metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×C28).290D4, C2.9(C28⋊2D4), (C22×D7).34D4, C22.249(D4×D7), C14.92(C4⋊D4), (C22×C4).105D14, C7⋊5(C23.11D4), C14.C42⋊20C2, C2.7(C28.23D4), C14.54(C4.4D4), (C23×D7).22C22, C23.382(C22×D7), C14.29(C42⋊2C2), C2.22(D14.5D4), C22.110(C4○D28), (C22×C28).393C22, (C22×C14).357C23, C22.53(Q8⋊2D7), C22.104(D4⋊2D7), C14.64(C22.D4), (C22×Dic7).62C22, C2.15(C23.23D14), (C2×C4⋊C4)⋊11D7, (C14×C4⋊C4)⋊27C2, (C2×D14⋊C4).15C2, (C2×C14).337(C2×D4), (C2×C4).43(C7⋊D4), C2.14(C4⋊C4⋊D7), C22.142(C2×C7⋊D4), (C2×C14).192(C4○D4), SmallGroup(448,527)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×C28).290D4
G = < a,b,c,d | a2=b28=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=ab-1, dbd=ab13, dcd=ac-1 >
Subgroups: 932 in 170 conjugacy classes, 57 normal (25 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, C23, C23, D7, C14, C14, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C24, Dic7, C28, D14, C2×C14, C2×C14, C2.C42, C2×C22⋊C4, C2×C4⋊C4, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C23.11D4, D14⋊C4, C7×C4⋊C4, C22×Dic7, C22×Dic7, C22×C28, C22×C28, C23×D7, C14.C42, C14.C42, C2×D14⋊C4, C2×D14⋊C4, C14×C4⋊C4, (C2×C28).290D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4⋊D4, C22.D4, C4.4D4, C42⋊2C2, C7⋊D4, C22×D7, C23.11D4, C4○D28, D4×D7, D4⋊2D7, Q8⋊2D7, C2×C7⋊D4, D14.5D4, C4⋊C4⋊D7, C23.23D14, C28⋊2D4, C28.23D4, (C2×C28).290D4
►On 224 points
Generators in S224
(1 161)(2 162)(3 163)(4 164)(5 165)(6 166)(7 167)(8 168)(9 141)(10 142)(11 143)(12 144)(13 145)(14 146)(15 147)(16 148)(17 149)(18 150)(19 151)(20 152)(21 153)(22 154)(23 155)(24 156)(25 157)(26 158)(27 159)(28 160)(29 104)(30 105)(31 106)(32 107)(33 108)(34 109)(35 110)(36 111)(37 112)(38 85)(39 86)(40 87)(41 88)(42 89)(43 90)(44 91)(45 92)(46 93)(47 94)(48 95)(49 96)(50 97)(51 98)(52 99)(53 100)(54 101)(55 102)(56 103)(57 218)(58 219)(59 220)(60 221)(61 222)(62 223)(63 224)(64 197)(65 198)(66 199)(67 200)(68 201)(69 202)(70 203)(71 204)(72 205)(73 206)(74 207)(75 208)(76 209)(77 210)(78 211)(79 212)(80 213)(81 214)(82 215)(83 216)(84 217)(113 180)(114 181)(115 182)(116 183)(117 184)(118 185)(119 186)(120 187)(121 188)(122 189)(123 190)(124 191)(125 192)(126 193)(127 194)(128 195)(129 196)(130 169)(131 170)(132 171)(133 172)(134 173)(135 174)(136 175)(137 176)(138 177)(139 178)(140 179)
(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 54 74 138)(2 100 75 176)(3 52 76 136)(4 98 77 174)(5 50 78 134)(6 96 79 172)(7 48 80 132)(8 94 81 170)(9 46 82 130)(10 92 83 196)(11 44 84 128)(12 90 57 194)(13 42 58 126)(14 88 59 192)(15 40 60 124)(16 86 61 190)(17 38 62 122)(18 112 63 188)(19 36 64 120)(20 110 65 186)(21 34 66 118)(22 108 67 184)(23 32 68 116)(24 106 69 182)(25 30 70 114)(26 104 71 180)(27 56 72 140)(28 102 73 178)(29 204 113 158)(31 202 115 156)(33 200 117 154)(35 198 119 152)(37 224 121 150)(39 222 123 148)(41 220 125 146)(43 218 127 144)(45 216 129 142)(47 214 131 168)(49 212 133 166)(51 210 135 164)(53 208 137 162)(55 206 139 160)(85 223 189 149)(87 221 191 147)(89 219 193 145)(91 217 195 143)(93 215 169 141)(95 213 171 167)(97 211 173 165)(99 209 175 163)(101 207 177 161)(103 205 179 159)(105 203 181 157)(107 201 183 155)(109 199 185 153)(111 197 187 151)
(1 15)(2 160)(3 13)(4 158)(5 11)(6 156)(7 9)(8 154)(10 152)(12 150)(14 148)(16 146)(17 27)(18 144)(19 25)(20 142)(21 23)(22 168)(24 166)(26 164)(28 162)(29 135)(30 187)(31 133)(32 185)(33 131)(34 183)(35 129)(36 181)(37 127)(38 179)(39 125)(40 177)(41 123)(42 175)(43 121)(44 173)(45 119)(46 171)(47 117)(48 169)(49 115)(50 195)(51 113)(52 193)(53 139)(54 191)(55 137)(56 189)(57 224)(58 76)(59 222)(60 74)(61 220)(62 72)(63 218)(64 70)(65 216)(66 68)(67 214)(69 212)(71 210)(73 208)(75 206)(77 204)(78 84)(79 202)(80 82)(81 200)(83 198)(85 140)(86 192)(87 138)(88 190)(89 136)(90 188)(91 134)(92 186)(93 132)(94 184)(95 130)(96 182)(97 128)(98 180)(99 126)(100 178)(101 124)(102 176)(103 122)(104 174)(105 120)(106 172)(107 118)(108 170)(109 116)(110 196)(111 114)(112 194)(141 167)(143 165)(145 163)(147 161)(149 159)(151 157)(153 155)(197 203)(199 201)(205 223)(207 221)(209 219)(211 217)(213 215)
G:=sub<Sym(224)| (1,161)(2,162)(3,163)(4,164)(5,165)(6,166)(7,167)(8,168)(9,141)(10,142)(11,143)(12,144)(13,145)(14,146)(15,147)(16,148)(17,149)(18,150)(19,151)(20,152)(21,153)(22,154)(23,155)(24,156)(25,157)(26,158)(27,159)(28,160)(29,104)(30,105)(31,106)(32,107)(33,108)(34,109)(35,110)(36,111)(37,112)(38,85)(39,86)(40,87)(41,88)(42,89)(43,90)(44,91)(45,92)(46,93)(47,94)(48,95)(49,96)(50,97)(51,98)(52,99)(53,100)(54,101)(55,102)(56,103)(57,218)(58,219)(59,220)(60,221)(61,222)(62,223)(63,224)(64,197)(65,198)(66,199)(67,200)(68,201)(69,202)(70,203)(71,204)(72,205)(73,206)(74,207)(75,208)(76,209)(77,210)(78,211)(79,212)(80,213)(81,214)(82,215)(83,216)(84,217)(113,180)(114,181)(115,182)(116,183)(117,184)(118,185)(119,186)(120,187)(121,188)(122,189)(123,190)(124,191)(125,192)(126,193)(127,194)(128,195)(129,196)(130,169)(131,170)(132,171)(133,172)(134,173)(135,174)(136,175)(137,176)(138,177)(139,178)(140,179), (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), (1,54,74,138)(2,100,75,176)(3,52,76,136)(4,98,77,174)(5,50,78,134)(6,96,79,172)(7,48,80,132)(8,94,81,170)(9,46,82,130)(10,92,83,196)(11,44,84,128)(12,90,57,194)(13,42,58,126)(14,88,59,192)(15,40,60,124)(16,86,61,190)(17,38,62,122)(18,112,63,188)(19,36,64,120)(20,110,65,186)(21,34,66,118)(22,108,67,184)(23,32,68,116)(24,106,69,182)(25,30,70,114)(26,104,71,180)(27,56,72,140)(28,102,73,178)(29,204,113,158)(31,202,115,156)(33,200,117,154)(35,198,119,152)(37,224,121,150)(39,222,123,148)(41,220,125,146)(43,218,127,144)(45,216,129,142)(47,214,131,168)(49,212,133,166)(51,210,135,164)(53,208,137,162)(55,206,139,160)(85,223,189,149)(87,221,191,147)(89,219,193,145)(91,217,195,143)(93,215,169,141)(95,213,171,167)(97,211,173,165)(99,209,175,163)(101,207,177,161)(103,205,179,159)(105,203,181,157)(107,201,183,155)(109,199,185,153)(111,197,187,151), (1,15)(2,160)(3,13)(4,158)(5,11)(6,156)(7,9)(8,154)(10,152)(12,150)(14,148)(16,146)(17,27)(18,144)(19,25)(20,142)(21,23)(22,168)(24,166)(26,164)(28,162)(29,135)(30,187)(31,133)(32,185)(33,131)(34,183)(35,129)(36,181)(37,127)(38,179)(39,125)(40,177)(41,123)(42,175)(43,121)(44,173)(45,119)(46,171)(47,117)(48,169)(49,115)(50,195)(51,113)(52,193)(53,139)(54,191)(55,137)(56,189)(57,224)(58,76)(59,222)(60,74)(61,220)(62,72)(63,218)(64,70)(65,216)(66,68)(67,214)(69,212)(71,210)(73,208)(75,206)(77,204)(78,84)(79,202)(80,82)(81,200)(83,198)(85,140)(86,192)(87,138)(88,190)(89,136)(90,188)(91,134)(92,186)(93,132)(94,184)(95,130)(96,182)(97,128)(98,180)(99,126)(100,178)(101,124)(102,176)(103,122)(104,174)(105,120)(106,172)(107,118)(108,170)(109,116)(110,196)(111,114)(112,194)(141,167)(143,165)(145,163)(147,161)(149,159)(151,157)(153,155)(197,203)(199,201)(205,223)(207,221)(209,219)(211,217)(213,215)>;
G:=Group( (1,161)(2,162)(3,163)(4,164)(5,165)(6,166)(7,167)(8,168)(9,141)(10,142)(11,143)(12,144)(13,145)(14,146)(15,147)(16,148)(17,149)(18,150)(19,151)(20,152)(21,153)(22,154)(23,155)(24,156)(25,157)(26,158)(27,159)(28,160)(29,104)(30,105)(31,106)(32,107)(33,108)(34,109)(35,110)(36,111)(37,112)(38,85)(39,86)(40,87)(41,88)(42,89)(43,90)(44,91)(45,92)(46,93)(47,94)(48,95)(49,96)(50,97)(51,98)(52,99)(53,100)(54,101)(55,102)(56,103)(57,218)(58,219)(59,220)(60,221)(61,222)(62,223)(63,224)(64,197)(65,198)(66,199)(67,200)(68,201)(69,202)(70,203)(71,204)(72,205)(73,206)(74,207)(75,208)(76,209)(77,210)(78,211)(79,212)(80,213)(81,214)(82,215)(83,216)(84,217)(113,180)(114,181)(115,182)(116,183)(117,184)(118,185)(119,186)(120,187)(121,188)(122,189)(123,190)(124,191)(125,192)(126,193)(127,194)(128,195)(129,196)(130,169)(131,170)(132,171)(133,172)(134,173)(135,174)(136,175)(137,176)(138,177)(139,178)(140,179), (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), (1,54,74,138)(2,100,75,176)(3,52,76,136)(4,98,77,174)(5,50,78,134)(6,96,79,172)(7,48,80,132)(8,94,81,170)(9,46,82,130)(10,92,83,196)(11,44,84,128)(12,90,57,194)(13,42,58,126)(14,88,59,192)(15,40,60,124)(16,86,61,190)(17,38,62,122)(18,112,63,188)(19,36,64,120)(20,110,65,186)(21,34,66,118)(22,108,67,184)(23,32,68,116)(24,106,69,182)(25,30,70,114)(26,104,71,180)(27,56,72,140)(28,102,73,178)(29,204,113,158)(31,202,115,156)(33,200,117,154)(35,198,119,152)(37,224,121,150)(39,222,123,148)(41,220,125,146)(43,218,127,144)(45,216,129,142)(47,214,131,168)(49,212,133,166)(51,210,135,164)(53,208,137,162)(55,206,139,160)(85,223,189,149)(87,221,191,147)(89,219,193,145)(91,217,195,143)(93,215,169,141)(95,213,171,167)(97,211,173,165)(99,209,175,163)(101,207,177,161)(103,205,179,159)(105,203,181,157)(107,201,183,155)(109,199,185,153)(111,197,187,151), (1,15)(2,160)(3,13)(4,158)(5,11)(6,156)(7,9)(8,154)(10,152)(12,150)(14,148)(16,146)(17,27)(18,144)(19,25)(20,142)(21,23)(22,168)(24,166)(26,164)(28,162)(29,135)(30,187)(31,133)(32,185)(33,131)(34,183)(35,129)(36,181)(37,127)(38,179)(39,125)(40,177)(41,123)(42,175)(43,121)(44,173)(45,119)(46,171)(47,117)(48,169)(49,115)(50,195)(51,113)(52,193)(53,139)(54,191)(55,137)(56,189)(57,224)(58,76)(59,222)(60,74)(61,220)(62,72)(63,218)(64,70)(65,216)(66,68)(67,214)(69,212)(71,210)(73,208)(75,206)(77,204)(78,84)(79,202)(80,82)(81,200)(83,198)(85,140)(86,192)(87,138)(88,190)(89,136)(90,188)(91,134)(92,186)(93,132)(94,184)(95,130)(96,182)(97,128)(98,180)(99,126)(100,178)(101,124)(102,176)(103,122)(104,174)(105,120)(106,172)(107,118)(108,170)(109,116)(110,196)(111,114)(112,194)(141,167)(143,165)(145,163)(147,161)(149,159)(151,157)(153,155)(197,203)(199,201)(205,223)(207,221)(209,219)(211,217)(213,215) );
G=PermutationGroup([[(1,161),(2,162),(3,163),(4,164),(5,165),(6,166),(7,167),(8,168),(9,141),(10,142),(11,143),(12,144),(13,145),(14,146),(15,147),(16,148),(17,149),(18,150),(19,151),(20,152),(21,153),(22,154),(23,155),(24,156),(25,157),(26,158),(27,159),(28,160),(29,104),(30,105),(31,106),(32,107),(33,108),(34,109),(35,110),(36,111),(37,112),(38,85),(39,86),(40,87),(41,88),(42,89),(43,90),(44,91),(45,92),(46,93),(47,94),(48,95),(49,96),(50,97),(51,98),(52,99),(53,100),(54,101),(55,102),(56,103),(57,218),(58,219),(59,220),(60,221),(61,222),(62,223),(63,224),(64,197),(65,198),(66,199),(67,200),(68,201),(69,202),(70,203),(71,204),(72,205),(73,206),(74,207),(75,208),(76,209),(77,210),(78,211),(79,212),(80,213),(81,214),(82,215),(83,216),(84,217),(113,180),(114,181),(115,182),(116,183),(117,184),(118,185),(119,186),(120,187),(121,188),(122,189),(123,190),(124,191),(125,192),(126,193),(127,194),(128,195),(129,196),(130,169),(131,170),(132,171),(133,172),(134,173),(135,174),(136,175),(137,176),(138,177),(139,178),(140,179)], [(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)], [(1,54,74,138),(2,100,75,176),(3,52,76,136),(4,98,77,174),(5,50,78,134),(6,96,79,172),(7,48,80,132),(8,94,81,170),(9,46,82,130),(10,92,83,196),(11,44,84,128),(12,90,57,194),(13,42,58,126),(14,88,59,192),(15,40,60,124),(16,86,61,190),(17,38,62,122),(18,112,63,188),(19,36,64,120),(20,110,65,186),(21,34,66,118),(22,108,67,184),(23,32,68,116),(24,106,69,182),(25,30,70,114),(26,104,71,180),(27,56,72,140),(28,102,73,178),(29,204,113,158),(31,202,115,156),(33,200,117,154),(35,198,119,152),(37,224,121,150),(39,222,123,148),(41,220,125,146),(43,218,127,144),(45,216,129,142),(47,214,131,168),(49,212,133,166),(51,210,135,164),(53,208,137,162),(55,206,139,160),(85,223,189,149),(87,221,191,147),(89,219,193,145),(91,217,195,143),(93,215,169,141),(95,213,171,167),(97,211,173,165),(99,209,175,163),(101,207,177,161),(103,205,179,159),(105,203,181,157),(107,201,183,155),(109,199,185,153),(111,197,187,151)], [(1,15),(2,160),(3,13),(4,158),(5,11),(6,156),(7,9),(8,154),(10,152),(12,150),(14,148),(16,146),(17,27),(18,144),(19,25),(20,142),(21,23),(22,168),(24,166),(26,164),(28,162),(29,135),(30,187),(31,133),(32,185),(33,131),(34,183),(35,129),(36,181),(37,127),(38,179),(39,125),(40,177),(41,123),(42,175),(43,121),(44,173),(45,119),(46,171),(47,117),(48,169),(49,115),(50,195),(51,113),(52,193),(53,139),(54,191),(55,137),(56,189),(57,224),(58,76),(59,222),(60,74),(61,220),(62,72),(63,218),(64,70),(65,216),(66,68),(67,214),(69,212),(71,210),(73,208),(75,206),(77,204),(78,84),(79,202),(80,82),(81,200),(83,198),(85,140),(86,192),(87,138),(88,190),(89,136),(90,188),(91,134),(92,186),(93,132),(94,184),(95,130),(96,182),(97,128),(98,180),(99,126),(100,178),(101,124),(102,176),(103,122),(104,174),(105,120),(106,172),(107,118),(108,170),(109,116),(110,196),(111,114),(112,194),(141,167),(143,165),(145,163),(147,161),(149,159),(151,157),(153,155),(197,203),(199,201),(205,223),(207,221),(209,219),(211,217),(213,215)]])
82 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 4A | ··· | 4F | 4G | ··· | 4L | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 28 | 28 | 4 | ··· | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | + | |||
| image | C1 | C2 | C2 | C2 | D4 | D4 | D7 | C4○D4 | D14 | C7⋊D4 | C4○D28 | D4×D7 | D4⋊2D7 | Q8⋊2D7 |
| kernel | (C2×C28).290D4 | C14.C42 | C2×D14⋊C4 | C14×C4⋊C4 | C2×C28 | C22×D7 | C2×C4⋊C4 | C2×C14 | C22×C4 | C2×C4 | C22 | C22 | C22 | C22 |
| # reps | 1 | 3 | 3 | 1 | 2 | 2 | 3 | 10 | 9 | 12 | 24 | 3 | 3 | 6 |
Matrix representation of (C2×C28).290D4 ►in GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 11 | 21 | 0 | 0 | 0 | 0 |
| 8 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 26 | 0 | 0 |
| 0 | 0 | 2 | 19 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 3 |
| 0 | 0 | 0 | 0 | 26 | 7 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 13 | 0 | 0 |
| 0 | 0 | 5 | 20 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 16 | 12 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 1 | 0 | 0 |
| 0 | 0 | 17 | 19 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 18 | 28 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[11,8,0,0,0,0,21,18,0,0,0,0,0,0,21,2,0,0,0,0,26,19,0,0,0,0,0,0,11,26,0,0,0,0,3,7],[0,28,0,0,0,0,28,0,0,0,0,0,0,0,9,5,0,0,0,0,13,20,0,0,0,0,0,0,17,16,0,0,0,0,0,12],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,10,17,0,0,0,0,1,19,0,0,0,0,0,0,1,18,0,0,0,0,0,28] >;
(C2×C28).290D4 in GAP, Magma, Sage, TeX
(C_2\times C_{28})._{290}D_4 % in TeX
G:=Group("(C2xC28).290D4"); // GroupNames label
G:=SmallGroup(448,527);
// by ID
G=gap.SmallGroup(448,527);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,232,254,387,100,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^28=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=a*b^-1,d*b*d=a*b^13,d*c*d=a*c^-1>;
// generators/relations