metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C28⋊3SD16, Dic14⋊9D4, C42.75D14, C4.54(D4×D7), C4⋊2(D4.D7), C28⋊C8⋊32C2, C7⋊4(C4⋊SD16), C4⋊1D4.5D7, C28.33(C2×D4), (C2×D4).58D14, (C2×C28).149D4, (C4×Dic14)⋊22C2, C28.77(C4○D4), D4⋊Dic7⋊23C2, C4.4(D4⋊2D7), C14.58(C2×SD16), C2.13(C28⋊2D4), C14.96(C8⋊C22), (C4×C28).123C22, (C2×C28).393C23, (D4×C14).74C22, C14.104(C4⋊D4), C4⋊Dic7.345C22, C2.17(D4.D14), (C2×Dic14).274C22, (C2×D4.D7)⋊14C2, (C7×C4⋊1D4).4C2, C2.12(C2×D4.D7), (C2×C14).524(C2×D4), (C2×C7⋊C8).132C22, (C2×C4).186(C7⋊D4), (C2×C4).491(C22×D7), C22.197(C2×C7⋊D4), SmallGroup(448,609)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic14⋊9D4
G = < a,b,c,d | a28=c4=d2=1, b2=a14, bab-1=a-1, ac=ca, dad=a15, bc=cb, dbd=a21b, dcd=c-1 >
Subgroups: 524 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, C14, C14, C42, C42, C4⋊C4, C2×C8, SD16, C2×D4, C2×D4, C2×Q8, Dic7, C28, C28, C28, C2×C14, C2×C14, D4⋊C4, C4⋊C8, C4×Q8, C4⋊1D4, C2×SD16, C7⋊C8, Dic14, Dic14, C2×Dic7, C2×C28, C7×D4, C22×C14, C4⋊SD16, C2×C7⋊C8, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D4.D7, C4×C28, C2×Dic14, D4×C14, D4×C14, C28⋊C8, D4⋊Dic7, C4×Dic14, C2×D4.D7, C7×C4⋊1D4, Dic14⋊9D4
Quotients: C1, C2, C22, D4, C23, D7, SD16, C2×D4, C4○D4, D14, C4⋊D4, C2×SD16, C8⋊C22, C7⋊D4, C22×D7, C4⋊SD16, D4.D7, D4×D7, D4⋊2D7, C2×C7⋊D4, D4.D14, C2×D4.D7, C28⋊2D4, Dic14⋊9D4
►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)
(1 120 15 134)(2 119 16 133)(3 118 17 132)(4 117 18 131)(5 116 19 130)(6 115 20 129)(7 114 21 128)(8 113 22 127)(9 140 23 126)(10 139 24 125)(11 138 25 124)(12 137 26 123)(13 136 27 122)(14 135 28 121)(29 74 43 60)(30 73 44 59)(31 72 45 58)(32 71 46 57)(33 70 47 84)(34 69 48 83)(35 68 49 82)(36 67 50 81)(37 66 51 80)(38 65 52 79)(39 64 53 78)(40 63 54 77)(41 62 55 76)(42 61 56 75)(85 216 99 202)(86 215 100 201)(87 214 101 200)(88 213 102 199)(89 212 103 198)(90 211 104 197)(91 210 105 224)(92 209 106 223)(93 208 107 222)(94 207 108 221)(95 206 109 220)(96 205 110 219)(97 204 111 218)(98 203 112 217)(141 186 155 172)(142 185 156 171)(143 184 157 170)(144 183 158 169)(145 182 159 196)(146 181 160 195)(147 180 161 194)(148 179 162 193)(149 178 163 192)(150 177 164 191)(151 176 165 190)(152 175 166 189)(153 174 167 188)(154 173 168 187)
(1 217 193 67)(2 218 194 68)(3 219 195 69)(4 220 196 70)(5 221 169 71)(6 222 170 72)(7 223 171 73)(8 224 172 74)(9 197 173 75)(10 198 174 76)(11 199 175 77)(12 200 176 78)(13 201 177 79)(14 202 178 80)(15 203 179 81)(16 204 180 82)(17 205 181 83)(18 206 182 84)(19 207 183 57)(20 208 184 58)(21 209 185 59)(22 210 186 60)(23 211 187 61)(24 212 188 62)(25 213 189 63)(26 214 190 64)(27 215 191 65)(28 216 192 66)(29 127 105 155)(30 128 106 156)(31 129 107 157)(32 130 108 158)(33 131 109 159)(34 132 110 160)(35 133 111 161)(36 134 112 162)(37 135 85 163)(38 136 86 164)(39 137 87 165)(40 138 88 166)(41 139 89 167)(42 140 90 168)(43 113 91 141)(44 114 92 142)(45 115 93 143)(46 116 94 144)(47 117 95 145)(48 118 96 146)(49 119 97 147)(50 120 98 148)(51 121 99 149)(52 122 100 150)(53 123 101 151)(54 124 102 152)(55 125 103 153)(56 126 104 154)
(2 16)(4 18)(6 20)(8 22)(10 24)(12 26)(14 28)(29 98)(30 85)(31 100)(32 87)(33 102)(34 89)(35 104)(36 91)(37 106)(38 93)(39 108)(40 95)(41 110)(42 97)(43 112)(44 99)(45 86)(46 101)(47 88)(48 103)(49 90)(50 105)(51 92)(52 107)(53 94)(54 109)(55 96)(56 111)(57 207)(58 222)(59 209)(60 224)(61 211)(62 198)(63 213)(64 200)(65 215)(66 202)(67 217)(68 204)(69 219)(70 206)(71 221)(72 208)(73 223)(74 210)(75 197)(76 212)(77 199)(78 214)(79 201)(80 216)(81 203)(82 218)(83 205)(84 220)(113 134)(114 121)(115 136)(116 123)(117 138)(118 125)(119 140)(120 127)(122 129)(124 131)(126 133)(128 135)(130 137)(132 139)(141 162)(142 149)(143 164)(144 151)(145 166)(146 153)(147 168)(148 155)(150 157)(152 159)(154 161)(156 163)(158 165)(160 167)(170 184)(172 186)(174 188)(176 190)(178 192)(180 194)(182 196)
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), (1,120,15,134)(2,119,16,133)(3,118,17,132)(4,117,18,131)(5,116,19,130)(6,115,20,129)(7,114,21,128)(8,113,22,127)(9,140,23,126)(10,139,24,125)(11,138,25,124)(12,137,26,123)(13,136,27,122)(14,135,28,121)(29,74,43,60)(30,73,44,59)(31,72,45,58)(32,71,46,57)(33,70,47,84)(34,69,48,83)(35,68,49,82)(36,67,50,81)(37,66,51,80)(38,65,52,79)(39,64,53,78)(40,63,54,77)(41,62,55,76)(42,61,56,75)(85,216,99,202)(86,215,100,201)(87,214,101,200)(88,213,102,199)(89,212,103,198)(90,211,104,197)(91,210,105,224)(92,209,106,223)(93,208,107,222)(94,207,108,221)(95,206,109,220)(96,205,110,219)(97,204,111,218)(98,203,112,217)(141,186,155,172)(142,185,156,171)(143,184,157,170)(144,183,158,169)(145,182,159,196)(146,181,160,195)(147,180,161,194)(148,179,162,193)(149,178,163,192)(150,177,164,191)(151,176,165,190)(152,175,166,189)(153,174,167,188)(154,173,168,187), (1,217,193,67)(2,218,194,68)(3,219,195,69)(4,220,196,70)(5,221,169,71)(6,222,170,72)(7,223,171,73)(8,224,172,74)(9,197,173,75)(10,198,174,76)(11,199,175,77)(12,200,176,78)(13,201,177,79)(14,202,178,80)(15,203,179,81)(16,204,180,82)(17,205,181,83)(18,206,182,84)(19,207,183,57)(20,208,184,58)(21,209,185,59)(22,210,186,60)(23,211,187,61)(24,212,188,62)(25,213,189,63)(26,214,190,64)(27,215,191,65)(28,216,192,66)(29,127,105,155)(30,128,106,156)(31,129,107,157)(32,130,108,158)(33,131,109,159)(34,132,110,160)(35,133,111,161)(36,134,112,162)(37,135,85,163)(38,136,86,164)(39,137,87,165)(40,138,88,166)(41,139,89,167)(42,140,90,168)(43,113,91,141)(44,114,92,142)(45,115,93,143)(46,116,94,144)(47,117,95,145)(48,118,96,146)(49,119,97,147)(50,120,98,148)(51,121,99,149)(52,122,100,150)(53,123,101,151)(54,124,102,152)(55,125,103,153)(56,126,104,154), (2,16)(4,18)(6,20)(8,22)(10,24)(12,26)(14,28)(29,98)(30,85)(31,100)(32,87)(33,102)(34,89)(35,104)(36,91)(37,106)(38,93)(39,108)(40,95)(41,110)(42,97)(43,112)(44,99)(45,86)(46,101)(47,88)(48,103)(49,90)(50,105)(51,92)(52,107)(53,94)(54,109)(55,96)(56,111)(57,207)(58,222)(59,209)(60,224)(61,211)(62,198)(63,213)(64,200)(65,215)(66,202)(67,217)(68,204)(69,219)(70,206)(71,221)(72,208)(73,223)(74,210)(75,197)(76,212)(77,199)(78,214)(79,201)(80,216)(81,203)(82,218)(83,205)(84,220)(113,134)(114,121)(115,136)(116,123)(117,138)(118,125)(119,140)(120,127)(122,129)(124,131)(126,133)(128,135)(130,137)(132,139)(141,162)(142,149)(143,164)(144,151)(145,166)(146,153)(147,168)(148,155)(150,157)(152,159)(154,161)(156,163)(158,165)(160,167)(170,184)(172,186)(174,188)(176,190)(178,192)(180,194)(182,196)>;
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), (1,120,15,134)(2,119,16,133)(3,118,17,132)(4,117,18,131)(5,116,19,130)(6,115,20,129)(7,114,21,128)(8,113,22,127)(9,140,23,126)(10,139,24,125)(11,138,25,124)(12,137,26,123)(13,136,27,122)(14,135,28,121)(29,74,43,60)(30,73,44,59)(31,72,45,58)(32,71,46,57)(33,70,47,84)(34,69,48,83)(35,68,49,82)(36,67,50,81)(37,66,51,80)(38,65,52,79)(39,64,53,78)(40,63,54,77)(41,62,55,76)(42,61,56,75)(85,216,99,202)(86,215,100,201)(87,214,101,200)(88,213,102,199)(89,212,103,198)(90,211,104,197)(91,210,105,224)(92,209,106,223)(93,208,107,222)(94,207,108,221)(95,206,109,220)(96,205,110,219)(97,204,111,218)(98,203,112,217)(141,186,155,172)(142,185,156,171)(143,184,157,170)(144,183,158,169)(145,182,159,196)(146,181,160,195)(147,180,161,194)(148,179,162,193)(149,178,163,192)(150,177,164,191)(151,176,165,190)(152,175,166,189)(153,174,167,188)(154,173,168,187), (1,217,193,67)(2,218,194,68)(3,219,195,69)(4,220,196,70)(5,221,169,71)(6,222,170,72)(7,223,171,73)(8,224,172,74)(9,197,173,75)(10,198,174,76)(11,199,175,77)(12,200,176,78)(13,201,177,79)(14,202,178,80)(15,203,179,81)(16,204,180,82)(17,205,181,83)(18,206,182,84)(19,207,183,57)(20,208,184,58)(21,209,185,59)(22,210,186,60)(23,211,187,61)(24,212,188,62)(25,213,189,63)(26,214,190,64)(27,215,191,65)(28,216,192,66)(29,127,105,155)(30,128,106,156)(31,129,107,157)(32,130,108,158)(33,131,109,159)(34,132,110,160)(35,133,111,161)(36,134,112,162)(37,135,85,163)(38,136,86,164)(39,137,87,165)(40,138,88,166)(41,139,89,167)(42,140,90,168)(43,113,91,141)(44,114,92,142)(45,115,93,143)(46,116,94,144)(47,117,95,145)(48,118,96,146)(49,119,97,147)(50,120,98,148)(51,121,99,149)(52,122,100,150)(53,123,101,151)(54,124,102,152)(55,125,103,153)(56,126,104,154), (2,16)(4,18)(6,20)(8,22)(10,24)(12,26)(14,28)(29,98)(30,85)(31,100)(32,87)(33,102)(34,89)(35,104)(36,91)(37,106)(38,93)(39,108)(40,95)(41,110)(42,97)(43,112)(44,99)(45,86)(46,101)(47,88)(48,103)(49,90)(50,105)(51,92)(52,107)(53,94)(54,109)(55,96)(56,111)(57,207)(58,222)(59,209)(60,224)(61,211)(62,198)(63,213)(64,200)(65,215)(66,202)(67,217)(68,204)(69,219)(70,206)(71,221)(72,208)(73,223)(74,210)(75,197)(76,212)(77,199)(78,214)(79,201)(80,216)(81,203)(82,218)(83,205)(84,220)(113,134)(114,121)(115,136)(116,123)(117,138)(118,125)(119,140)(120,127)(122,129)(124,131)(126,133)(128,135)(130,137)(132,139)(141,162)(142,149)(143,164)(144,151)(145,166)(146,153)(147,168)(148,155)(150,157)(152,159)(154,161)(156,163)(158,165)(160,167)(170,184)(172,186)(174,188)(176,190)(178,192)(180,194)(182,196) );
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)], [(1,120,15,134),(2,119,16,133),(3,118,17,132),(4,117,18,131),(5,116,19,130),(6,115,20,129),(7,114,21,128),(8,113,22,127),(9,140,23,126),(10,139,24,125),(11,138,25,124),(12,137,26,123),(13,136,27,122),(14,135,28,121),(29,74,43,60),(30,73,44,59),(31,72,45,58),(32,71,46,57),(33,70,47,84),(34,69,48,83),(35,68,49,82),(36,67,50,81),(37,66,51,80),(38,65,52,79),(39,64,53,78),(40,63,54,77),(41,62,55,76),(42,61,56,75),(85,216,99,202),(86,215,100,201),(87,214,101,200),(88,213,102,199),(89,212,103,198),(90,211,104,197),(91,210,105,224),(92,209,106,223),(93,208,107,222),(94,207,108,221),(95,206,109,220),(96,205,110,219),(97,204,111,218),(98,203,112,217),(141,186,155,172),(142,185,156,171),(143,184,157,170),(144,183,158,169),(145,182,159,196),(146,181,160,195),(147,180,161,194),(148,179,162,193),(149,178,163,192),(150,177,164,191),(151,176,165,190),(152,175,166,189),(153,174,167,188),(154,173,168,187)], [(1,217,193,67),(2,218,194,68),(3,219,195,69),(4,220,196,70),(5,221,169,71),(6,222,170,72),(7,223,171,73),(8,224,172,74),(9,197,173,75),(10,198,174,76),(11,199,175,77),(12,200,176,78),(13,201,177,79),(14,202,178,80),(15,203,179,81),(16,204,180,82),(17,205,181,83),(18,206,182,84),(19,207,183,57),(20,208,184,58),(21,209,185,59),(22,210,186,60),(23,211,187,61),(24,212,188,62),(25,213,189,63),(26,214,190,64),(27,215,191,65),(28,216,192,66),(29,127,105,155),(30,128,106,156),(31,129,107,157),(32,130,108,158),(33,131,109,159),(34,132,110,160),(35,133,111,161),(36,134,112,162),(37,135,85,163),(38,136,86,164),(39,137,87,165),(40,138,88,166),(41,139,89,167),(42,140,90,168),(43,113,91,141),(44,114,92,142),(45,115,93,143),(46,116,94,144),(47,117,95,145),(48,118,96,146),(49,119,97,147),(50,120,98,148),(51,121,99,149),(52,122,100,150),(53,123,101,151),(54,124,102,152),(55,125,103,153),(56,126,104,154)], [(2,16),(4,18),(6,20),(8,22),(10,24),(12,26),(14,28),(29,98),(30,85),(31,100),(32,87),(33,102),(34,89),(35,104),(36,91),(37,106),(38,93),(39,108),(40,95),(41,110),(42,97),(43,112),(44,99),(45,86),(46,101),(47,88),(48,103),(49,90),(50,105),(51,92),(52,107),(53,94),(54,109),(55,96),(56,111),(57,207),(58,222),(59,209),(60,224),(61,211),(62,198),(63,213),(64,200),(65,215),(66,202),(67,217),(68,204),(69,219),(70,206),(71,221),(72,208),(73,223),(74,210),(75,197),(76,212),(77,199),(78,214),(79,201),(80,216),(81,203),(82,218),(83,205),(84,220),(113,134),(114,121),(115,136),(116,123),(117,138),(118,125),(119,140),(120,127),(122,129),(124,131),(126,133),(128,135),(130,137),(132,139),(141,162),(142,149),(143,164),(144,151),(145,166),(146,153),(147,168),(148,155),(150,157),(152,159),(154,161),(156,163),(158,165),(160,167),(170,184),(172,186),(174,188),(176,190),(178,192),(180,194),(182,196)]])
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 | 14J | ··· | 14U | 28A | ··· | 28R |
| 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 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 8 | 8 | 2 | 2 | 2 | 2 | 4 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | SD16 | C4○D4 | D14 | D14 | C7⋊D4 | C8⋊C22 | D4.D7 | D4×D7 | D4⋊2D7 | D4.D14 |
| kernel | Dic14⋊9D4 | C28⋊C8 | D4⋊Dic7 | C4×Dic14 | C2×D4.D7 | C7×C4⋊1D4 | Dic14 | C2×C28 | C4⋊1D4 | C28 | C28 | C42 | C2×D4 | C2×C4 | C14 | C4 | C4 | C4 | C2 |
| # reps | 1 | 1 | 2 | 1 | 2 | 1 | 2 | 2 | 3 | 4 | 2 | 3 | 6 | 12 | 1 | 6 | 3 | 3 | 6 |
Matrix representation of Dic14⋊9D4 ►in GL6(𝔽113)
| 0 | 1 | 0 | 0 | 0 | 0 |
| 112 | 79 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 26 | 0 | 0 |
| 0 | 0 | 26 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 79 | 112 | 0 | 0 | 0 | 0 |
| 25 | 34 | 0 | 0 | 0 | 0 |
| 0 | 0 | 87 | 112 | 0 | 0 |
| 0 | 0 | 112 | 26 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 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 | 19 | 106 |
| 0 | 0 | 0 | 0 | 84 | 94 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 87 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 70 | 112 |
G:=sub<GL(6,GF(113))| [0,112,0,0,0,0,1,79,0,0,0,0,0,0,112,26,0,0,0,0,26,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[79,25,0,0,0,0,112,34,0,0,0,0,0,0,87,112,0,0,0,0,112,26,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,19,84,0,0,0,0,106,94],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,87,0,0,0,0,0,112,0,0,0,0,0,0,1,70,0,0,0,0,0,112] >;
Dic14⋊9D4 in GAP, Magma, Sage, TeX
{\rm Dic}_{14}\rtimes_9D_4 % in TeX
G:=Group("Dic14:9D4"); // GroupNames label
G:=SmallGroup(448,609);
// by ID
G=gap.SmallGroup(448,609);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,120,254,219,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=c^4=d^2=1,b^2=a^14,b*a*b^-1=a^-1,a*c=c*a,d*a*d=a^15,b*c=c*b,d*b*d=a^21*b,d*c*d=c^-1>;
// generators/relations