metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28.23D4, C42.63D14, C4.50(D4×D7), (C4×D28)⋊21C2, C28⋊C8⋊29C2, C4.4D4⋊1D7, C28.24(C2×D4), (C2×D4).47D14, (C2×C28).271D4, C7⋊5(D4.2D4), (C2×Q8).37D14, C28.68(C4○D4), Q8⋊Dic7⋊22C2, C4.2(D4⋊2D7), D4⋊Dic7⋊19C2, C14.105(C4○D8), C2.11(C28⋊2D4), (C4×C28).106C22, (C2×C28).375C23, (D4×C14).63C22, (Q8×C14).55C22, C2.18(D4⋊D14), C14.102(C4⋊D4), C14.119(C8⋊C22), (C2×D28).244C22, C4⋊Dic7.341C22, C2.24(D4.8D14), (C2×Q8⋊D7)⋊12C2, (C2×D4⋊D7).6C2, (C7×C4.4D4)⋊1C2, (C2×C14).506(C2×D4), (C2×C4).61(C7⋊D4), (C2×C7⋊C8).121C22, (C2×C4).475(C22×D7), C22.181(C2×C7⋊D4), SmallGroup(448,591)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28.23D4
G = < a,b,c,d | a28=b2=c4=1, d2=a14, bab=a-1, ac=ca, dad-1=a15, bc=cb, dbd-1=a7b, dcd-1=a14c-1 >
Subgroups: 652 in 124 conjugacy classes, 41 normal (39 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C14, C42, C22⋊C4, C4⋊C4, C2×C8, D8, SD16, C22×C4, C2×D4, C2×D4, C2×Q8, Dic7, C28, C28, D14, C2×C14, C2×C14, D4⋊C4, Q8⋊C4, C4⋊C8, C4×D4, C4.4D4, C2×D8, C2×SD16, C7⋊C8, C4×D7, D28, D28, C2×Dic7, C2×C28, C2×C28, C7×D4, C7×Q8, C22×D7, C22×C14, D4.2D4, C2×C7⋊C8, C4⋊Dic7, D14⋊C4, D4⋊D7, Q8⋊D7, C4×C28, C7×C22⋊C4, C2×C4×D7, C2×D28, D4×C14, Q8×C14, C28⋊C8, D4⋊Dic7, Q8⋊Dic7, C4×D28, C2×D4⋊D7, C2×Q8⋊D7, C7×C4.4D4, D28.23D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4⋊D4, C4○D8, C8⋊C22, C7⋊D4, C22×D7, D4.2D4, D4×D7, D4⋊2D7, C2×C7⋊D4, C28⋊2D4, D4⋊D14, D4.8D14, D28.23D4
►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 14)(2 13)(3 12)(4 11)(5 10)(6 9)(7 8)(15 28)(16 27)(17 26)(18 25)(19 24)(20 23)(21 22)(29 56)(30 55)(31 54)(32 53)(33 52)(34 51)(35 50)(36 49)(37 48)(38 47)(39 46)(40 45)(41 44)(42 43)(57 67)(58 66)(59 65)(60 64)(61 63)(68 84)(69 83)(70 82)(71 81)(72 80)(73 79)(74 78)(75 77)(86 112)(87 111)(88 110)(89 109)(90 108)(91 107)(92 106)(93 105)(94 104)(95 103)(96 102)(97 101)(98 100)(113 114)(115 140)(116 139)(117 138)(118 137)(119 136)(120 135)(121 134)(122 133)(123 132)(124 131)(125 130)(126 129)(127 128)(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)(169 191)(170 190)(171 189)(172 188)(173 187)(174 186)(175 185)(176 184)(177 183)(178 182)(179 181)(192 196)(193 195)(197 204)(198 203)(199 202)(200 201)(205 224)(206 223)(207 222)(208 221)(209 220)(210 219)(211 218)(212 217)(213 216)(214 215)
(1 50 222 135)(2 51 223 136)(3 52 224 137)(4 53 197 138)(5 54 198 139)(6 55 199 140)(7 56 200 113)(8 29 201 114)(9 30 202 115)(10 31 203 116)(11 32 204 117)(12 33 205 118)(13 34 206 119)(14 35 207 120)(15 36 208 121)(16 37 209 122)(17 38 210 123)(18 39 211 124)(19 40 212 125)(20 41 213 126)(21 42 214 127)(22 43 215 128)(23 44 216 129)(24 45 217 130)(25 46 218 131)(26 47 219 132)(27 48 220 133)(28 49 221 134)(57 189 142 94)(58 190 143 95)(59 191 144 96)(60 192 145 97)(61 193 146 98)(62 194 147 99)(63 195 148 100)(64 196 149 101)(65 169 150 102)(66 170 151 103)(67 171 152 104)(68 172 153 105)(69 173 154 106)(70 174 155 107)(71 175 156 108)(72 176 157 109)(73 177 158 110)(74 178 159 111)(75 179 160 112)(76 180 161 85)(77 181 162 86)(78 182 163 87)(79 183 164 88)(80 184 165 89)(81 185 166 90)(82 186 167 91)(83 187 168 92)(84 188 141 93)
(1 177 15 191)(2 192 16 178)(3 179 17 193)(4 194 18 180)(5 181 19 195)(6 196 20 182)(7 183 21 169)(8 170 22 184)(9 185 23 171)(10 172 24 186)(11 187 25 173)(12 174 26 188)(13 189 27 175)(14 176 28 190)(29 80 43 66)(30 67 44 81)(31 82 45 68)(32 69 46 83)(33 84 47 70)(34 71 48 57)(35 58 49 72)(36 73 50 59)(37 60 51 74)(38 75 52 61)(39 62 53 76)(40 77 54 63)(41 64 55 78)(42 79 56 65)(85 197 99 211)(86 212 100 198)(87 199 101 213)(88 214 102 200)(89 201 103 215)(90 216 104 202)(91 203 105 217)(92 218 106 204)(93 205 107 219)(94 220 108 206)(95 207 109 221)(96 222 110 208)(97 209 111 223)(98 224 112 210)(113 150 127 164)(114 165 128 151)(115 152 129 166)(116 167 130 153)(117 154 131 168)(118 141 132 155)(119 156 133 142)(120 143 134 157)(121 158 135 144)(122 145 136 159)(123 160 137 146)(124 147 138 161)(125 162 139 148)(126 149 140 163)
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), (1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(29,56)(30,55)(31,54)(32,53)(33,52)(34,51)(35,50)(36,49)(37,48)(38,47)(39,46)(40,45)(41,44)(42,43)(57,67)(58,66)(59,65)(60,64)(61,63)(68,84)(69,83)(70,82)(71,81)(72,80)(73,79)(74,78)(75,77)(86,112)(87,111)(88,110)(89,109)(90,108)(91,107)(92,106)(93,105)(94,104)(95,103)(96,102)(97,101)(98,100)(113,114)(115,140)(116,139)(117,138)(118,137)(119,136)(120,135)(121,134)(122,133)(123,132)(124,131)(125,130)(126,129)(127,128)(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)(169,191)(170,190)(171,189)(172,188)(173,187)(174,186)(175,185)(176,184)(177,183)(178,182)(179,181)(192,196)(193,195)(197,204)(198,203)(199,202)(200,201)(205,224)(206,223)(207,222)(208,221)(209,220)(210,219)(211,218)(212,217)(213,216)(214,215), (1,50,222,135)(2,51,223,136)(3,52,224,137)(4,53,197,138)(5,54,198,139)(6,55,199,140)(7,56,200,113)(8,29,201,114)(9,30,202,115)(10,31,203,116)(11,32,204,117)(12,33,205,118)(13,34,206,119)(14,35,207,120)(15,36,208,121)(16,37,209,122)(17,38,210,123)(18,39,211,124)(19,40,212,125)(20,41,213,126)(21,42,214,127)(22,43,215,128)(23,44,216,129)(24,45,217,130)(25,46,218,131)(26,47,219,132)(27,48,220,133)(28,49,221,134)(57,189,142,94)(58,190,143,95)(59,191,144,96)(60,192,145,97)(61,193,146,98)(62,194,147,99)(63,195,148,100)(64,196,149,101)(65,169,150,102)(66,170,151,103)(67,171,152,104)(68,172,153,105)(69,173,154,106)(70,174,155,107)(71,175,156,108)(72,176,157,109)(73,177,158,110)(74,178,159,111)(75,179,160,112)(76,180,161,85)(77,181,162,86)(78,182,163,87)(79,183,164,88)(80,184,165,89)(81,185,166,90)(82,186,167,91)(83,187,168,92)(84,188,141,93), (1,177,15,191)(2,192,16,178)(3,179,17,193)(4,194,18,180)(5,181,19,195)(6,196,20,182)(7,183,21,169)(8,170,22,184)(9,185,23,171)(10,172,24,186)(11,187,25,173)(12,174,26,188)(13,189,27,175)(14,176,28,190)(29,80,43,66)(30,67,44,81)(31,82,45,68)(32,69,46,83)(33,84,47,70)(34,71,48,57)(35,58,49,72)(36,73,50,59)(37,60,51,74)(38,75,52,61)(39,62,53,76)(40,77,54,63)(41,64,55,78)(42,79,56,65)(85,197,99,211)(86,212,100,198)(87,199,101,213)(88,214,102,200)(89,201,103,215)(90,216,104,202)(91,203,105,217)(92,218,106,204)(93,205,107,219)(94,220,108,206)(95,207,109,221)(96,222,110,208)(97,209,111,223)(98,224,112,210)(113,150,127,164)(114,165,128,151)(115,152,129,166)(116,167,130,153)(117,154,131,168)(118,141,132,155)(119,156,133,142)(120,143,134,157)(121,158,135,144)(122,145,136,159)(123,160,137,146)(124,147,138,161)(125,162,139,148)(126,149,140,163)>;
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), (1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(29,56)(30,55)(31,54)(32,53)(33,52)(34,51)(35,50)(36,49)(37,48)(38,47)(39,46)(40,45)(41,44)(42,43)(57,67)(58,66)(59,65)(60,64)(61,63)(68,84)(69,83)(70,82)(71,81)(72,80)(73,79)(74,78)(75,77)(86,112)(87,111)(88,110)(89,109)(90,108)(91,107)(92,106)(93,105)(94,104)(95,103)(96,102)(97,101)(98,100)(113,114)(115,140)(116,139)(117,138)(118,137)(119,136)(120,135)(121,134)(122,133)(123,132)(124,131)(125,130)(126,129)(127,128)(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)(169,191)(170,190)(171,189)(172,188)(173,187)(174,186)(175,185)(176,184)(177,183)(178,182)(179,181)(192,196)(193,195)(197,204)(198,203)(199,202)(200,201)(205,224)(206,223)(207,222)(208,221)(209,220)(210,219)(211,218)(212,217)(213,216)(214,215), (1,50,222,135)(2,51,223,136)(3,52,224,137)(4,53,197,138)(5,54,198,139)(6,55,199,140)(7,56,200,113)(8,29,201,114)(9,30,202,115)(10,31,203,116)(11,32,204,117)(12,33,205,118)(13,34,206,119)(14,35,207,120)(15,36,208,121)(16,37,209,122)(17,38,210,123)(18,39,211,124)(19,40,212,125)(20,41,213,126)(21,42,214,127)(22,43,215,128)(23,44,216,129)(24,45,217,130)(25,46,218,131)(26,47,219,132)(27,48,220,133)(28,49,221,134)(57,189,142,94)(58,190,143,95)(59,191,144,96)(60,192,145,97)(61,193,146,98)(62,194,147,99)(63,195,148,100)(64,196,149,101)(65,169,150,102)(66,170,151,103)(67,171,152,104)(68,172,153,105)(69,173,154,106)(70,174,155,107)(71,175,156,108)(72,176,157,109)(73,177,158,110)(74,178,159,111)(75,179,160,112)(76,180,161,85)(77,181,162,86)(78,182,163,87)(79,183,164,88)(80,184,165,89)(81,185,166,90)(82,186,167,91)(83,187,168,92)(84,188,141,93), (1,177,15,191)(2,192,16,178)(3,179,17,193)(4,194,18,180)(5,181,19,195)(6,196,20,182)(7,183,21,169)(8,170,22,184)(9,185,23,171)(10,172,24,186)(11,187,25,173)(12,174,26,188)(13,189,27,175)(14,176,28,190)(29,80,43,66)(30,67,44,81)(31,82,45,68)(32,69,46,83)(33,84,47,70)(34,71,48,57)(35,58,49,72)(36,73,50,59)(37,60,51,74)(38,75,52,61)(39,62,53,76)(40,77,54,63)(41,64,55,78)(42,79,56,65)(85,197,99,211)(86,212,100,198)(87,199,101,213)(88,214,102,200)(89,201,103,215)(90,216,104,202)(91,203,105,217)(92,218,106,204)(93,205,107,219)(94,220,108,206)(95,207,109,221)(96,222,110,208)(97,209,111,223)(98,224,112,210)(113,150,127,164)(114,165,128,151)(115,152,129,166)(116,167,130,153)(117,154,131,168)(118,141,132,155)(119,156,133,142)(120,143,134,157)(121,158,135,144)(122,145,136,159)(123,160,137,146)(124,147,138,161)(125,162,139,148)(126,149,140,163) );
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)], [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,28),(16,27),(17,26),(18,25),(19,24),(20,23),(21,22),(29,56),(30,55),(31,54),(32,53),(33,52),(34,51),(35,50),(36,49),(37,48),(38,47),(39,46),(40,45),(41,44),(42,43),(57,67),(58,66),(59,65),(60,64),(61,63),(68,84),(69,83),(70,82),(71,81),(72,80),(73,79),(74,78),(75,77),(86,112),(87,111),(88,110),(89,109),(90,108),(91,107),(92,106),(93,105),(94,104),(95,103),(96,102),(97,101),(98,100),(113,114),(115,140),(116,139),(117,138),(118,137),(119,136),(120,135),(121,134),(122,133),(123,132),(124,131),(125,130),(126,129),(127,128),(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),(169,191),(170,190),(171,189),(172,188),(173,187),(174,186),(175,185),(176,184),(177,183),(178,182),(179,181),(192,196),(193,195),(197,204),(198,203),(199,202),(200,201),(205,224),(206,223),(207,222),(208,221),(209,220),(210,219),(211,218),(212,217),(213,216),(214,215)], [(1,50,222,135),(2,51,223,136),(3,52,224,137),(4,53,197,138),(5,54,198,139),(6,55,199,140),(7,56,200,113),(8,29,201,114),(9,30,202,115),(10,31,203,116),(11,32,204,117),(12,33,205,118),(13,34,206,119),(14,35,207,120),(15,36,208,121),(16,37,209,122),(17,38,210,123),(18,39,211,124),(19,40,212,125),(20,41,213,126),(21,42,214,127),(22,43,215,128),(23,44,216,129),(24,45,217,130),(25,46,218,131),(26,47,219,132),(27,48,220,133),(28,49,221,134),(57,189,142,94),(58,190,143,95),(59,191,144,96),(60,192,145,97),(61,193,146,98),(62,194,147,99),(63,195,148,100),(64,196,149,101),(65,169,150,102),(66,170,151,103),(67,171,152,104),(68,172,153,105),(69,173,154,106),(70,174,155,107),(71,175,156,108),(72,176,157,109),(73,177,158,110),(74,178,159,111),(75,179,160,112),(76,180,161,85),(77,181,162,86),(78,182,163,87),(79,183,164,88),(80,184,165,89),(81,185,166,90),(82,186,167,91),(83,187,168,92),(84,188,141,93)], [(1,177,15,191),(2,192,16,178),(3,179,17,193),(4,194,18,180),(5,181,19,195),(6,196,20,182),(7,183,21,169),(8,170,22,184),(9,185,23,171),(10,172,24,186),(11,187,25,173),(12,174,26,188),(13,189,27,175),(14,176,28,190),(29,80,43,66),(30,67,44,81),(31,82,45,68),(32,69,46,83),(33,84,47,70),(34,71,48,57),(35,58,49,72),(36,73,50,59),(37,60,51,74),(38,75,52,61),(39,62,53,76),(40,77,54,63),(41,64,55,78),(42,79,56,65),(85,197,99,211),(86,212,100,198),(87,199,101,213),(88,214,102,200),(89,201,103,215),(90,216,104,202),(91,203,105,217),(92,218,106,204),(93,205,107,219),(94,220,108,206),(95,207,109,221),(96,222,110,208),(97,209,111,223),(98,224,112,210),(113,150,127,164),(114,165,128,151),(115,152,129,166),(116,167,130,153),(117,154,131,168),(118,141,132,155),(119,156,133,142),(120,143,134,157),(121,158,135,144),(122,145,136,159),(123,160,137,146),(124,147,138,161),(125,162,139,148),(126,149,140,163)]])
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 | ··· | 28R | 28S | ··· | 28X |
| 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 |
| size | 1 | 1 | 1 | 1 | 8 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 8 | 28 | 28 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
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 | C4○D4 | D14 | D14 | D14 | C4○D8 | C7⋊D4 | C8⋊C22 | D4×D7 | D4⋊2D7 | D4⋊D14 | D4.8D14 |
| kernel | D28.23D4 | C28⋊C8 | D4⋊Dic7 | Q8⋊Dic7 | C4×D28 | C2×D4⋊D7 | C2×Q8⋊D7 | C7×C4.4D4 | D28 | C2×C28 | C4.4D4 | C28 | C42 | C2×D4 | C2×Q8 | C14 | C2×C4 | C14 | C4 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 3 | 2 | 3 | 3 | 3 | 4 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of D28.23D4 ►in GL6(𝔽113)
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 98 | 89 | 0 | 0 |
| 0 | 0 | 48 | 24 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 41 |
| 0 | 0 | 0 | 0 | 22 | 112 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 28 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 90 | 10 | 0 | 0 |
| 0 | 0 | 15 | 23 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 91 | 1 |
| 15 | 0 | 0 | 0 | 0 | 0 |
| 32 | 98 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 98 | 0 |
| 0 | 0 | 0 | 0 | 0 | 98 |
| 97 | 15 | 0 | 0 | 0 | 0 |
| 96 | 16 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 32 |
| 0 | 0 | 0 | 0 | 60 | 0 |
G:=sub<GL(6,GF(113))| [112,0,0,0,0,0,0,112,0,0,0,0,0,0,98,48,0,0,0,0,89,24,0,0,0,0,0,0,1,22,0,0,0,0,41,112],[112,28,0,0,0,0,0,1,0,0,0,0,0,0,90,15,0,0,0,0,10,23,0,0,0,0,0,0,112,91,0,0,0,0,0,1],[15,32,0,0,0,0,0,98,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,98,0,0,0,0,0,0,98],[97,96,0,0,0,0,15,16,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,0,60,0,0,0,0,32,0] >;
D28.23D4 in GAP, Magma, Sage, TeX
D_{28}._{23}D_4 % in TeX
G:=Group("D28.23D4"); // GroupNames label
G:=SmallGroup(448,591);
// by ID
G=gap.SmallGroup(448,591);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,344,254,219,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=b^2=c^4=1,d^2=a^14,b*a*b=a^-1,a*c=c*a,d*a*d^-1=a^15,b*c=c*b,d*b*d^-1=a^7*b,d*c*d^-1=a^14*c^-1>;
// generators/relations