metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic14.16D4, C4.65(D4×D7), D14⋊C8⋊35C2, (C7×D4).10D4, D14⋊3Q8⋊5C2, (C2×SD16)⋊14D7, C28.177(C2×D4), (C2×C8).149D14, D4.9(C7⋊D4), C7⋊5(D4.7D4), (C2×Q8).55D14, C14.60C22≀C2, (C14×SD16)⋊23C2, (C2×D4).147D14, C14.65(C4○D8), D4⋊Dic7⋊35C2, (C22×D7).38D4, C22.270(D4×D7), C28.44D4⋊36C2, (C2×C56).296C22, (C2×C28).450C23, (C2×Dic7).185D4, (D4×C14).99C22, (Q8×C14).79C22, C2.28(C23⋊D14), C2.30(SD16⋊D7), C14.50(C8.C22), C4⋊Dic7.177C22, C2.31(SD16⋊3D7), (C2×Dic14).128C22, C4.45(C2×C7⋊D4), (C2×C7⋊Q16)⋊19C2, (C2×C4×D7).50C22, (C2×D4⋊2D7).6C2, (C2×C14).362(C2×D4), (C2×C7⋊C8).159C22, (C2×C4).539(C22×D7), SmallGroup(448,707)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic14.16D4
G = < a,b,c,d | a28=c4=d2=1, b2=a14, bab-1=cac-1=a-1, dad=a13, cbc-1=a21b, dbd=a14b, dcd=a14c-1 >
Subgroups: 772 in 152 conjugacy classes, 43 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, D4, Q8, C23, D7, C14, C14, C22⋊C4, C4⋊C4, C2×C8, C2×C8, SD16, Q16, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, C4○D4, Dic7, C28, C28, D14, C2×C14, C2×C14, C22⋊C8, D4⋊C4, Q8⋊C4, C22⋊Q8, C2×SD16, C2×Q16, C2×C4○D4, C7⋊C8, C56, Dic14, Dic14, C4×D7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C7×D4, C7×Q8, C22×D7, C22×C14, D4.7D4, C2×C7⋊C8, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C7⋊Q16, C2×C56, C7×SD16, C2×Dic14, C2×C4×D7, D4⋊2D7, C22×Dic7, C2×C7⋊D4, D4×C14, Q8×C14, C28.44D4, D14⋊C8, D4⋊Dic7, C2×C7⋊Q16, D14⋊3Q8, C14×SD16, C2×D4⋊2D7, Dic14.16D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, D14, C22≀C2, C4○D8, C8.C22, C7⋊D4, C22×D7, D4.7D4, D4×D7, C2×C7⋊D4, SD16⋊D7, SD16⋊3D7, C23⋊D14, Dic14.16D4
►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)
(1 146 15 160)(2 145 16 159)(3 144 17 158)(4 143 18 157)(5 142 19 156)(6 141 20 155)(7 168 21 154)(8 167 22 153)(9 166 23 152)(10 165 24 151)(11 164 25 150)(12 163 26 149)(13 162 27 148)(14 161 28 147)(29 67 43 81)(30 66 44 80)(31 65 45 79)(32 64 46 78)(33 63 47 77)(34 62 48 76)(35 61 49 75)(36 60 50 74)(37 59 51 73)(38 58 52 72)(39 57 53 71)(40 84 54 70)(41 83 55 69)(42 82 56 68)(85 186 99 172)(86 185 100 171)(87 184 101 170)(88 183 102 169)(89 182 103 196)(90 181 104 195)(91 180 105 194)(92 179 106 193)(93 178 107 192)(94 177 108 191)(95 176 109 190)(96 175 110 189)(97 174 111 188)(98 173 112 187)(113 218 127 204)(114 217 128 203)(115 216 129 202)(116 215 130 201)(117 214 131 200)(118 213 132 199)(119 212 133 198)(120 211 134 197)(121 210 135 224)(122 209 136 223)(123 208 137 222)(124 207 138 221)(125 206 139 220)(126 205 140 219)
(1 107 124 53)(2 106 125 52)(3 105 126 51)(4 104 127 50)(5 103 128 49)(6 102 129 48)(7 101 130 47)(8 100 131 46)(9 99 132 45)(10 98 133 44)(11 97 134 43)(12 96 135 42)(13 95 136 41)(14 94 137 40)(15 93 138 39)(16 92 139 38)(17 91 140 37)(18 90 113 36)(19 89 114 35)(20 88 115 34)(21 87 116 33)(22 86 117 32)(23 85 118 31)(24 112 119 30)(25 111 120 29)(26 110 121 56)(27 109 122 55)(28 108 123 54)(57 167 178 200)(58 166 179 199)(59 165 180 198)(60 164 181 197)(61 163 182 224)(62 162 183 223)(63 161 184 222)(64 160 185 221)(65 159 186 220)(66 158 187 219)(67 157 188 218)(68 156 189 217)(69 155 190 216)(70 154 191 215)(71 153 192 214)(72 152 193 213)(73 151 194 212)(74 150 195 211)(75 149 196 210)(76 148 169 209)(77 147 170 208)(78 146 171 207)(79 145 172 206)(80 144 173 205)(81 143 174 204)(82 142 175 203)(83 141 176 202)(84 168 177 201)
(1 138)(2 123)(3 136)(4 121)(5 134)(6 119)(7 132)(8 117)(9 130)(10 115)(11 128)(12 113)(13 126)(14 139)(15 124)(16 137)(17 122)(18 135)(19 120)(20 133)(21 118)(22 131)(23 116)(24 129)(25 114)(26 127)(27 140)(28 125)(29 49)(30 34)(31 47)(33 45)(35 43)(36 56)(37 41)(38 54)(40 52)(42 50)(44 48)(51 55)(57 71)(58 84)(59 69)(60 82)(61 67)(62 80)(63 65)(64 78)(66 76)(68 74)(70 72)(73 83)(75 81)(77 79)(85 101)(87 99)(88 112)(89 97)(90 110)(91 95)(92 108)(94 106)(96 104)(98 102)(103 111)(105 109)(141 198)(142 211)(143 224)(144 209)(145 222)(146 207)(147 220)(148 205)(149 218)(150 203)(151 216)(152 201)(153 214)(154 199)(155 212)(156 197)(157 210)(158 223)(159 208)(160 221)(161 206)(162 219)(163 204)(164 217)(165 202)(166 215)(167 200)(168 213)(169 187)(170 172)(171 185)(173 183)(174 196)(175 181)(176 194)(177 179)(178 192)(180 190)(182 188)(184 186)(189 195)(191 193)
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), (1,146,15,160)(2,145,16,159)(3,144,17,158)(4,143,18,157)(5,142,19,156)(6,141,20,155)(7,168,21,154)(8,167,22,153)(9,166,23,152)(10,165,24,151)(11,164,25,150)(12,163,26,149)(13,162,27,148)(14,161,28,147)(29,67,43,81)(30,66,44,80)(31,65,45,79)(32,64,46,78)(33,63,47,77)(34,62,48,76)(35,61,49,75)(36,60,50,74)(37,59,51,73)(38,58,52,72)(39,57,53,71)(40,84,54,70)(41,83,55,69)(42,82,56,68)(85,186,99,172)(86,185,100,171)(87,184,101,170)(88,183,102,169)(89,182,103,196)(90,181,104,195)(91,180,105,194)(92,179,106,193)(93,178,107,192)(94,177,108,191)(95,176,109,190)(96,175,110,189)(97,174,111,188)(98,173,112,187)(113,218,127,204)(114,217,128,203)(115,216,129,202)(116,215,130,201)(117,214,131,200)(118,213,132,199)(119,212,133,198)(120,211,134,197)(121,210,135,224)(122,209,136,223)(123,208,137,222)(124,207,138,221)(125,206,139,220)(126,205,140,219), (1,107,124,53)(2,106,125,52)(3,105,126,51)(4,104,127,50)(5,103,128,49)(6,102,129,48)(7,101,130,47)(8,100,131,46)(9,99,132,45)(10,98,133,44)(11,97,134,43)(12,96,135,42)(13,95,136,41)(14,94,137,40)(15,93,138,39)(16,92,139,38)(17,91,140,37)(18,90,113,36)(19,89,114,35)(20,88,115,34)(21,87,116,33)(22,86,117,32)(23,85,118,31)(24,112,119,30)(25,111,120,29)(26,110,121,56)(27,109,122,55)(28,108,123,54)(57,167,178,200)(58,166,179,199)(59,165,180,198)(60,164,181,197)(61,163,182,224)(62,162,183,223)(63,161,184,222)(64,160,185,221)(65,159,186,220)(66,158,187,219)(67,157,188,218)(68,156,189,217)(69,155,190,216)(70,154,191,215)(71,153,192,214)(72,152,193,213)(73,151,194,212)(74,150,195,211)(75,149,196,210)(76,148,169,209)(77,147,170,208)(78,146,171,207)(79,145,172,206)(80,144,173,205)(81,143,174,204)(82,142,175,203)(83,141,176,202)(84,168,177,201), (1,138)(2,123)(3,136)(4,121)(5,134)(6,119)(7,132)(8,117)(9,130)(10,115)(11,128)(12,113)(13,126)(14,139)(15,124)(16,137)(17,122)(18,135)(19,120)(20,133)(21,118)(22,131)(23,116)(24,129)(25,114)(26,127)(27,140)(28,125)(29,49)(30,34)(31,47)(33,45)(35,43)(36,56)(37,41)(38,54)(40,52)(42,50)(44,48)(51,55)(57,71)(58,84)(59,69)(60,82)(61,67)(62,80)(63,65)(64,78)(66,76)(68,74)(70,72)(73,83)(75,81)(77,79)(85,101)(87,99)(88,112)(89,97)(90,110)(91,95)(92,108)(94,106)(96,104)(98,102)(103,111)(105,109)(141,198)(142,211)(143,224)(144,209)(145,222)(146,207)(147,220)(148,205)(149,218)(150,203)(151,216)(152,201)(153,214)(154,199)(155,212)(156,197)(157,210)(158,223)(159,208)(160,221)(161,206)(162,219)(163,204)(164,217)(165,202)(166,215)(167,200)(168,213)(169,187)(170,172)(171,185)(173,183)(174,196)(175,181)(176,194)(177,179)(178,192)(180,190)(182,188)(184,186)(189,195)(191,193)>;
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), (1,146,15,160)(2,145,16,159)(3,144,17,158)(4,143,18,157)(5,142,19,156)(6,141,20,155)(7,168,21,154)(8,167,22,153)(9,166,23,152)(10,165,24,151)(11,164,25,150)(12,163,26,149)(13,162,27,148)(14,161,28,147)(29,67,43,81)(30,66,44,80)(31,65,45,79)(32,64,46,78)(33,63,47,77)(34,62,48,76)(35,61,49,75)(36,60,50,74)(37,59,51,73)(38,58,52,72)(39,57,53,71)(40,84,54,70)(41,83,55,69)(42,82,56,68)(85,186,99,172)(86,185,100,171)(87,184,101,170)(88,183,102,169)(89,182,103,196)(90,181,104,195)(91,180,105,194)(92,179,106,193)(93,178,107,192)(94,177,108,191)(95,176,109,190)(96,175,110,189)(97,174,111,188)(98,173,112,187)(113,218,127,204)(114,217,128,203)(115,216,129,202)(116,215,130,201)(117,214,131,200)(118,213,132,199)(119,212,133,198)(120,211,134,197)(121,210,135,224)(122,209,136,223)(123,208,137,222)(124,207,138,221)(125,206,139,220)(126,205,140,219), (1,107,124,53)(2,106,125,52)(3,105,126,51)(4,104,127,50)(5,103,128,49)(6,102,129,48)(7,101,130,47)(8,100,131,46)(9,99,132,45)(10,98,133,44)(11,97,134,43)(12,96,135,42)(13,95,136,41)(14,94,137,40)(15,93,138,39)(16,92,139,38)(17,91,140,37)(18,90,113,36)(19,89,114,35)(20,88,115,34)(21,87,116,33)(22,86,117,32)(23,85,118,31)(24,112,119,30)(25,111,120,29)(26,110,121,56)(27,109,122,55)(28,108,123,54)(57,167,178,200)(58,166,179,199)(59,165,180,198)(60,164,181,197)(61,163,182,224)(62,162,183,223)(63,161,184,222)(64,160,185,221)(65,159,186,220)(66,158,187,219)(67,157,188,218)(68,156,189,217)(69,155,190,216)(70,154,191,215)(71,153,192,214)(72,152,193,213)(73,151,194,212)(74,150,195,211)(75,149,196,210)(76,148,169,209)(77,147,170,208)(78,146,171,207)(79,145,172,206)(80,144,173,205)(81,143,174,204)(82,142,175,203)(83,141,176,202)(84,168,177,201), (1,138)(2,123)(3,136)(4,121)(5,134)(6,119)(7,132)(8,117)(9,130)(10,115)(11,128)(12,113)(13,126)(14,139)(15,124)(16,137)(17,122)(18,135)(19,120)(20,133)(21,118)(22,131)(23,116)(24,129)(25,114)(26,127)(27,140)(28,125)(29,49)(30,34)(31,47)(33,45)(35,43)(36,56)(37,41)(38,54)(40,52)(42,50)(44,48)(51,55)(57,71)(58,84)(59,69)(60,82)(61,67)(62,80)(63,65)(64,78)(66,76)(68,74)(70,72)(73,83)(75,81)(77,79)(85,101)(87,99)(88,112)(89,97)(90,110)(91,95)(92,108)(94,106)(96,104)(98,102)(103,111)(105,109)(141,198)(142,211)(143,224)(144,209)(145,222)(146,207)(147,220)(148,205)(149,218)(150,203)(151,216)(152,201)(153,214)(154,199)(155,212)(156,197)(157,210)(158,223)(159,208)(160,221)(161,206)(162,219)(163,204)(164,217)(165,202)(166,215)(167,200)(168,213)(169,187)(170,172)(171,185)(173,183)(174,196)(175,181)(176,194)(177,179)(178,192)(180,190)(182,188)(184,186)(189,195)(191,193) );
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)], [(1,146,15,160),(2,145,16,159),(3,144,17,158),(4,143,18,157),(5,142,19,156),(6,141,20,155),(7,168,21,154),(8,167,22,153),(9,166,23,152),(10,165,24,151),(11,164,25,150),(12,163,26,149),(13,162,27,148),(14,161,28,147),(29,67,43,81),(30,66,44,80),(31,65,45,79),(32,64,46,78),(33,63,47,77),(34,62,48,76),(35,61,49,75),(36,60,50,74),(37,59,51,73),(38,58,52,72),(39,57,53,71),(40,84,54,70),(41,83,55,69),(42,82,56,68),(85,186,99,172),(86,185,100,171),(87,184,101,170),(88,183,102,169),(89,182,103,196),(90,181,104,195),(91,180,105,194),(92,179,106,193),(93,178,107,192),(94,177,108,191),(95,176,109,190),(96,175,110,189),(97,174,111,188),(98,173,112,187),(113,218,127,204),(114,217,128,203),(115,216,129,202),(116,215,130,201),(117,214,131,200),(118,213,132,199),(119,212,133,198),(120,211,134,197),(121,210,135,224),(122,209,136,223),(123,208,137,222),(124,207,138,221),(125,206,139,220),(126,205,140,219)], [(1,107,124,53),(2,106,125,52),(3,105,126,51),(4,104,127,50),(5,103,128,49),(6,102,129,48),(7,101,130,47),(8,100,131,46),(9,99,132,45),(10,98,133,44),(11,97,134,43),(12,96,135,42),(13,95,136,41),(14,94,137,40),(15,93,138,39),(16,92,139,38),(17,91,140,37),(18,90,113,36),(19,89,114,35),(20,88,115,34),(21,87,116,33),(22,86,117,32),(23,85,118,31),(24,112,119,30),(25,111,120,29),(26,110,121,56),(27,109,122,55),(28,108,123,54),(57,167,178,200),(58,166,179,199),(59,165,180,198),(60,164,181,197),(61,163,182,224),(62,162,183,223),(63,161,184,222),(64,160,185,221),(65,159,186,220),(66,158,187,219),(67,157,188,218),(68,156,189,217),(69,155,190,216),(70,154,191,215),(71,153,192,214),(72,152,193,213),(73,151,194,212),(74,150,195,211),(75,149,196,210),(76,148,169,209),(77,147,170,208),(78,146,171,207),(79,145,172,206),(80,144,173,205),(81,143,174,204),(82,142,175,203),(83,141,176,202),(84,168,177,201)], [(1,138),(2,123),(3,136),(4,121),(5,134),(6,119),(7,132),(8,117),(9,130),(10,115),(11,128),(12,113),(13,126),(14,139),(15,124),(16,137),(17,122),(18,135),(19,120),(20,133),(21,118),(22,131),(23,116),(24,129),(25,114),(26,127),(27,140),(28,125),(29,49),(30,34),(31,47),(33,45),(35,43),(36,56),(37,41),(38,54),(40,52),(42,50),(44,48),(51,55),(57,71),(58,84),(59,69),(60,82),(61,67),(62,80),(63,65),(64,78),(66,76),(68,74),(70,72),(73,83),(75,81),(77,79),(85,101),(87,99),(88,112),(89,97),(90,110),(91,95),(92,108),(94,106),(96,104),(98,102),(103,111),(105,109),(141,198),(142,211),(143,224),(144,209),(145,222),(146,207),(147,220),(148,205),(149,218),(150,203),(151,216),(152,201),(153,214),(154,199),(155,212),(156,197),(157,210),(158,223),(159,208),(160,221),(161,206),(162,219),(163,204),(164,217),(165,202),(166,215),(167,200),(168,213),(169,187),(170,172),(171,185),(173,183),(174,196),(175,181),(176,194),(177,179),(178,192),(180,190),(182,188),(184,186),(189,195),(191,193)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28F | 28G | ··· | 28L | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 28 | 2 | 2 | 8 | 14 | 14 | 28 | 28 | 56 | 2 | 2 | 2 | 4 | 4 | 28 | 28 | 2 | ··· | 2 | 8 | ··· | 8 | 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 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D4 | D7 | D14 | D14 | D14 | C4○D8 | C7⋊D4 | C8.C22 | D4×D7 | D4×D7 | SD16⋊D7 | SD16⋊3D7 |
| kernel | Dic14.16D4 | C28.44D4 | D14⋊C8 | D4⋊Dic7 | C2×C7⋊Q16 | D14⋊3Q8 | C14×SD16 | C2×D4⋊2D7 | Dic14 | C2×Dic7 | C7×D4 | C22×D7 | C2×SD16 | C2×C8 | C2×D4 | C2×Q8 | C14 | D4 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 2 | 1 | 3 | 3 | 3 | 3 | 4 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of Dic14.16D4 ►in GL4(𝔽113) generated by
| 15 | 0 | 0 | 0 |
| 88 | 98 | 0 | 0 |
| 0 | 0 | 24 | 112 |
| 0 | 0 | 100 | 10 |
| 18 | 112 | 0 | 0 |
| 99 | 95 | 0 | 0 |
| 0 | 0 | 0 | 34 |
| 0 | 0 | 10 | 0 |
| 1 | 69 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 106 | 31 |
| 0 | 0 | 64 | 7 |
| 112 | 0 | 0 | 0 |
| 77 | 1 | 0 | 0 |
| 0 | 0 | 0 | 79 |
| 0 | 0 | 103 | 0 |
G:=sub<GL(4,GF(113))| [15,88,0,0,0,98,0,0,0,0,24,100,0,0,112,10],[18,99,0,0,112,95,0,0,0,0,0,10,0,0,34,0],[1,0,0,0,69,112,0,0,0,0,106,64,0,0,31,7],[112,77,0,0,0,1,0,0,0,0,0,103,0,0,79,0] >;
Dic14.16D4 in GAP, Magma, Sage, TeX
{\rm Dic}_{14}._{16}D_4 % in TeX
G:=Group("Dic14.16D4"); // GroupNames label
G:=SmallGroup(448,707);
// by ID
G=gap.SmallGroup(448,707);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,254,219,184,851,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=c^4=d^2=1,b^2=a^14,b*a*b^-1=c*a*c^-1=a^-1,d*a*d=a^13,c*b*c^-1=a^21*b,d*b*d=a^14*b,d*c*d=a^14*c^-1>;
// generators/relations