metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28⋊12D4, C42.172D14, C14.352- 1+4, C4⋊Q8⋊10D7, C4.73(D4×D7), (C4×D28)⋊51C2, C28⋊7(C4○D4), C7⋊7(D4⋊6D4), C28.71(C2×D4), C4⋊D28⋊40C2, C4⋊C4.123D14, C4⋊2(Q8⋊2D7), D14.25(C2×D4), D14⋊3Q8⋊35C2, (C2×Q8).145D14, D14.5D4⋊46C2, (C2×C28).103C23, (C4×C28).211C22, (C2×C14).270C24, C14.100(C22×D4), D14⋊C4.151C22, (C2×D28).271C22, Dic7⋊C4.60C22, C4⋊Dic7.384C22, (Q8×C14).137C22, C22.291(C23×D7), (C2×Dic7).141C23, (C22×D7).231C23, C2.36(Q8.10D14), C2.73(C2×D4×D7), (D7×C4⋊C4)⋊44C2, (C7×C4⋊Q8)⋊12C2, (C2×Q8⋊2D7)⋊13C2, C14.121(C2×C4○D4), C2.28(C2×Q8⋊2D7), (C2×C4×D7).144C22, (C2×C4).93(C22×D7), (C7×C4⋊C4).213C22, SmallGroup(448,1179)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28⋊12D4
G = < a,b,c,d | a28=b2=c4=d2=1, bab=a-1, ac=ca, dad=a13, bc=cb, dbd=a26b, dcd=c-1 >
Subgroups: 1452 in 292 conjugacy classes, 107 normal (27 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic7, C28, C28, D14, D14, C2×C14, C2×C4⋊C4, C4×D4, C4⋊D4, C22⋊Q8, C22.D4, C4⋊Q8, C2×C4○D4, C4×D7, D28, D28, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, D4⋊6D4, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C4×C28, C7×C4⋊C4, C2×C4×D7, C2×D28, C2×D28, Q8⋊2D7, Q8×C14, C4×D28, D7×C4⋊C4, D14.5D4, C4⋊D28, D14⋊3Q8, C7×C4⋊Q8, C2×Q8⋊2D7, D28⋊12D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C22×D4, C2×C4○D4, 2- 1+4, C22×D7, D4⋊6D4, D4×D7, Q8⋊2D7, C23×D7, C2×D4×D7, C2×Q8⋊2D7, Q8.10D14, D28⋊12D4
►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 7)(2 6)(3 5)(8 28)(9 27)(10 26)(11 25)(12 24)(13 23)(14 22)(15 21)(16 20)(17 19)(30 56)(31 55)(32 54)(33 53)(34 52)(35 51)(36 50)(37 49)(38 48)(39 47)(40 46)(41 45)(42 44)(57 69)(58 68)(59 67)(60 66)(61 65)(62 64)(70 84)(71 83)(72 82)(73 81)(74 80)(75 79)(76 78)(85 107)(86 106)(87 105)(88 104)(89 103)(90 102)(91 101)(92 100)(93 99)(94 98)(95 97)(108 112)(109 111)(113 121)(114 120)(115 119)(116 118)(122 140)(123 139)(124 138)(125 137)(126 136)(127 135)(128 134)(129 133)(130 132)(141 149)(142 148)(143 147)(144 146)(150 168)(151 167)(152 166)(153 165)(154 164)(155 163)(156 162)(157 161)(158 160)(169 183)(170 182)(171 181)(172 180)(173 179)(174 178)(175 177)(184 196)(185 195)(186 194)(187 193)(188 192)(189 191)(197 207)(198 206)(199 205)(200 204)(201 203)(208 224)(209 223)(210 222)(211 221)(212 220)(213 219)(214 218)(215 217)
(1 142 173 114)(2 143 174 115)(3 144 175 116)(4 145 176 117)(5 146 177 118)(6 147 178 119)(7 148 179 120)(8 149 180 121)(9 150 181 122)(10 151 182 123)(11 152 183 124)(12 153 184 125)(13 154 185 126)(14 155 186 127)(15 156 187 128)(16 157 188 129)(17 158 189 130)(18 159 190 131)(19 160 191 132)(20 161 192 133)(21 162 193 134)(22 163 194 135)(23 164 195 136)(24 165 196 137)(25 166 169 138)(26 167 170 139)(27 168 171 140)(28 141 172 113)(29 110 77 202)(30 111 78 203)(31 112 79 204)(32 85 80 205)(33 86 81 206)(34 87 82 207)(35 88 83 208)(36 89 84 209)(37 90 57 210)(38 91 58 211)(39 92 59 212)(40 93 60 213)(41 94 61 214)(42 95 62 215)(43 96 63 216)(44 97 64 217)(45 98 65 218)(46 99 66 219)(47 100 67 220)(48 101 68 221)(49 102 69 222)(50 103 70 223)(51 104 71 224)(52 105 72 197)(53 106 73 198)(54 107 74 199)(55 108 75 200)(56 109 76 201)
(1 81)(2 66)(3 79)(4 64)(5 77)(6 62)(7 75)(8 60)(9 73)(10 58)(11 71)(12 84)(13 69)(14 82)(15 67)(16 80)(17 65)(18 78)(19 63)(20 76)(21 61)(22 74)(23 59)(24 72)(25 57)(26 70)(27 83)(28 68)(29 177)(30 190)(31 175)(32 188)(33 173)(34 186)(35 171)(36 184)(37 169)(38 182)(39 195)(40 180)(41 193)(42 178)(43 191)(44 176)(45 189)(46 174)(47 187)(48 172)(49 185)(50 170)(51 183)(52 196)(53 181)(54 194)(55 179)(56 192)(85 157)(86 142)(87 155)(88 168)(89 153)(90 166)(91 151)(92 164)(93 149)(94 162)(95 147)(96 160)(97 145)(98 158)(99 143)(100 156)(101 141)(102 154)(103 167)(104 152)(105 165)(106 150)(107 163)(108 148)(109 161)(110 146)(111 159)(112 144)(113 221)(114 206)(115 219)(116 204)(117 217)(118 202)(119 215)(120 200)(121 213)(122 198)(123 211)(124 224)(125 209)(126 222)(127 207)(128 220)(129 205)(130 218)(131 203)(132 216)(133 201)(134 214)(135 199)(136 212)(137 197)(138 210)(139 223)(140 208)
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), (1,7)(2,6)(3,5)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)(30,56)(31,55)(32,54)(33,53)(34,52)(35,51)(36,50)(37,49)(38,48)(39,47)(40,46)(41,45)(42,44)(57,69)(58,68)(59,67)(60,66)(61,65)(62,64)(70,84)(71,83)(72,82)(73,81)(74,80)(75,79)(76,78)(85,107)(86,106)(87,105)(88,104)(89,103)(90,102)(91,101)(92,100)(93,99)(94,98)(95,97)(108,112)(109,111)(113,121)(114,120)(115,119)(116,118)(122,140)(123,139)(124,138)(125,137)(126,136)(127,135)(128,134)(129,133)(130,132)(141,149)(142,148)(143,147)(144,146)(150,168)(151,167)(152,166)(153,165)(154,164)(155,163)(156,162)(157,161)(158,160)(169,183)(170,182)(171,181)(172,180)(173,179)(174,178)(175,177)(184,196)(185,195)(186,194)(187,193)(188,192)(189,191)(197,207)(198,206)(199,205)(200,204)(201,203)(208,224)(209,223)(210,222)(211,221)(212,220)(213,219)(214,218)(215,217), (1,142,173,114)(2,143,174,115)(3,144,175,116)(4,145,176,117)(5,146,177,118)(6,147,178,119)(7,148,179,120)(8,149,180,121)(9,150,181,122)(10,151,182,123)(11,152,183,124)(12,153,184,125)(13,154,185,126)(14,155,186,127)(15,156,187,128)(16,157,188,129)(17,158,189,130)(18,159,190,131)(19,160,191,132)(20,161,192,133)(21,162,193,134)(22,163,194,135)(23,164,195,136)(24,165,196,137)(25,166,169,138)(26,167,170,139)(27,168,171,140)(28,141,172,113)(29,110,77,202)(30,111,78,203)(31,112,79,204)(32,85,80,205)(33,86,81,206)(34,87,82,207)(35,88,83,208)(36,89,84,209)(37,90,57,210)(38,91,58,211)(39,92,59,212)(40,93,60,213)(41,94,61,214)(42,95,62,215)(43,96,63,216)(44,97,64,217)(45,98,65,218)(46,99,66,219)(47,100,67,220)(48,101,68,221)(49,102,69,222)(50,103,70,223)(51,104,71,224)(52,105,72,197)(53,106,73,198)(54,107,74,199)(55,108,75,200)(56,109,76,201), (1,81)(2,66)(3,79)(4,64)(5,77)(6,62)(7,75)(8,60)(9,73)(10,58)(11,71)(12,84)(13,69)(14,82)(15,67)(16,80)(17,65)(18,78)(19,63)(20,76)(21,61)(22,74)(23,59)(24,72)(25,57)(26,70)(27,83)(28,68)(29,177)(30,190)(31,175)(32,188)(33,173)(34,186)(35,171)(36,184)(37,169)(38,182)(39,195)(40,180)(41,193)(42,178)(43,191)(44,176)(45,189)(46,174)(47,187)(48,172)(49,185)(50,170)(51,183)(52,196)(53,181)(54,194)(55,179)(56,192)(85,157)(86,142)(87,155)(88,168)(89,153)(90,166)(91,151)(92,164)(93,149)(94,162)(95,147)(96,160)(97,145)(98,158)(99,143)(100,156)(101,141)(102,154)(103,167)(104,152)(105,165)(106,150)(107,163)(108,148)(109,161)(110,146)(111,159)(112,144)(113,221)(114,206)(115,219)(116,204)(117,217)(118,202)(119,215)(120,200)(121,213)(122,198)(123,211)(124,224)(125,209)(126,222)(127,207)(128,220)(129,205)(130,218)(131,203)(132,216)(133,201)(134,214)(135,199)(136,212)(137,197)(138,210)(139,223)(140,208)>;
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), (1,7)(2,6)(3,5)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)(30,56)(31,55)(32,54)(33,53)(34,52)(35,51)(36,50)(37,49)(38,48)(39,47)(40,46)(41,45)(42,44)(57,69)(58,68)(59,67)(60,66)(61,65)(62,64)(70,84)(71,83)(72,82)(73,81)(74,80)(75,79)(76,78)(85,107)(86,106)(87,105)(88,104)(89,103)(90,102)(91,101)(92,100)(93,99)(94,98)(95,97)(108,112)(109,111)(113,121)(114,120)(115,119)(116,118)(122,140)(123,139)(124,138)(125,137)(126,136)(127,135)(128,134)(129,133)(130,132)(141,149)(142,148)(143,147)(144,146)(150,168)(151,167)(152,166)(153,165)(154,164)(155,163)(156,162)(157,161)(158,160)(169,183)(170,182)(171,181)(172,180)(173,179)(174,178)(175,177)(184,196)(185,195)(186,194)(187,193)(188,192)(189,191)(197,207)(198,206)(199,205)(200,204)(201,203)(208,224)(209,223)(210,222)(211,221)(212,220)(213,219)(214,218)(215,217), (1,142,173,114)(2,143,174,115)(3,144,175,116)(4,145,176,117)(5,146,177,118)(6,147,178,119)(7,148,179,120)(8,149,180,121)(9,150,181,122)(10,151,182,123)(11,152,183,124)(12,153,184,125)(13,154,185,126)(14,155,186,127)(15,156,187,128)(16,157,188,129)(17,158,189,130)(18,159,190,131)(19,160,191,132)(20,161,192,133)(21,162,193,134)(22,163,194,135)(23,164,195,136)(24,165,196,137)(25,166,169,138)(26,167,170,139)(27,168,171,140)(28,141,172,113)(29,110,77,202)(30,111,78,203)(31,112,79,204)(32,85,80,205)(33,86,81,206)(34,87,82,207)(35,88,83,208)(36,89,84,209)(37,90,57,210)(38,91,58,211)(39,92,59,212)(40,93,60,213)(41,94,61,214)(42,95,62,215)(43,96,63,216)(44,97,64,217)(45,98,65,218)(46,99,66,219)(47,100,67,220)(48,101,68,221)(49,102,69,222)(50,103,70,223)(51,104,71,224)(52,105,72,197)(53,106,73,198)(54,107,74,199)(55,108,75,200)(56,109,76,201), (1,81)(2,66)(3,79)(4,64)(5,77)(6,62)(7,75)(8,60)(9,73)(10,58)(11,71)(12,84)(13,69)(14,82)(15,67)(16,80)(17,65)(18,78)(19,63)(20,76)(21,61)(22,74)(23,59)(24,72)(25,57)(26,70)(27,83)(28,68)(29,177)(30,190)(31,175)(32,188)(33,173)(34,186)(35,171)(36,184)(37,169)(38,182)(39,195)(40,180)(41,193)(42,178)(43,191)(44,176)(45,189)(46,174)(47,187)(48,172)(49,185)(50,170)(51,183)(52,196)(53,181)(54,194)(55,179)(56,192)(85,157)(86,142)(87,155)(88,168)(89,153)(90,166)(91,151)(92,164)(93,149)(94,162)(95,147)(96,160)(97,145)(98,158)(99,143)(100,156)(101,141)(102,154)(103,167)(104,152)(105,165)(106,150)(107,163)(108,148)(109,161)(110,146)(111,159)(112,144)(113,221)(114,206)(115,219)(116,204)(117,217)(118,202)(119,215)(120,200)(121,213)(122,198)(123,211)(124,224)(125,209)(126,222)(127,207)(128,220)(129,205)(130,218)(131,203)(132,216)(133,201)(134,214)(135,199)(136,212)(137,197)(138,210)(139,223)(140,208) );
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)], [(1,7),(2,6),(3,5),(8,28),(9,27),(10,26),(11,25),(12,24),(13,23),(14,22),(15,21),(16,20),(17,19),(30,56),(31,55),(32,54),(33,53),(34,52),(35,51),(36,50),(37,49),(38,48),(39,47),(40,46),(41,45),(42,44),(57,69),(58,68),(59,67),(60,66),(61,65),(62,64),(70,84),(71,83),(72,82),(73,81),(74,80),(75,79),(76,78),(85,107),(86,106),(87,105),(88,104),(89,103),(90,102),(91,101),(92,100),(93,99),(94,98),(95,97),(108,112),(109,111),(113,121),(114,120),(115,119),(116,118),(122,140),(123,139),(124,138),(125,137),(126,136),(127,135),(128,134),(129,133),(130,132),(141,149),(142,148),(143,147),(144,146),(150,168),(151,167),(152,166),(153,165),(154,164),(155,163),(156,162),(157,161),(158,160),(169,183),(170,182),(171,181),(172,180),(173,179),(174,178),(175,177),(184,196),(185,195),(186,194),(187,193),(188,192),(189,191),(197,207),(198,206),(199,205),(200,204),(201,203),(208,224),(209,223),(210,222),(211,221),(212,220),(213,219),(214,218),(215,217)], [(1,142,173,114),(2,143,174,115),(3,144,175,116),(4,145,176,117),(5,146,177,118),(6,147,178,119),(7,148,179,120),(8,149,180,121),(9,150,181,122),(10,151,182,123),(11,152,183,124),(12,153,184,125),(13,154,185,126),(14,155,186,127),(15,156,187,128),(16,157,188,129),(17,158,189,130),(18,159,190,131),(19,160,191,132),(20,161,192,133),(21,162,193,134),(22,163,194,135),(23,164,195,136),(24,165,196,137),(25,166,169,138),(26,167,170,139),(27,168,171,140),(28,141,172,113),(29,110,77,202),(30,111,78,203),(31,112,79,204),(32,85,80,205),(33,86,81,206),(34,87,82,207),(35,88,83,208),(36,89,84,209),(37,90,57,210),(38,91,58,211),(39,92,59,212),(40,93,60,213),(41,94,61,214),(42,95,62,215),(43,96,63,216),(44,97,64,217),(45,98,65,218),(46,99,66,219),(47,100,67,220),(48,101,68,221),(49,102,69,222),(50,103,70,223),(51,104,71,224),(52,105,72,197),(53,106,73,198),(54,107,74,199),(55,108,75,200),(56,109,76,201)], [(1,81),(2,66),(3,79),(4,64),(5,77),(6,62),(7,75),(8,60),(9,73),(10,58),(11,71),(12,84),(13,69),(14,82),(15,67),(16,80),(17,65),(18,78),(19,63),(20,76),(21,61),(22,74),(23,59),(24,72),(25,57),(26,70),(27,83),(28,68),(29,177),(30,190),(31,175),(32,188),(33,173),(34,186),(35,171),(36,184),(37,169),(38,182),(39,195),(40,180),(41,193),(42,178),(43,191),(44,176),(45,189),(46,174),(47,187),(48,172),(49,185),(50,170),(51,183),(52,196),(53,181),(54,194),(55,179),(56,192),(85,157),(86,142),(87,155),(88,168),(89,153),(90,166),(91,151),(92,164),(93,149),(94,162),(95,147),(96,160),(97,145),(98,158),(99,143),(100,156),(101,141),(102,154),(103,167),(104,152),(105,165),(106,150),(107,163),(108,148),(109,161),(110,146),(111,159),(112,144),(113,221),(114,206),(115,219),(116,204),(117,217),(118,202),(119,215),(120,200),(121,213),(122,198),(123,211),(124,224),(125,209),(126,222),(127,207),(128,220),(129,205),(130,218),(131,203),(132,216),(133,201),(134,214),(135,199),(136,212),(137,197),(138,210),(139,223),(140,208)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | ··· | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 14 | 14 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | 2- 1+4 | D4×D7 | Q8⋊2D7 | Q8.10D14 |
| kernel | D28⋊12D4 | C4×D28 | D7×C4⋊C4 | D14.5D4 | C4⋊D28 | D14⋊3Q8 | C7×C4⋊Q8 | C2×Q8⋊2D7 | D28 | C4⋊Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | C14 | C4 | C4 | C2 |
| # reps | 1 | 2 | 2 | 4 | 2 | 2 | 1 | 2 | 4 | 3 | 4 | 3 | 12 | 6 | 1 | 6 | 6 | 6 |
Matrix representation of D28⋊12D4 ►in GL6(𝔽29)
| 28 | 5 | 0 | 0 | 0 | 0 |
| 17 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 3 | 0 | 0 |
| 0 | 0 | 26 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 17 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 3 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 6 | 5 |
| 0 | 0 | 0 | 0 | 10 | 23 |
| 17 | 2 | 0 | 0 | 0 | 0 |
| 1 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 26 | 0 | 0 |
| 0 | 0 | 21 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 10 | 4 |
| 0 | 0 | 0 | 0 | 26 | 19 |
G:=sub<GL(6,GF(29))| [28,17,0,0,0,0,5,1,0,0,0,0,0,0,1,26,0,0,0,0,3,21,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,17,0,0,0,0,0,1,0,0,0,0,0,0,28,3,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,6,10,0,0,0,0,5,23],[17,1,0,0,0,0,2,12,0,0,0,0,0,0,21,21,0,0,0,0,26,8,0,0,0,0,0,0,10,26,0,0,0,0,4,19] >;
D28⋊12D4 in GAP, Magma, Sage, TeX
D_{28}\rtimes_{12}D_4 % in TeX
G:=Group("D28:12D4"); // GroupNames label
G:=SmallGroup(448,1179);
// by ID
G=gap.SmallGroup(448,1179);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,268,1571,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=b^2=c^4=d^2=1,b*a*b=a^-1,a*c=c*a,d*a*d=a^13,b*c=c*b,d*b*d=a^26*b,d*c*d=c^-1>;
// generators/relations