metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D4⋊6D28, C42.112D14, C14.612- 1+4, (C4×D4)⋊17D7, (C7×D4)⋊11D4, (D4×C28)⋊19C2, (C4×D28)⋊31C2, C7⋊3(D4⋊6D4), C28.55(C2×D4), C4.23(C2×D28), C28⋊14(C4○D4), C4⋊5(D4⋊2D7), C28⋊7D4⋊10C2, C4⋊C4.284D14, C28⋊2Q8⋊25C2, C22.2(C2×D28), D14⋊2Q8⋊15C2, (C2×D4).249D14, (C2×C14).99C24, D14⋊C4.5C22, C2.19(C22×D28), C14.17(C22×D4), (C4×C28).155C22, (C2×C28).160C23, C22⋊C4.113D14, C22.D28⋊6C2, (C22×C4).211D14, C4⋊Dic7.39C22, (C2×D28).212C22, (D4×C14).260C22, (C22×C28).81C22, (C22×D7).34C23, C22.124(C23×D7), C23.173(C22×D7), (C22×C14).169C23, (C2×Dic7).206C23, C2.18(D4.10D14), (C2×Dic14).144C22, (C22×Dic7).97C22, (C2×C14).2(C2×D4), (C2×D4⋊2D7)⋊4C2, (C2×C4⋊Dic7)⋊25C2, C14.74(C2×C4○D4), (C2×C4×D7).65C22, C2.22(C2×D4⋊2D7), (C7×C4⋊C4).329C22, (C2×C4).732(C22×D7), (C2×C7⋊D4).15C22, (C7×C22⋊C4).106C22, SmallGroup(448,1008)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D4⋊6D28
G = < a,b,c,d | a4=b2=c28=d2=1, bab=a-1, ac=ca, ad=da, bc=cb, dbd=a2b, dcd=c-1 >
Subgroups: 1332 in 292 conjugacy classes, 115 normal (29 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, D4, Q8, C23, C23, D7, C14, C14, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C4○D4, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C14, C2×C4⋊C4, C4×D4, C4×D4, C4⋊D4, C22⋊Q8, C22.D4, C4⋊Q8, C2×C4○D4, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, D4⋊6D4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, D4⋊2D7, C22×Dic7, C2×C7⋊D4, C22×C28, D4×C14, C28⋊2Q8, C4×D28, C22.D28, D14⋊2Q8, C2×C4⋊Dic7, C28⋊7D4, D4×C28, C2×D4⋊2D7, D4⋊6D28
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C22×D4, C2×C4○D4, 2- 1+4, D28, C22×D7, D4⋊6D4, C2×D28, D4⋊2D7, C23×D7, C22×D28, C2×D4⋊2D7, D4.10D14, D4⋊6D28
►On 224 points
Generators in S224
(1 107 224 148)(2 108 197 149)(3 109 198 150)(4 110 199 151)(5 111 200 152)(6 112 201 153)(7 85 202 154)(8 86 203 155)(9 87 204 156)(10 88 205 157)(11 89 206 158)(12 90 207 159)(13 91 208 160)(14 92 209 161)(15 93 210 162)(16 94 211 163)(17 95 212 164)(18 96 213 165)(19 97 214 166)(20 98 215 167)(21 99 216 168)(22 100 217 141)(23 101 218 142)(24 102 219 143)(25 103 220 144)(26 104 221 145)(27 105 222 146)(28 106 223 147)(29 170 137 71)(30 171 138 72)(31 172 139 73)(32 173 140 74)(33 174 113 75)(34 175 114 76)(35 176 115 77)(36 177 116 78)(37 178 117 79)(38 179 118 80)(39 180 119 81)(40 181 120 82)(41 182 121 83)(42 183 122 84)(43 184 123 57)(44 185 124 58)(45 186 125 59)(46 187 126 60)(47 188 127 61)(48 189 128 62)(49 190 129 63)(50 191 130 64)(51 192 131 65)(52 193 132 66)(53 194 133 67)(54 195 134 68)(55 196 135 69)(56 169 136 70)
(1 15)(2 16)(3 17)(4 18)(5 19)(6 20)(7 21)(8 22)(9 23)(10 24)(11 25)(12 26)(13 27)(14 28)(29 123)(30 124)(31 125)(32 126)(33 127)(34 128)(35 129)(36 130)(37 131)(38 132)(39 133)(40 134)(41 135)(42 136)(43 137)(44 138)(45 139)(46 140)(47 113)(48 114)(49 115)(50 116)(51 117)(52 118)(53 119)(54 120)(55 121)(56 122)(57 71)(58 72)(59 73)(60 74)(61 75)(62 76)(63 77)(64 78)(65 79)(66 80)(67 81)(68 82)(69 83)(70 84)(85 168)(86 141)(87 142)(88 143)(89 144)(90 145)(91 146)(92 147)(93 148)(94 149)(95 150)(96 151)(97 152)(98 153)(99 154)(100 155)(101 156)(102 157)(103 158)(104 159)(105 160)(106 161)(107 162)(108 163)(109 164)(110 165)(111 166)(112 167)(169 183)(170 184)(171 185)(172 186)(173 187)(174 188)(175 189)(176 190)(177 191)(178 192)(179 193)(180 194)(181 195)(182 196)(197 211)(198 212)(199 213)(200 214)(201 215)(202 216)(203 217)(204 218)(205 219)(206 220)(207 221)(208 222)(209 223)(210 224)
(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 53)(2 52)(3 51)(4 50)(5 49)(6 48)(7 47)(8 46)(9 45)(10 44)(11 43)(12 42)(13 41)(14 40)(15 39)(16 38)(17 37)(18 36)(19 35)(20 34)(21 33)(22 32)(23 31)(24 30)(25 29)(26 56)(27 55)(28 54)(57 158)(58 157)(59 156)(60 155)(61 154)(62 153)(63 152)(64 151)(65 150)(66 149)(67 148)(68 147)(69 146)(70 145)(71 144)(72 143)(73 142)(74 141)(75 168)(76 167)(77 166)(78 165)(79 164)(80 163)(81 162)(82 161)(83 160)(84 159)(85 188)(86 187)(87 186)(88 185)(89 184)(90 183)(91 182)(92 181)(93 180)(94 179)(95 178)(96 177)(97 176)(98 175)(99 174)(100 173)(101 172)(102 171)(103 170)(104 169)(105 196)(106 195)(107 194)(108 193)(109 192)(110 191)(111 190)(112 189)(113 216)(114 215)(115 214)(116 213)(117 212)(118 211)(119 210)(120 209)(121 208)(122 207)(123 206)(124 205)(125 204)(126 203)(127 202)(128 201)(129 200)(130 199)(131 198)(132 197)(133 224)(134 223)(135 222)(136 221)(137 220)(138 219)(139 218)(140 217)
G:=sub<Sym(224)| (1,107,224,148)(2,108,197,149)(3,109,198,150)(4,110,199,151)(5,111,200,152)(6,112,201,153)(7,85,202,154)(8,86,203,155)(9,87,204,156)(10,88,205,157)(11,89,206,158)(12,90,207,159)(13,91,208,160)(14,92,209,161)(15,93,210,162)(16,94,211,163)(17,95,212,164)(18,96,213,165)(19,97,214,166)(20,98,215,167)(21,99,216,168)(22,100,217,141)(23,101,218,142)(24,102,219,143)(25,103,220,144)(26,104,221,145)(27,105,222,146)(28,106,223,147)(29,170,137,71)(30,171,138,72)(31,172,139,73)(32,173,140,74)(33,174,113,75)(34,175,114,76)(35,176,115,77)(36,177,116,78)(37,178,117,79)(38,179,118,80)(39,180,119,81)(40,181,120,82)(41,182,121,83)(42,183,122,84)(43,184,123,57)(44,185,124,58)(45,186,125,59)(46,187,126,60)(47,188,127,61)(48,189,128,62)(49,190,129,63)(50,191,130,64)(51,192,131,65)(52,193,132,66)(53,194,133,67)(54,195,134,68)(55,196,135,69)(56,169,136,70), (1,15)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(29,123)(30,124)(31,125)(32,126)(33,127)(34,128)(35,129)(36,130)(37,131)(38,132)(39,133)(40,134)(41,135)(42,136)(43,137)(44,138)(45,139)(46,140)(47,113)(48,114)(49,115)(50,116)(51,117)(52,118)(53,119)(54,120)(55,121)(56,122)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81)(68,82)(69,83)(70,84)(85,168)(86,141)(87,142)(88,143)(89,144)(90,145)(91,146)(92,147)(93,148)(94,149)(95,150)(96,151)(97,152)(98,153)(99,154)(100,155)(101,156)(102,157)(103,158)(104,159)(105,160)(106,161)(107,162)(108,163)(109,164)(110,165)(111,166)(112,167)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224), (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), (1,53)(2,52)(3,51)(4,50)(5,49)(6,48)(7,47)(8,46)(9,45)(10,44)(11,43)(12,42)(13,41)(14,40)(15,39)(16,38)(17,37)(18,36)(19,35)(20,34)(21,33)(22,32)(23,31)(24,30)(25,29)(26,56)(27,55)(28,54)(57,158)(58,157)(59,156)(60,155)(61,154)(62,153)(63,152)(64,151)(65,150)(66,149)(67,148)(68,147)(69,146)(70,145)(71,144)(72,143)(73,142)(74,141)(75,168)(76,167)(77,166)(78,165)(79,164)(80,163)(81,162)(82,161)(83,160)(84,159)(85,188)(86,187)(87,186)(88,185)(89,184)(90,183)(91,182)(92,181)(93,180)(94,179)(95,178)(96,177)(97,176)(98,175)(99,174)(100,173)(101,172)(102,171)(103,170)(104,169)(105,196)(106,195)(107,194)(108,193)(109,192)(110,191)(111,190)(112,189)(113,216)(114,215)(115,214)(116,213)(117,212)(118,211)(119,210)(120,209)(121,208)(122,207)(123,206)(124,205)(125,204)(126,203)(127,202)(128,201)(129,200)(130,199)(131,198)(132,197)(133,224)(134,223)(135,222)(136,221)(137,220)(138,219)(139,218)(140,217)>;
G:=Group( (1,107,224,148)(2,108,197,149)(3,109,198,150)(4,110,199,151)(5,111,200,152)(6,112,201,153)(7,85,202,154)(8,86,203,155)(9,87,204,156)(10,88,205,157)(11,89,206,158)(12,90,207,159)(13,91,208,160)(14,92,209,161)(15,93,210,162)(16,94,211,163)(17,95,212,164)(18,96,213,165)(19,97,214,166)(20,98,215,167)(21,99,216,168)(22,100,217,141)(23,101,218,142)(24,102,219,143)(25,103,220,144)(26,104,221,145)(27,105,222,146)(28,106,223,147)(29,170,137,71)(30,171,138,72)(31,172,139,73)(32,173,140,74)(33,174,113,75)(34,175,114,76)(35,176,115,77)(36,177,116,78)(37,178,117,79)(38,179,118,80)(39,180,119,81)(40,181,120,82)(41,182,121,83)(42,183,122,84)(43,184,123,57)(44,185,124,58)(45,186,125,59)(46,187,126,60)(47,188,127,61)(48,189,128,62)(49,190,129,63)(50,191,130,64)(51,192,131,65)(52,193,132,66)(53,194,133,67)(54,195,134,68)(55,196,135,69)(56,169,136,70), (1,15)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(29,123)(30,124)(31,125)(32,126)(33,127)(34,128)(35,129)(36,130)(37,131)(38,132)(39,133)(40,134)(41,135)(42,136)(43,137)(44,138)(45,139)(46,140)(47,113)(48,114)(49,115)(50,116)(51,117)(52,118)(53,119)(54,120)(55,121)(56,122)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81)(68,82)(69,83)(70,84)(85,168)(86,141)(87,142)(88,143)(89,144)(90,145)(91,146)(92,147)(93,148)(94,149)(95,150)(96,151)(97,152)(98,153)(99,154)(100,155)(101,156)(102,157)(103,158)(104,159)(105,160)(106,161)(107,162)(108,163)(109,164)(110,165)(111,166)(112,167)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224), (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), (1,53)(2,52)(3,51)(4,50)(5,49)(6,48)(7,47)(8,46)(9,45)(10,44)(11,43)(12,42)(13,41)(14,40)(15,39)(16,38)(17,37)(18,36)(19,35)(20,34)(21,33)(22,32)(23,31)(24,30)(25,29)(26,56)(27,55)(28,54)(57,158)(58,157)(59,156)(60,155)(61,154)(62,153)(63,152)(64,151)(65,150)(66,149)(67,148)(68,147)(69,146)(70,145)(71,144)(72,143)(73,142)(74,141)(75,168)(76,167)(77,166)(78,165)(79,164)(80,163)(81,162)(82,161)(83,160)(84,159)(85,188)(86,187)(87,186)(88,185)(89,184)(90,183)(91,182)(92,181)(93,180)(94,179)(95,178)(96,177)(97,176)(98,175)(99,174)(100,173)(101,172)(102,171)(103,170)(104,169)(105,196)(106,195)(107,194)(108,193)(109,192)(110,191)(111,190)(112,189)(113,216)(114,215)(115,214)(116,213)(117,212)(118,211)(119,210)(120,209)(121,208)(122,207)(123,206)(124,205)(125,204)(126,203)(127,202)(128,201)(129,200)(130,199)(131,198)(132,197)(133,224)(134,223)(135,222)(136,221)(137,220)(138,219)(139,218)(140,217) );
G=PermutationGroup([[(1,107,224,148),(2,108,197,149),(3,109,198,150),(4,110,199,151),(5,111,200,152),(6,112,201,153),(7,85,202,154),(8,86,203,155),(9,87,204,156),(10,88,205,157),(11,89,206,158),(12,90,207,159),(13,91,208,160),(14,92,209,161),(15,93,210,162),(16,94,211,163),(17,95,212,164),(18,96,213,165),(19,97,214,166),(20,98,215,167),(21,99,216,168),(22,100,217,141),(23,101,218,142),(24,102,219,143),(25,103,220,144),(26,104,221,145),(27,105,222,146),(28,106,223,147),(29,170,137,71),(30,171,138,72),(31,172,139,73),(32,173,140,74),(33,174,113,75),(34,175,114,76),(35,176,115,77),(36,177,116,78),(37,178,117,79),(38,179,118,80),(39,180,119,81),(40,181,120,82),(41,182,121,83),(42,183,122,84),(43,184,123,57),(44,185,124,58),(45,186,125,59),(46,187,126,60),(47,188,127,61),(48,189,128,62),(49,190,129,63),(50,191,130,64),(51,192,131,65),(52,193,132,66),(53,194,133,67),(54,195,134,68),(55,196,135,69),(56,169,136,70)], [(1,15),(2,16),(3,17),(4,18),(5,19),(6,20),(7,21),(8,22),(9,23),(10,24),(11,25),(12,26),(13,27),(14,28),(29,123),(30,124),(31,125),(32,126),(33,127),(34,128),(35,129),(36,130),(37,131),(38,132),(39,133),(40,134),(41,135),(42,136),(43,137),(44,138),(45,139),(46,140),(47,113),(48,114),(49,115),(50,116),(51,117),(52,118),(53,119),(54,120),(55,121),(56,122),(57,71),(58,72),(59,73),(60,74),(61,75),(62,76),(63,77),(64,78),(65,79),(66,80),(67,81),(68,82),(69,83),(70,84),(85,168),(86,141),(87,142),(88,143),(89,144),(90,145),(91,146),(92,147),(93,148),(94,149),(95,150),(96,151),(97,152),(98,153),(99,154),(100,155),(101,156),(102,157),(103,158),(104,159),(105,160),(106,161),(107,162),(108,163),(109,164),(110,165),(111,166),(112,167),(169,183),(170,184),(171,185),(172,186),(173,187),(174,188),(175,189),(176,190),(177,191),(178,192),(179,193),(180,194),(181,195),(182,196),(197,211),(198,212),(199,213),(200,214),(201,215),(202,216),(203,217),(204,218),(205,219),(206,220),(207,221),(208,222),(209,223),(210,224)], [(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)], [(1,53),(2,52),(3,51),(4,50),(5,49),(6,48),(7,47),(8,46),(9,45),(10,44),(11,43),(12,42),(13,41),(14,40),(15,39),(16,38),(17,37),(18,36),(19,35),(20,34),(21,33),(22,32),(23,31),(24,30),(25,29),(26,56),(27,55),(28,54),(57,158),(58,157),(59,156),(60,155),(61,154),(62,153),(63,152),(64,151),(65,150),(66,149),(67,148),(68,147),(69,146),(70,145),(71,144),(72,143),(73,142),(74,141),(75,168),(76,167),(77,166),(78,165),(79,164),(80,163),(81,162),(82,161),(83,160),(84,159),(85,188),(86,187),(87,186),(88,185),(89,184),(90,183),(91,182),(92,181),(93,180),(94,179),(95,178),(96,177),(97,176),(98,175),(99,174),(100,173),(101,172),(102,171),(103,170),(104,169),(105,196),(106,195),(107,194),(108,193),(109,192),(110,191),(111,190),(112,189),(113,216),(114,215),(115,214),(116,213),(117,212),(118,211),(119,210),(120,209),(121,208),(122,207),(123,206),(124,205),(125,204),(126,203),(127,202),(128,201),(129,200),(130,199),(131,198),(132,197),(133,224),(134,223),(135,222),(136,221),(137,220),(138,219),(139,218),(140,217)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | D14 | D14 | D28 | 2- 1+4 | D4⋊2D7 | D4.10D14 |
| kernel | D4⋊6D28 | C28⋊2Q8 | C4×D28 | C22.D28 | D14⋊2Q8 | C2×C4⋊Dic7 | C28⋊7D4 | D4×C28 | C2×D4⋊2D7 | C7×D4 | C4×D4 | C28 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | D4 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 4 | 2 | 2 | 2 | 1 | 2 | 4 | 3 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of D4⋊6D28 ►in GL4(𝔽29) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 28 | 2 |
| 0 | 0 | 28 | 1 |
| 28 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 1 | 28 |
| 4 | 5 | 0 | 0 |
| 22 | 6 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 28 |
| 0 | 3 | 0 | 0 |
| 10 | 0 | 0 | 0 |
| 0 | 0 | 12 | 5 |
| 0 | 0 | 12 | 17 |
G:=sub<GL(4,GF(29))| [1,0,0,0,0,1,0,0,0,0,28,28,0,0,2,1],[28,0,0,0,0,28,0,0,0,0,1,1,0,0,0,28],[4,22,0,0,5,6,0,0,0,0,28,0,0,0,0,28],[0,10,0,0,3,0,0,0,0,0,12,12,0,0,5,17] >;
D4⋊6D28 in GAP, Magma, Sage, TeX
D_4\rtimes_6D_{28} % in TeX
G:=Group("D4:6D28"); // GroupNames label
G:=SmallGroup(448,1008);
// by ID
G=gap.SmallGroup(448,1008);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,387,675,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^2=c^28=d^2=1,b*a*b=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d=a^2*b,d*c*d=c^-1>;
// generators/relations