82,24,75),(18,81,25,74),(19,80,26,73),(20,79,27,72),(21,78,28,71),(29,58,36,65),(30,57,37,64),(31,70,38,63),(32,69,39,62),(33,68,40,61),(34,67,41,60),(35,66,42,59),(43,154,50,147),(44,153,51,146),(45,152,52,145),(46,151,53,144),(47,150,54,143),(48,149,55,142),(49,148,56,141),(85,138,92,131),(86,137,93,130),(87,136,94,129),(88,135,95,128),(89,134,96,127),(90,133,97,140),(91,132,98,139),(99,199,106,206),(100,198,107,205),(101,197,108,204),(102,210,109,203),(103,209,110,202),(104,208,111,201),(105,207,112,200),(113,216,120,223),(114,215,121,222),(115,214,122,221),(116,213,123,220),(117,212,124,219),(118,211,125,218),(119,224,126,217),(155,177,162,170),(156,176,163,169),(157,175,164,182),(158,174,165,181),(159,173,166,180),(160,172,167,179),(161,171,168,178)], [(1,56,130,35,27,104,180,221),(2,55,131,34,28,103,181,220),(3,54,132,33,15,102,182,219),(4,53,133,32,16,101,169,218),(5,52,134,31,17,100,170,217),(6,51,135,30,18,99,171,216),(7,50,136,29,19,112,172,215),(8,49,137,42,20,111,173,214),(9,48,138,41,21,110,174,213),(10,47,139,40,22,109,175,212),(11,46,140,39,23,108,176,211),(12,45,127,38,24,107,177,224),(13,44,128,37,25,106,178,223),(14,43,129,36,26,105,179,222),(57,74,199,161,120,190,146,88),(58,73,200,160,121,189,147,87),(59,72,201,159,122,188,148,86),(60,71,202,158,123,187,149,85),(61,84,203,157,124,186,150,98),(62,83,204,156,125,185,151,97),(63,82,205,155,126,184,152,96),(64,81,206,168,113,183,153,95),(65,80,207,167,114,196,154,94),(66,79,208,166,115,195,141,93),(67,78,209,165,116,194,142,92),(68,77,210,164,117,193,143,91),(69,76,197,163,118,192,144,90),(70,75,198,162,119,191,145,89)], [(1,137),(2,136),(3,135),(4,134),(5,133),(6,132),(7,131),(8,130),(9,129),(10,128),(11,127),(12,140),(13,139),(14,138),(15,171),(16,170),(17,169),(18,182),(19,181),(20,180),(21,179),(22,178),(23,177),(24,176),(25,175),(26,174),(27,173),(28,172),(29,34),(30,33),(31,32),(35,42),(36,41),(37,40),(38,39),(43,110),(44,109),(45,108),(46,107),(47,106),(48,105),(49,104),(50,103),(51,102),(52,101),(53,100),(54,99),(55,112),(56,111),(57,68),(58,67),(59,66),(60,65),(61,64),(62,63),(69,70),(71,167),(72,166),(73,165),(74,164),(75,163),(76,162),(77,161),(78,160),(79,159),(80,158),(81,157),(82,156),(83,155),(84,168),(85,196),(86,195),(87,194),(88,193),(89,192),(90,191),(91,190),(92,189),(93,188),(94,187),(95,186),(96,185),(97,184),(98,183),(113,124),(114,123),(115,122),(116,121),(117,120),(118,119),(125,126),(141,201),(142,200),(143,199),(144,198),(145,197),(146,210),(147,209),(148,208),(149,207),(150,206),(151,205),(152,204),(153,203),(154,202),(211,224),(212,223),(213,222),(214,221),(215,220),(216,219),(217,218)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 28A | ··· | 28F | 28G | ··· | 28R | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 2 | 2 | 4 | 4 | 8 | 14 | 14 | 28 | 56 | 2 | 2 | 2 | 4 | 4 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | SD16 | C4○D4 | D14 | D14 | D14 | C4○D28 | C8.C22 | D4×D7 | D4×D7 | D7×SD16 | Q16⋊D7 |
| kernel | Dic7⋊SD16 | C14.Q16 | Dic7⋊C8 | C7×Q8⋊C4 | D28⋊C4 | C2×C56⋊C2 | C2×Q8⋊D7 | Dic7⋊Q8 | D28 | C2×Dic7 | Q8⋊C4 | Dic7 | C28 | C4⋊C4 | C2×C8 | C2×Q8 | C4 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 3 | 4 | 2 | 3 | 3 | 3 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of Dic7⋊SD16 ►in GL6(𝔽113)
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 104 | 1 | 0 | 0 |
| 0 | 0 | 111 | 88 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 15 | 0 | 0 | 0 | 0 | 0 |
| 104 | 98 | 0 | 0 | 0 | 0 |
| 0 | 0 | 55 | 79 | 0 | 0 |
| 0 | 0 | 69 | 58 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 112 | 72 | 0 | 0 | 0 | 0 |
| 91 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 55 | 79 | 0 | 0 |
| 0 | 0 | 69 | 58 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 13 |
| 0 | 0 | 0 | 0 | 100 | 13 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 22 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 58 | 34 | 0 | 0 |
| 0 | 0 | 44 | 55 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
G:=sub<GL(6,GF(113))| [112,0,0,0,0,0,0,112,0,0,0,0,0,0,104,111,0,0,0,0,1,88,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[15,104,0,0,0,0,0,98,0,0,0,0,0,0,55,69,0,0,0,0,79,58,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[112,91,0,0,0,0,72,1,0,0,0,0,0,0,55,69,0,0,0,0,79,58,0,0,0,0,0,0,13,100,0,0,0,0,13,13],[1,22,0,0,0,0,0,112,0,0,0,0,0,0,58,44,0,0,0,0,34,55,0,0,0,0,0,0,0,1,0,0,0,0,1,0] >;
Dic7⋊SD16 in GAP, Magma, Sage, TeX
{\rm Dic}_7\rtimes {\rm SD}_{16} % in TeX
G:=Group("Dic7:SD16"); // GroupNames label
G:=SmallGroup(448,352);
// by ID
G=gap.SmallGroup(448,352);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,64,590,219,184,1684,851,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^14=c^8=d^2=1,b^2=a^7,b*a*b^-1=c*a*c^-1=d*a*d=a^-1,c*b*c^-1=a^7*b,b*d=d*b,d*c*d=c^3>;
// generators/relations