metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic14⋊6D4, (C2×D8)⋊6D7, (C7×D4)⋊6D4, C4.60(D4×D7), D14⋊C8⋊28C2, (C14×D8)⋊14C2, C28⋊2D4⋊5C2, D4⋊3(C7⋊D4), C7⋊5(D4⋊D4), (C2×C8).35D14, (C2×D4).65D14, C28.167(C2×D4), C14.56C22≀C2, C14.35(C4○D8), D4⋊Dic7⋊30C2, (C22×D7).35D4, C22.258(D4×D7), C28.44D4⋊29C2, C2.19(D8⋊3D7), C2.30(D8⋊D7), C14.51(C8⋊C22), (C2×C28).435C23, (C2×C56).249C22, (C2×Dic7).181D4, (D4×C14).84C22, C2.24(C23⋊D14), C4⋊Dic7.166C22, (C2×Dic14).122C22, C4.37(C2×C7⋊D4), (C2×D4⋊2D7)⋊2C2, (C2×D4.D7)⋊19C2, (C2×C4×D7).45C22, (C2×C14).348(C2×D4), (C2×C7⋊C8).149C22, (C2×C4).525(C22×D7), SmallGroup(448,692)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic14⋊D4
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=c-1 >
Subgroups: 868 in 162 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, D8, SD16, C22×C4, C2×D4, C2×D4, C2×Q8, C4○D4, Dic7, C28, D14, C2×C14, C2×C14, C22⋊C8, D4⋊C4, Q8⋊C4, C4⋊D4, C2×D8, C2×SD16, C2×C4○D4, C7⋊C8, C56, Dic14, Dic14, C4×D7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C7×D4, C7×D4, C22×D7, C22×C14, D4⋊D4, C2×C7⋊C8, C4⋊Dic7, D4.D7, C23.D7, C2×C56, C7×D8, C2×Dic14, C2×C4×D7, D4⋊2D7, C22×Dic7, C2×C7⋊D4, D4×C14, C28.44D4, D14⋊C8, D4⋊Dic7, C2×D4.D7, C28⋊2D4, C14×D8, C2×D4⋊2D7, Dic14⋊D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, D14, C22≀C2, C4○D8, C8⋊C22, C7⋊D4, C22×D7, D4⋊D4, D4×D7, C2×C7⋊D4, D8⋊D7, D8⋊3D7, C23⋊D14, Dic14⋊D4
►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 73 15 59)(2 72 16 58)(3 71 17 57)(4 70 18 84)(5 69 19 83)(6 68 20 82)(7 67 21 81)(8 66 22 80)(9 65 23 79)(10 64 24 78)(11 63 25 77)(12 62 26 76)(13 61 27 75)(14 60 28 74)(29 125 43 139)(30 124 44 138)(31 123 45 137)(32 122 46 136)(33 121 47 135)(34 120 48 134)(35 119 49 133)(36 118 50 132)(37 117 51 131)(38 116 52 130)(39 115 53 129)(40 114 54 128)(41 113 55 127)(42 140 56 126)(85 153 99 167)(86 152 100 166)(87 151 101 165)(88 150 102 164)(89 149 103 163)(90 148 104 162)(91 147 105 161)(92 146 106 160)(93 145 107 159)(94 144 108 158)(95 143 109 157)(96 142 110 156)(97 141 111 155)(98 168 112 154)(169 203 183 217)(170 202 184 216)(171 201 185 215)(172 200 186 214)(173 199 187 213)(174 198 188 212)(175 197 189 211)(176 224 190 210)(177 223 191 209)(178 222 192 208)(179 221 193 207)(180 220 194 206)(181 219 195 205)(182 218 196 204)
(1 33 143 183)(2 32 144 182)(3 31 145 181)(4 30 146 180)(5 29 147 179)(6 56 148 178)(7 55 149 177)(8 54 150 176)(9 53 151 175)(10 52 152 174)(11 51 153 173)(12 50 154 172)(13 49 155 171)(14 48 156 170)(15 47 157 169)(16 46 158 196)(17 45 159 195)(18 44 160 194)(19 43 161 193)(20 42 162 192)(21 41 163 191)(22 40 164 190)(23 39 165 189)(24 38 166 188)(25 37 167 187)(26 36 168 186)(27 35 141 185)(28 34 142 184)(57 116 93 212)(58 115 94 211)(59 114 95 210)(60 113 96 209)(61 140 97 208)(62 139 98 207)(63 138 99 206)(64 137 100 205)(65 136 101 204)(66 135 102 203)(67 134 103 202)(68 133 104 201)(69 132 105 200)(70 131 106 199)(71 130 107 198)(72 129 108 197)(73 128 109 224)(74 127 110 223)(75 126 111 222)(76 125 112 221)(77 124 85 220)(78 123 86 219)(79 122 87 218)(80 121 88 217)(81 120 89 216)(82 119 90 215)(83 118 91 214)(84 117 92 213)
(1 143)(2 156)(3 141)(4 154)(5 167)(6 152)(7 165)(8 150)(9 163)(10 148)(11 161)(12 146)(13 159)(14 144)(15 157)(16 142)(17 155)(18 168)(19 153)(20 166)(21 151)(22 164)(23 149)(24 162)(25 147)(26 160)(27 145)(28 158)(29 37)(30 50)(31 35)(32 48)(34 46)(36 44)(38 42)(39 55)(41 53)(43 51)(45 49)(52 56)(57 111)(58 96)(59 109)(60 94)(61 107)(62 92)(63 105)(64 90)(65 103)(66 88)(67 101)(68 86)(69 99)(70 112)(71 97)(72 110)(73 95)(74 108)(75 93)(76 106)(77 91)(78 104)(79 89)(80 102)(81 87)(82 100)(83 85)(84 98)(113 115)(114 128)(116 126)(117 139)(118 124)(119 137)(120 122)(121 135)(123 133)(125 131)(127 129)(130 140)(132 138)(134 136)(170 182)(171 195)(172 180)(173 193)(174 178)(175 191)(177 189)(179 187)(181 185)(184 196)(186 194)(188 192)(197 223)(198 208)(199 221)(200 206)(201 219)(202 204)(203 217)(205 215)(207 213)(209 211)(210 224)(212 222)(214 220)(216 218)
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), (1,73,15,59)(2,72,16,58)(3,71,17,57)(4,70,18,84)(5,69,19,83)(6,68,20,82)(7,67,21,81)(8,66,22,80)(9,65,23,79)(10,64,24,78)(11,63,25,77)(12,62,26,76)(13,61,27,75)(14,60,28,74)(29,125,43,139)(30,124,44,138)(31,123,45,137)(32,122,46,136)(33,121,47,135)(34,120,48,134)(35,119,49,133)(36,118,50,132)(37,117,51,131)(38,116,52,130)(39,115,53,129)(40,114,54,128)(41,113,55,127)(42,140,56,126)(85,153,99,167)(86,152,100,166)(87,151,101,165)(88,150,102,164)(89,149,103,163)(90,148,104,162)(91,147,105,161)(92,146,106,160)(93,145,107,159)(94,144,108,158)(95,143,109,157)(96,142,110,156)(97,141,111,155)(98,168,112,154)(169,203,183,217)(170,202,184,216)(171,201,185,215)(172,200,186,214)(173,199,187,213)(174,198,188,212)(175,197,189,211)(176,224,190,210)(177,223,191,209)(178,222,192,208)(179,221,193,207)(180,220,194,206)(181,219,195,205)(182,218,196,204), (1,33,143,183)(2,32,144,182)(3,31,145,181)(4,30,146,180)(5,29,147,179)(6,56,148,178)(7,55,149,177)(8,54,150,176)(9,53,151,175)(10,52,152,174)(11,51,153,173)(12,50,154,172)(13,49,155,171)(14,48,156,170)(15,47,157,169)(16,46,158,196)(17,45,159,195)(18,44,160,194)(19,43,161,193)(20,42,162,192)(21,41,163,191)(22,40,164,190)(23,39,165,189)(24,38,166,188)(25,37,167,187)(26,36,168,186)(27,35,141,185)(28,34,142,184)(57,116,93,212)(58,115,94,211)(59,114,95,210)(60,113,96,209)(61,140,97,208)(62,139,98,207)(63,138,99,206)(64,137,100,205)(65,136,101,204)(66,135,102,203)(67,134,103,202)(68,133,104,201)(69,132,105,200)(70,131,106,199)(71,130,107,198)(72,129,108,197)(73,128,109,224)(74,127,110,223)(75,126,111,222)(76,125,112,221)(77,124,85,220)(78,123,86,219)(79,122,87,218)(80,121,88,217)(81,120,89,216)(82,119,90,215)(83,118,91,214)(84,117,92,213), (1,143)(2,156)(3,141)(4,154)(5,167)(6,152)(7,165)(8,150)(9,163)(10,148)(11,161)(12,146)(13,159)(14,144)(15,157)(16,142)(17,155)(18,168)(19,153)(20,166)(21,151)(22,164)(23,149)(24,162)(25,147)(26,160)(27,145)(28,158)(29,37)(30,50)(31,35)(32,48)(34,46)(36,44)(38,42)(39,55)(41,53)(43,51)(45,49)(52,56)(57,111)(58,96)(59,109)(60,94)(61,107)(62,92)(63,105)(64,90)(65,103)(66,88)(67,101)(68,86)(69,99)(70,112)(71,97)(72,110)(73,95)(74,108)(75,93)(76,106)(77,91)(78,104)(79,89)(80,102)(81,87)(82,100)(83,85)(84,98)(113,115)(114,128)(116,126)(117,139)(118,124)(119,137)(120,122)(121,135)(123,133)(125,131)(127,129)(130,140)(132,138)(134,136)(170,182)(171,195)(172,180)(173,193)(174,178)(175,191)(177,189)(179,187)(181,185)(184,196)(186,194)(188,192)(197,223)(198,208)(199,221)(200,206)(201,219)(202,204)(203,217)(205,215)(207,213)(209,211)(210,224)(212,222)(214,220)(216,218)>;
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), (1,73,15,59)(2,72,16,58)(3,71,17,57)(4,70,18,84)(5,69,19,83)(6,68,20,82)(7,67,21,81)(8,66,22,80)(9,65,23,79)(10,64,24,78)(11,63,25,77)(12,62,26,76)(13,61,27,75)(14,60,28,74)(29,125,43,139)(30,124,44,138)(31,123,45,137)(32,122,46,136)(33,121,47,135)(34,120,48,134)(35,119,49,133)(36,118,50,132)(37,117,51,131)(38,116,52,130)(39,115,53,129)(40,114,54,128)(41,113,55,127)(42,140,56,126)(85,153,99,167)(86,152,100,166)(87,151,101,165)(88,150,102,164)(89,149,103,163)(90,148,104,162)(91,147,105,161)(92,146,106,160)(93,145,107,159)(94,144,108,158)(95,143,109,157)(96,142,110,156)(97,141,111,155)(98,168,112,154)(169,203,183,217)(170,202,184,216)(171,201,185,215)(172,200,186,214)(173,199,187,213)(174,198,188,212)(175,197,189,211)(176,224,190,210)(177,223,191,209)(178,222,192,208)(179,221,193,207)(180,220,194,206)(181,219,195,205)(182,218,196,204), (1,33,143,183)(2,32,144,182)(3,31,145,181)(4,30,146,180)(5,29,147,179)(6,56,148,178)(7,55,149,177)(8,54,150,176)(9,53,151,175)(10,52,152,174)(11,51,153,173)(12,50,154,172)(13,49,155,171)(14,48,156,170)(15,47,157,169)(16,46,158,196)(17,45,159,195)(18,44,160,194)(19,43,161,193)(20,42,162,192)(21,41,163,191)(22,40,164,190)(23,39,165,189)(24,38,166,188)(25,37,167,187)(26,36,168,186)(27,35,141,185)(28,34,142,184)(57,116,93,212)(58,115,94,211)(59,114,95,210)(60,113,96,209)(61,140,97,208)(62,139,98,207)(63,138,99,206)(64,137,100,205)(65,136,101,204)(66,135,102,203)(67,134,103,202)(68,133,104,201)(69,132,105,200)(70,131,106,199)(71,130,107,198)(72,129,108,197)(73,128,109,224)(74,127,110,223)(75,126,111,222)(76,125,112,221)(77,124,85,220)(78,123,86,219)(79,122,87,218)(80,121,88,217)(81,120,89,216)(82,119,90,215)(83,118,91,214)(84,117,92,213), (1,143)(2,156)(3,141)(4,154)(5,167)(6,152)(7,165)(8,150)(9,163)(10,148)(11,161)(12,146)(13,159)(14,144)(15,157)(16,142)(17,155)(18,168)(19,153)(20,166)(21,151)(22,164)(23,149)(24,162)(25,147)(26,160)(27,145)(28,158)(29,37)(30,50)(31,35)(32,48)(34,46)(36,44)(38,42)(39,55)(41,53)(43,51)(45,49)(52,56)(57,111)(58,96)(59,109)(60,94)(61,107)(62,92)(63,105)(64,90)(65,103)(66,88)(67,101)(68,86)(69,99)(70,112)(71,97)(72,110)(73,95)(74,108)(75,93)(76,106)(77,91)(78,104)(79,89)(80,102)(81,87)(82,100)(83,85)(84,98)(113,115)(114,128)(116,126)(117,139)(118,124)(119,137)(120,122)(121,135)(123,133)(125,131)(127,129)(130,140)(132,138)(134,136)(170,182)(171,195)(172,180)(173,193)(174,178)(175,191)(177,189)(179,187)(181,185)(184,196)(186,194)(188,192)(197,223)(198,208)(199,221)(200,206)(201,219)(202,204)(203,217)(205,215)(207,213)(209,211)(210,224)(212,222)(214,220)(216,218) );
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)], [(1,73,15,59),(2,72,16,58),(3,71,17,57),(4,70,18,84),(5,69,19,83),(6,68,20,82),(7,67,21,81),(8,66,22,80),(9,65,23,79),(10,64,24,78),(11,63,25,77),(12,62,26,76),(13,61,27,75),(14,60,28,74),(29,125,43,139),(30,124,44,138),(31,123,45,137),(32,122,46,136),(33,121,47,135),(34,120,48,134),(35,119,49,133),(36,118,50,132),(37,117,51,131),(38,116,52,130),(39,115,53,129),(40,114,54,128),(41,113,55,127),(42,140,56,126),(85,153,99,167),(86,152,100,166),(87,151,101,165),(88,150,102,164),(89,149,103,163),(90,148,104,162),(91,147,105,161),(92,146,106,160),(93,145,107,159),(94,144,108,158),(95,143,109,157),(96,142,110,156),(97,141,111,155),(98,168,112,154),(169,203,183,217),(170,202,184,216),(171,201,185,215),(172,200,186,214),(173,199,187,213),(174,198,188,212),(175,197,189,211),(176,224,190,210),(177,223,191,209),(178,222,192,208),(179,221,193,207),(180,220,194,206),(181,219,195,205),(182,218,196,204)], [(1,33,143,183),(2,32,144,182),(3,31,145,181),(4,30,146,180),(5,29,147,179),(6,56,148,178),(7,55,149,177),(8,54,150,176),(9,53,151,175),(10,52,152,174),(11,51,153,173),(12,50,154,172),(13,49,155,171),(14,48,156,170),(15,47,157,169),(16,46,158,196),(17,45,159,195),(18,44,160,194),(19,43,161,193),(20,42,162,192),(21,41,163,191),(22,40,164,190),(23,39,165,189),(24,38,166,188),(25,37,167,187),(26,36,168,186),(27,35,141,185),(28,34,142,184),(57,116,93,212),(58,115,94,211),(59,114,95,210),(60,113,96,209),(61,140,97,208),(62,139,98,207),(63,138,99,206),(64,137,100,205),(65,136,101,204),(66,135,102,203),(67,134,103,202),(68,133,104,201),(69,132,105,200),(70,131,106,199),(71,130,107,198),(72,129,108,197),(73,128,109,224),(74,127,110,223),(75,126,111,222),(76,125,112,221),(77,124,85,220),(78,123,86,219),(79,122,87,218),(80,121,88,217),(81,120,89,216),(82,119,90,215),(83,118,91,214),(84,117,92,213)], [(1,143),(2,156),(3,141),(4,154),(5,167),(6,152),(7,165),(8,150),(9,163),(10,148),(11,161),(12,146),(13,159),(14,144),(15,157),(16,142),(17,155),(18,168),(19,153),(20,166),(21,151),(22,164),(23,149),(24,162),(25,147),(26,160),(27,145),(28,158),(29,37),(30,50),(31,35),(32,48),(34,46),(36,44),(38,42),(39,55),(41,53),(43,51),(45,49),(52,56),(57,111),(58,96),(59,109),(60,94),(61,107),(62,92),(63,105),(64,90),(65,103),(66,88),(67,101),(68,86),(69,99),(70,112),(71,97),(72,110),(73,95),(74,108),(75,93),(76,106),(77,91),(78,104),(79,89),(80,102),(81,87),(82,100),(83,85),(84,98),(113,115),(114,128),(116,126),(117,139),(118,124),(119,137),(120,122),(121,135),(123,133),(125,131),(127,129),(130,140),(132,138),(134,136),(170,182),(171,195),(172,180),(173,193),(174,178),(175,191),(177,189),(179,187),(181,185),(184,196),(186,194),(188,192),(197,223),(198,208),(199,221),(200,206),(201,219),(202,204),(203,217),(205,215),(207,213),(209,211),(210,224),(212,222),(214,220),(216,218)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28F | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 8 | 28 | 2 | 2 | 14 | 14 | 28 | 28 | 56 | 2 | 2 | 2 | 4 | 4 | 28 | 28 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 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 | D4 | D4 | D7 | D14 | D14 | C4○D8 | C7⋊D4 | C8⋊C22 | D4×D7 | D4×D7 | D8⋊D7 | D8⋊3D7 |
| kernel | Dic14⋊D4 | C28.44D4 | D14⋊C8 | D4⋊Dic7 | C2×D4.D7 | C28⋊2D4 | C14×D8 | C2×D4⋊2D7 | Dic14 | C2×Dic7 | C7×D4 | C22×D7 | C2×D8 | C2×C8 | C2×D4 | C14 | D4 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 2 | 1 | 3 | 3 | 6 | 4 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of Dic14⋊D4 ►in GL6(𝔽113)
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 112 | 24 | 0 | 0 |
| 0 | 0 | 0 | 0 | 15 | 0 |
| 0 | 0 | 0 | 0 | 99 | 98 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 30 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 24 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 106 | 98 |
| 0 | 0 | 0 | 0 | 41 | 7 |
| 83 | 2 | 0 | 0 | 0 | 0 |
| 58 | 30 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 89 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 44 |
| 0 | 0 | 0 | 0 | 104 | 100 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 83 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 24 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 16 | 1 |
G:=sub<GL(6,GF(113))| [112,0,0,0,0,0,0,112,0,0,0,0,0,0,0,112,0,0,0,0,1,24,0,0,0,0,0,0,15,99,0,0,0,0,0,98],[1,30,0,0,0,0,0,112,0,0,0,0,0,0,1,24,0,0,0,0,0,112,0,0,0,0,0,0,106,41,0,0,0,0,98,7],[83,58,0,0,0,0,2,30,0,0,0,0,0,0,112,89,0,0,0,0,0,1,0,0,0,0,0,0,13,104,0,0,0,0,44,100],[112,83,0,0,0,0,0,1,0,0,0,0,0,0,1,24,0,0,0,0,0,112,0,0,0,0,0,0,112,16,0,0,0,0,0,1] >;
Dic14⋊D4 in GAP, Magma, Sage, TeX
{\rm Dic}_{14}\rtimes D_4 % in TeX
G:=Group("Dic14:D4"); // GroupNames label
G:=SmallGroup(448,692);
// by ID
G=gap.SmallGroup(448,692);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,254,219,851,438,102,18822]);
// 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=c^-1>;
// generators/relations