metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C28⋊2SD16, Dic14⋊8D4, C42.39D14, C4⋊C8⋊10D7, C4⋊2(C56⋊C2), C7⋊2(C4⋊SD16), C4.133(D4×D7), C28⋊4D4.5C2, (C2×C8).133D14, (C2×C28).124D4, (C2×C4).135D28, C28.342(C2×D4), C2.D56⋊13C2, (C4×Dic14)⋊18C2, (C4×C28).74C22, C14.12(C2×SD16), C28.331(C4○D4), C14.41(C4⋊D4), C2.14(C4⋊D28), C2.20(C8⋊D14), C14.17(C8⋊C22), (C2×C28).758C23, (C2×C56).140C22, C4.47(Q8⋊2D7), (C2×D28).17C22, C22.121(C2×D28), C4⋊Dic7.276C22, (C2×Dic14).215C22, (C7×C4⋊C8)⋊12C2, (C2×C56⋊C2)⋊20C2, C2.15(C2×C56⋊C2), (C2×C14).141(C2×D4), (C2×C4).703(C22×D7), SmallGroup(448,382)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic14⋊8D4
G = < a,b,c,d | a28=c4=d2=1, b2=a14, bab-1=dad=a-1, ac=ca, bc=cb, dbd=a21b, dcd=c-1 >
Subgroups: 932 in 128 conjugacy classes, 45 normal (29 characteristic)
C1, C2, C2, C4, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C42, C4⋊C4, C2×C8, SD16, C2×D4, C2×Q8, Dic7, C28, C28, C28, D14, C2×C14, D4⋊C4, C4⋊C8, C4×Q8, C4⋊1D4, C2×SD16, C56, Dic14, Dic14, D28, C2×Dic7, C2×C28, C22×D7, C4⋊SD16, C56⋊C2, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4×C28, C2×C56, C2×Dic14, C2×D28, C2×D28, C2.D56, C7×C4⋊C8, C4×Dic14, C28⋊4D4, C2×C56⋊C2, Dic14⋊8D4
Quotients: C1, C2, C22, D4, C23, D7, SD16, C2×D4, C4○D4, D14, C4⋊D4, C2×SD16, C8⋊C22, D28, C22×D7, C4⋊SD16, C56⋊C2, C2×D28, D4×D7, Q8⋊2D7, C4⋊D28, C2×C56⋊C2, C8⋊D14, Dic14⋊8D4
►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 91 15 105)(2 90 16 104)(3 89 17 103)(4 88 18 102)(5 87 19 101)(6 86 20 100)(7 85 21 99)(8 112 22 98)(9 111 23 97)(10 110 24 96)(11 109 25 95)(12 108 26 94)(13 107 27 93)(14 106 28 92)(29 82 43 68)(30 81 44 67)(31 80 45 66)(32 79 46 65)(33 78 47 64)(34 77 48 63)(35 76 49 62)(36 75 50 61)(37 74 51 60)(38 73 52 59)(39 72 53 58)(40 71 54 57)(41 70 55 84)(42 69 56 83)(113 187 127 173)(114 186 128 172)(115 185 129 171)(116 184 130 170)(117 183 131 169)(118 182 132 196)(119 181 133 195)(120 180 134 194)(121 179 135 193)(122 178 136 192)(123 177 137 191)(124 176 138 190)(125 175 139 189)(126 174 140 188)(141 202 155 216)(142 201 156 215)(143 200 157 214)(144 199 158 213)(145 198 159 212)(146 197 160 211)(147 224 161 210)(148 223 162 209)(149 222 163 208)(150 221 164 207)(151 220 165 206)(152 219 166 205)(153 218 167 204)(154 217 168 203)
(1 147 57 133)(2 148 58 134)(3 149 59 135)(4 150 60 136)(5 151 61 137)(6 152 62 138)(7 153 63 139)(8 154 64 140)(9 155 65 113)(10 156 66 114)(11 157 67 115)(12 158 68 116)(13 159 69 117)(14 160 70 118)(15 161 71 119)(16 162 72 120)(17 163 73 121)(18 164 74 122)(19 165 75 123)(20 166 76 124)(21 167 77 125)(22 168 78 126)(23 141 79 127)(24 142 80 128)(25 143 81 129)(26 144 82 130)(27 145 83 131)(28 146 84 132)(29 184 108 213)(30 185 109 214)(31 186 110 215)(32 187 111 216)(33 188 112 217)(34 189 85 218)(35 190 86 219)(36 191 87 220)(37 192 88 221)(38 193 89 222)(39 194 90 223)(40 195 91 224)(41 196 92 197)(42 169 93 198)(43 170 94 199)(44 171 95 200)(45 172 96 201)(46 173 97 202)(47 174 98 203)(48 175 99 204)(49 176 100 205)(50 177 101 206)(51 178 102 207)(52 179 103 208)(53 180 104 209)(54 181 105 210)(55 182 106 211)(56 183 107 212)
(1 57)(2 84)(3 83)(4 82)(5 81)(6 80)(7 79)(8 78)(9 77)(10 76)(11 75)(12 74)(13 73)(14 72)(15 71)(16 70)(17 69)(18 68)(19 67)(20 66)(21 65)(22 64)(23 63)(24 62)(25 61)(26 60)(27 59)(28 58)(29 109)(30 108)(31 107)(32 106)(33 105)(34 104)(35 103)(36 102)(37 101)(38 100)(39 99)(40 98)(41 97)(42 96)(43 95)(44 94)(45 93)(46 92)(47 91)(48 90)(49 89)(50 88)(51 87)(52 86)(53 85)(54 112)(55 111)(56 110)(113 125)(114 124)(115 123)(116 122)(117 121)(118 120)(126 140)(127 139)(128 138)(129 137)(130 136)(131 135)(132 134)(141 153)(142 152)(143 151)(144 150)(145 149)(146 148)(154 168)(155 167)(156 166)(157 165)(158 164)(159 163)(160 162)(169 172)(170 171)(173 196)(174 195)(175 194)(176 193)(177 192)(178 191)(179 190)(180 189)(181 188)(182 187)(183 186)(184 185)(197 202)(198 201)(199 200)(203 224)(204 223)(205 222)(206 221)(207 220)(208 219)(209 218)(210 217)(211 216)(212 215)(213 214)
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), (1,91,15,105)(2,90,16,104)(3,89,17,103)(4,88,18,102)(5,87,19,101)(6,86,20,100)(7,85,21,99)(8,112,22,98)(9,111,23,97)(10,110,24,96)(11,109,25,95)(12,108,26,94)(13,107,27,93)(14,106,28,92)(29,82,43,68)(30,81,44,67)(31,80,45,66)(32,79,46,65)(33,78,47,64)(34,77,48,63)(35,76,49,62)(36,75,50,61)(37,74,51,60)(38,73,52,59)(39,72,53,58)(40,71,54,57)(41,70,55,84)(42,69,56,83)(113,187,127,173)(114,186,128,172)(115,185,129,171)(116,184,130,170)(117,183,131,169)(118,182,132,196)(119,181,133,195)(120,180,134,194)(121,179,135,193)(122,178,136,192)(123,177,137,191)(124,176,138,190)(125,175,139,189)(126,174,140,188)(141,202,155,216)(142,201,156,215)(143,200,157,214)(144,199,158,213)(145,198,159,212)(146,197,160,211)(147,224,161,210)(148,223,162,209)(149,222,163,208)(150,221,164,207)(151,220,165,206)(152,219,166,205)(153,218,167,204)(154,217,168,203), (1,147,57,133)(2,148,58,134)(3,149,59,135)(4,150,60,136)(5,151,61,137)(6,152,62,138)(7,153,63,139)(8,154,64,140)(9,155,65,113)(10,156,66,114)(11,157,67,115)(12,158,68,116)(13,159,69,117)(14,160,70,118)(15,161,71,119)(16,162,72,120)(17,163,73,121)(18,164,74,122)(19,165,75,123)(20,166,76,124)(21,167,77,125)(22,168,78,126)(23,141,79,127)(24,142,80,128)(25,143,81,129)(26,144,82,130)(27,145,83,131)(28,146,84,132)(29,184,108,213)(30,185,109,214)(31,186,110,215)(32,187,111,216)(33,188,112,217)(34,189,85,218)(35,190,86,219)(36,191,87,220)(37,192,88,221)(38,193,89,222)(39,194,90,223)(40,195,91,224)(41,196,92,197)(42,169,93,198)(43,170,94,199)(44,171,95,200)(45,172,96,201)(46,173,97,202)(47,174,98,203)(48,175,99,204)(49,176,100,205)(50,177,101,206)(51,178,102,207)(52,179,103,208)(53,180,104,209)(54,181,105,210)(55,182,106,211)(56,183,107,212), (1,57)(2,84)(3,83)(4,82)(5,81)(6,80)(7,79)(8,78)(9,77)(10,76)(11,75)(12,74)(13,73)(14,72)(15,71)(16,70)(17,69)(18,68)(19,67)(20,66)(21,65)(22,64)(23,63)(24,62)(25,61)(26,60)(27,59)(28,58)(29,109)(30,108)(31,107)(32,106)(33,105)(34,104)(35,103)(36,102)(37,101)(38,100)(39,99)(40,98)(41,97)(42,96)(43,95)(44,94)(45,93)(46,92)(47,91)(48,90)(49,89)(50,88)(51,87)(52,86)(53,85)(54,112)(55,111)(56,110)(113,125)(114,124)(115,123)(116,122)(117,121)(118,120)(126,140)(127,139)(128,138)(129,137)(130,136)(131,135)(132,134)(141,153)(142,152)(143,151)(144,150)(145,149)(146,148)(154,168)(155,167)(156,166)(157,165)(158,164)(159,163)(160,162)(169,172)(170,171)(173,196)(174,195)(175,194)(176,193)(177,192)(178,191)(179,190)(180,189)(181,188)(182,187)(183,186)(184,185)(197,202)(198,201)(199,200)(203,224)(204,223)(205,222)(206,221)(207,220)(208,219)(209,218)(210,217)(211,216)(212,215)(213,214)>;
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), (1,91,15,105)(2,90,16,104)(3,89,17,103)(4,88,18,102)(5,87,19,101)(6,86,20,100)(7,85,21,99)(8,112,22,98)(9,111,23,97)(10,110,24,96)(11,109,25,95)(12,108,26,94)(13,107,27,93)(14,106,28,92)(29,82,43,68)(30,81,44,67)(31,80,45,66)(32,79,46,65)(33,78,47,64)(34,77,48,63)(35,76,49,62)(36,75,50,61)(37,74,51,60)(38,73,52,59)(39,72,53,58)(40,71,54,57)(41,70,55,84)(42,69,56,83)(113,187,127,173)(114,186,128,172)(115,185,129,171)(116,184,130,170)(117,183,131,169)(118,182,132,196)(119,181,133,195)(120,180,134,194)(121,179,135,193)(122,178,136,192)(123,177,137,191)(124,176,138,190)(125,175,139,189)(126,174,140,188)(141,202,155,216)(142,201,156,215)(143,200,157,214)(144,199,158,213)(145,198,159,212)(146,197,160,211)(147,224,161,210)(148,223,162,209)(149,222,163,208)(150,221,164,207)(151,220,165,206)(152,219,166,205)(153,218,167,204)(154,217,168,203), (1,147,57,133)(2,148,58,134)(3,149,59,135)(4,150,60,136)(5,151,61,137)(6,152,62,138)(7,153,63,139)(8,154,64,140)(9,155,65,113)(10,156,66,114)(11,157,67,115)(12,158,68,116)(13,159,69,117)(14,160,70,118)(15,161,71,119)(16,162,72,120)(17,163,73,121)(18,164,74,122)(19,165,75,123)(20,166,76,124)(21,167,77,125)(22,168,78,126)(23,141,79,127)(24,142,80,128)(25,143,81,129)(26,144,82,130)(27,145,83,131)(28,146,84,132)(29,184,108,213)(30,185,109,214)(31,186,110,215)(32,187,111,216)(33,188,112,217)(34,189,85,218)(35,190,86,219)(36,191,87,220)(37,192,88,221)(38,193,89,222)(39,194,90,223)(40,195,91,224)(41,196,92,197)(42,169,93,198)(43,170,94,199)(44,171,95,200)(45,172,96,201)(46,173,97,202)(47,174,98,203)(48,175,99,204)(49,176,100,205)(50,177,101,206)(51,178,102,207)(52,179,103,208)(53,180,104,209)(54,181,105,210)(55,182,106,211)(56,183,107,212), (1,57)(2,84)(3,83)(4,82)(5,81)(6,80)(7,79)(8,78)(9,77)(10,76)(11,75)(12,74)(13,73)(14,72)(15,71)(16,70)(17,69)(18,68)(19,67)(20,66)(21,65)(22,64)(23,63)(24,62)(25,61)(26,60)(27,59)(28,58)(29,109)(30,108)(31,107)(32,106)(33,105)(34,104)(35,103)(36,102)(37,101)(38,100)(39,99)(40,98)(41,97)(42,96)(43,95)(44,94)(45,93)(46,92)(47,91)(48,90)(49,89)(50,88)(51,87)(52,86)(53,85)(54,112)(55,111)(56,110)(113,125)(114,124)(115,123)(116,122)(117,121)(118,120)(126,140)(127,139)(128,138)(129,137)(130,136)(131,135)(132,134)(141,153)(142,152)(143,151)(144,150)(145,149)(146,148)(154,168)(155,167)(156,166)(157,165)(158,164)(159,163)(160,162)(169,172)(170,171)(173,196)(174,195)(175,194)(176,193)(177,192)(178,191)(179,190)(180,189)(181,188)(182,187)(183,186)(184,185)(197,202)(198,201)(199,200)(203,224)(204,223)(205,222)(206,221)(207,220)(208,219)(209,218)(210,217)(211,216)(212,215)(213,214) );
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)], [(1,91,15,105),(2,90,16,104),(3,89,17,103),(4,88,18,102),(5,87,19,101),(6,86,20,100),(7,85,21,99),(8,112,22,98),(9,111,23,97),(10,110,24,96),(11,109,25,95),(12,108,26,94),(13,107,27,93),(14,106,28,92),(29,82,43,68),(30,81,44,67),(31,80,45,66),(32,79,46,65),(33,78,47,64),(34,77,48,63),(35,76,49,62),(36,75,50,61),(37,74,51,60),(38,73,52,59),(39,72,53,58),(40,71,54,57),(41,70,55,84),(42,69,56,83),(113,187,127,173),(114,186,128,172),(115,185,129,171),(116,184,130,170),(117,183,131,169),(118,182,132,196),(119,181,133,195),(120,180,134,194),(121,179,135,193),(122,178,136,192),(123,177,137,191),(124,176,138,190),(125,175,139,189),(126,174,140,188),(141,202,155,216),(142,201,156,215),(143,200,157,214),(144,199,158,213),(145,198,159,212),(146,197,160,211),(147,224,161,210),(148,223,162,209),(149,222,163,208),(150,221,164,207),(151,220,165,206),(152,219,166,205),(153,218,167,204),(154,217,168,203)], [(1,147,57,133),(2,148,58,134),(3,149,59,135),(4,150,60,136),(5,151,61,137),(6,152,62,138),(7,153,63,139),(8,154,64,140),(9,155,65,113),(10,156,66,114),(11,157,67,115),(12,158,68,116),(13,159,69,117),(14,160,70,118),(15,161,71,119),(16,162,72,120),(17,163,73,121),(18,164,74,122),(19,165,75,123),(20,166,76,124),(21,167,77,125),(22,168,78,126),(23,141,79,127),(24,142,80,128),(25,143,81,129),(26,144,82,130),(27,145,83,131),(28,146,84,132),(29,184,108,213),(30,185,109,214),(31,186,110,215),(32,187,111,216),(33,188,112,217),(34,189,85,218),(35,190,86,219),(36,191,87,220),(37,192,88,221),(38,193,89,222),(39,194,90,223),(40,195,91,224),(41,196,92,197),(42,169,93,198),(43,170,94,199),(44,171,95,200),(45,172,96,201),(46,173,97,202),(47,174,98,203),(48,175,99,204),(49,176,100,205),(50,177,101,206),(51,178,102,207),(52,179,103,208),(53,180,104,209),(54,181,105,210),(55,182,106,211),(56,183,107,212)], [(1,57),(2,84),(3,83),(4,82),(5,81),(6,80),(7,79),(8,78),(9,77),(10,76),(11,75),(12,74),(13,73),(14,72),(15,71),(16,70),(17,69),(18,68),(19,67),(20,66),(21,65),(22,64),(23,63),(24,62),(25,61),(26,60),(27,59),(28,58),(29,109),(30,108),(31,107),(32,106),(33,105),(34,104),(35,103),(36,102),(37,101),(38,100),(39,99),(40,98),(41,97),(42,96),(43,95),(44,94),(45,93),(46,92),(47,91),(48,90),(49,89),(50,88),(51,87),(52,86),(53,85),(54,112),(55,111),(56,110),(113,125),(114,124),(115,123),(116,122),(117,121),(118,120),(126,140),(127,139),(128,138),(129,137),(130,136),(131,135),(132,134),(141,153),(142,152),(143,151),(144,150),(145,149),(146,148),(154,168),(155,167),(156,166),(157,165),(158,164),(159,163),(160,162),(169,172),(170,171),(173,196),(174,195),(175,194),(176,193),(177,192),(178,191),(179,190),(180,189),(181,188),(182,187),(183,186),(184,185),(197,202),(198,201),(199,200),(203,224),(204,223),(205,222),(206,221),(207,220),(208,219),(209,218),(210,217),(211,216),(212,215),(213,214)]])
79 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 | ··· | 28L | 28M | ··· | 28X | 56A | ··· | 56X |
| 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 | 56 | 56 | 2 | 2 | 2 | 2 | 4 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
79 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | SD16 | C4○D4 | D14 | D14 | D28 | C56⋊C2 | C8⋊C22 | D4×D7 | Q8⋊2D7 | C8⋊D14 |
| kernel | Dic14⋊8D4 | C2.D56 | C7×C4⋊C8 | C4×Dic14 | C28⋊4D4 | C2×C56⋊C2 | Dic14 | C2×C28 | C4⋊C8 | C28 | C28 | C42 | C2×C8 | C2×C4 | C4 | C14 | C4 | C4 | C2 |
| # reps | 1 | 2 | 1 | 1 | 1 | 2 | 2 | 2 | 3 | 4 | 2 | 3 | 6 | 12 | 24 | 1 | 3 | 3 | 6 |
Matrix representation of Dic14⋊8D4 ►in GL6(𝔽113)
| 0 | 1 | 0 | 0 | 0 | 0 |
| 112 | 79 | 0 | 0 | 0 | 0 |
| 0 | 0 | 54 | 87 | 0 | 0 |
| 0 | 0 | 47 | 59 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 34 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 1 | 0 | 0 |
| 0 | 0 | 104 | 102 | 0 | 0 |
| 0 | 0 | 0 | 0 | 32 | 30 |
| 0 | 0 | 0 | 0 | 45 | 81 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 85 | 2 |
| 0 | 0 | 0 | 0 | 3 | 28 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 79 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 65 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 85 | 1 |
G:=sub<GL(6,GF(113))| [0,112,0,0,0,0,1,79,0,0,0,0,0,0,54,47,0,0,0,0,87,59,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[112,34,0,0,0,0,0,1,0,0,0,0,0,0,11,104,0,0,0,0,1,102,0,0,0,0,0,0,32,45,0,0,0,0,30,81],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,85,3,0,0,0,0,2,28],[1,79,0,0,0,0,0,112,0,0,0,0,0,0,1,65,0,0,0,0,0,112,0,0,0,0,0,0,112,85,0,0,0,0,0,1] >;
Dic14⋊8D4 in GAP, Magma, Sage, TeX
{\rm Dic}_{14}\rtimes_8D_4 % in TeX
G:=Group("Dic14:8D4"); // GroupNames label
G:=SmallGroup(448,382);
// by ID
G=gap.SmallGroup(448,382);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,120,254,219,58,1123,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=c^4=d^2=1,b^2=a^14,b*a*b^-1=d*a*d=a^-1,a*c=c*a,b*c=c*b,d*b*d=a^21*b,d*c*d=c^-1>;
// generators/relations