metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×C4).21D28, (C2×C28).32D4, (C22×D7).8D4, C2.9(C4⋊D28), C22.158(D4×D7), C22.83(C2×D28), (C22×C4).19D14, C14.36(C4⋊D4), C14.C42⋊6C2, C14.3(C4.4D4), C2.8(C4.D28), C2.C42⋊13D7, C7⋊1(C23.11D4), (C23×D7).6C22, C22.91(C4○D28), (C22×C28).18C22, C23.362(C22×D7), C14.22(C42⋊2C2), C2.10(D14.D4), C22.89(D4⋊2D7), (C22×C14).299C23, C22.46(Q8⋊2D7), C2.8(C22.D28), C14.11(C22.D4), (C22×Dic7).21C22, (C2×C4⋊Dic7)⋊3C2, (C2×D14⋊C4).7C2, (C2×C14).97(C2×D4), C2.10(C4⋊C4⋊D7), (C2×C14).185(C4○D4), (C7×C2.C42)⋊11C2, SmallGroup(448,208)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×C4).21D28
G = < a,b,c,d | a2=b4=c28=1, d2=ab2, cbc-1=ab=ba, ac=ca, ad=da, dbd-1=b-1, dcd-1=ab2c-1 >
Subgroups: 956 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.C42, C2×C22⋊C4, C2×C4⋊C4, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C23.11D4, C4⋊Dic7, D14⋊C4, C22×Dic7, C22×Dic7, C22×C28, C22×C28, C23×D7, C14.C42, C7×C2.C42, C2×C4⋊Dic7, C2×D14⋊C4, C2×D14⋊C4, (C2×C4).21D28
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4⋊D4, C22.D4, C4.4D4, C42⋊2C2, D28, C22×D7, C23.11D4, C2×D28, C4○D28, D4×D7, D4⋊2D7, Q8⋊2D7, C4.D28, D14.D4, C22.D28, C4⋊D28, C4⋊C4⋊D7, (C2×C4).21D28
►On 224 points
Generators in S224
(1 39)(2 40)(3 41)(4 42)(5 43)(6 44)(7 45)(8 46)(9 47)(10 48)(11 49)(12 50)(13 51)(14 52)(15 53)(16 54)(17 55)(18 56)(19 29)(20 30)(21 31)(22 32)(23 33)(24 34)(25 35)(26 36)(27 37)(28 38)(57 210)(58 211)(59 212)(60 213)(61 214)(62 215)(63 216)(64 217)(65 218)(66 219)(67 220)(68 221)(69 222)(70 223)(71 224)(72 197)(73 198)(74 199)(75 200)(76 201)(77 202)(78 203)(79 204)(80 205)(81 206)(82 207)(83 208)(84 209)(85 147)(86 148)(87 149)(88 150)(89 151)(90 152)(91 153)(92 154)(93 155)(94 156)(95 157)(96 158)(97 159)(98 160)(99 161)(100 162)(101 163)(102 164)(103 165)(104 166)(105 167)(106 168)(107 141)(108 142)(109 143)(110 144)(111 145)(112 146)(113 176)(114 177)(115 178)(116 179)(117 180)(118 181)(119 182)(120 183)(121 184)(122 185)(123 186)(124 187)(125 188)(126 189)(127 190)(128 191)(129 192)(130 193)(131 194)(132 195)(133 196)(134 169)(135 170)(136 171)(137 172)(138 173)(139 174)(140 175)
(1 150 65 184)(2 89 66 122)(3 152 67 186)(4 91 68 124)(5 154 69 188)(6 93 70 126)(7 156 71 190)(8 95 72 128)(9 158 73 192)(10 97 74 130)(11 160 75 194)(12 99 76 132)(13 162 77 196)(14 101 78 134)(15 164 79 170)(16 103 80 136)(17 166 81 172)(18 105 82 138)(19 168 83 174)(20 107 84 140)(21 142 57 176)(22 109 58 114)(23 144 59 178)(24 111 60 116)(25 146 61 180)(26 85 62 118)(27 148 63 182)(28 87 64 120)(29 106 208 139)(30 141 209 175)(31 108 210 113)(32 143 211 177)(33 110 212 115)(34 145 213 179)(35 112 214 117)(36 147 215 181)(37 86 216 119)(38 149 217 183)(39 88 218 121)(40 151 219 185)(41 90 220 123)(42 153 221 187)(43 92 222 125)(44 155 223 189)(45 94 224 127)(46 157 197 191)(47 96 198 129)(48 159 199 193)(49 98 200 131)(50 161 201 195)(51 100 202 133)(52 163 203 169)(53 102 204 135)(54 165 205 171)(55 104 206 137)(56 167 207 173)
(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 64 218 38)(2 37 219 63)(3 62 220 36)(4 35 221 61)(5 60 222 34)(6 33 223 59)(7 58 224 32)(8 31 197 57)(9 84 198 30)(10 29 199 83)(11 82 200 56)(12 55 201 81)(13 80 202 54)(14 53 203 79)(15 78 204 52)(16 51 205 77)(17 76 206 50)(18 49 207 75)(19 74 208 48)(20 47 209 73)(21 72 210 46)(22 45 211 71)(23 70 212 44)(24 43 213 69)(25 68 214 42)(26 41 215 67)(27 66 216 40)(28 39 217 65)(85 123 181 152)(86 151 182 122)(87 121 183 150)(88 149 184 120)(89 119 185 148)(90 147 186 118)(91 117 187 146)(92 145 188 116)(93 115 189 144)(94 143 190 114)(95 113 191 142)(96 141 192 140)(97 139 193 168)(98 167 194 138)(99 137 195 166)(100 165 196 136)(101 135 169 164)(102 163 170 134)(103 133 171 162)(104 161 172 132)(105 131 173 160)(106 159 174 130)(107 129 175 158)(108 157 176 128)(109 127 177 156)(110 155 178 126)(111 125 179 154)(112 153 180 124)
G:=sub<Sym(224)| (1,39)(2,40)(3,41)(4,42)(5,43)(6,44)(7,45)(8,46)(9,47)(10,48)(11,49)(12,50)(13,51)(14,52)(15,53)(16,54)(17,55)(18,56)(19,29)(20,30)(21,31)(22,32)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(57,210)(58,211)(59,212)(60,213)(61,214)(62,215)(63,216)(64,217)(65,218)(66,219)(67,220)(68,221)(69,222)(70,223)(71,224)(72,197)(73,198)(74,199)(75,200)(76,201)(77,202)(78,203)(79,204)(80,205)(81,206)(82,207)(83,208)(84,209)(85,147)(86,148)(87,149)(88,150)(89,151)(90,152)(91,153)(92,154)(93,155)(94,156)(95,157)(96,158)(97,159)(98,160)(99,161)(100,162)(101,163)(102,164)(103,165)(104,166)(105,167)(106,168)(107,141)(108,142)(109,143)(110,144)(111,145)(112,146)(113,176)(114,177)(115,178)(116,179)(117,180)(118,181)(119,182)(120,183)(121,184)(122,185)(123,186)(124,187)(125,188)(126,189)(127,190)(128,191)(129,192)(130,193)(131,194)(132,195)(133,196)(134,169)(135,170)(136,171)(137,172)(138,173)(139,174)(140,175), (1,150,65,184)(2,89,66,122)(3,152,67,186)(4,91,68,124)(5,154,69,188)(6,93,70,126)(7,156,71,190)(8,95,72,128)(9,158,73,192)(10,97,74,130)(11,160,75,194)(12,99,76,132)(13,162,77,196)(14,101,78,134)(15,164,79,170)(16,103,80,136)(17,166,81,172)(18,105,82,138)(19,168,83,174)(20,107,84,140)(21,142,57,176)(22,109,58,114)(23,144,59,178)(24,111,60,116)(25,146,61,180)(26,85,62,118)(27,148,63,182)(28,87,64,120)(29,106,208,139)(30,141,209,175)(31,108,210,113)(32,143,211,177)(33,110,212,115)(34,145,213,179)(35,112,214,117)(36,147,215,181)(37,86,216,119)(38,149,217,183)(39,88,218,121)(40,151,219,185)(41,90,220,123)(42,153,221,187)(43,92,222,125)(44,155,223,189)(45,94,224,127)(46,157,197,191)(47,96,198,129)(48,159,199,193)(49,98,200,131)(50,161,201,195)(51,100,202,133)(52,163,203,169)(53,102,204,135)(54,165,205,171)(55,104,206,137)(56,167,207,173), (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), (1,64,218,38)(2,37,219,63)(3,62,220,36)(4,35,221,61)(5,60,222,34)(6,33,223,59)(7,58,224,32)(8,31,197,57)(9,84,198,30)(10,29,199,83)(11,82,200,56)(12,55,201,81)(13,80,202,54)(14,53,203,79)(15,78,204,52)(16,51,205,77)(17,76,206,50)(18,49,207,75)(19,74,208,48)(20,47,209,73)(21,72,210,46)(22,45,211,71)(23,70,212,44)(24,43,213,69)(25,68,214,42)(26,41,215,67)(27,66,216,40)(28,39,217,65)(85,123,181,152)(86,151,182,122)(87,121,183,150)(88,149,184,120)(89,119,185,148)(90,147,186,118)(91,117,187,146)(92,145,188,116)(93,115,189,144)(94,143,190,114)(95,113,191,142)(96,141,192,140)(97,139,193,168)(98,167,194,138)(99,137,195,166)(100,165,196,136)(101,135,169,164)(102,163,170,134)(103,133,171,162)(104,161,172,132)(105,131,173,160)(106,159,174,130)(107,129,175,158)(108,157,176,128)(109,127,177,156)(110,155,178,126)(111,125,179,154)(112,153,180,124)>;
G:=Group( (1,39)(2,40)(3,41)(4,42)(5,43)(6,44)(7,45)(8,46)(9,47)(10,48)(11,49)(12,50)(13,51)(14,52)(15,53)(16,54)(17,55)(18,56)(19,29)(20,30)(21,31)(22,32)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(57,210)(58,211)(59,212)(60,213)(61,214)(62,215)(63,216)(64,217)(65,218)(66,219)(67,220)(68,221)(69,222)(70,223)(71,224)(72,197)(73,198)(74,199)(75,200)(76,201)(77,202)(78,203)(79,204)(80,205)(81,206)(82,207)(83,208)(84,209)(85,147)(86,148)(87,149)(88,150)(89,151)(90,152)(91,153)(92,154)(93,155)(94,156)(95,157)(96,158)(97,159)(98,160)(99,161)(100,162)(101,163)(102,164)(103,165)(104,166)(105,167)(106,168)(107,141)(108,142)(109,143)(110,144)(111,145)(112,146)(113,176)(114,177)(115,178)(116,179)(117,180)(118,181)(119,182)(120,183)(121,184)(122,185)(123,186)(124,187)(125,188)(126,189)(127,190)(128,191)(129,192)(130,193)(131,194)(132,195)(133,196)(134,169)(135,170)(136,171)(137,172)(138,173)(139,174)(140,175), (1,150,65,184)(2,89,66,122)(3,152,67,186)(4,91,68,124)(5,154,69,188)(6,93,70,126)(7,156,71,190)(8,95,72,128)(9,158,73,192)(10,97,74,130)(11,160,75,194)(12,99,76,132)(13,162,77,196)(14,101,78,134)(15,164,79,170)(16,103,80,136)(17,166,81,172)(18,105,82,138)(19,168,83,174)(20,107,84,140)(21,142,57,176)(22,109,58,114)(23,144,59,178)(24,111,60,116)(25,146,61,180)(26,85,62,118)(27,148,63,182)(28,87,64,120)(29,106,208,139)(30,141,209,175)(31,108,210,113)(32,143,211,177)(33,110,212,115)(34,145,213,179)(35,112,214,117)(36,147,215,181)(37,86,216,119)(38,149,217,183)(39,88,218,121)(40,151,219,185)(41,90,220,123)(42,153,221,187)(43,92,222,125)(44,155,223,189)(45,94,224,127)(46,157,197,191)(47,96,198,129)(48,159,199,193)(49,98,200,131)(50,161,201,195)(51,100,202,133)(52,163,203,169)(53,102,204,135)(54,165,205,171)(55,104,206,137)(56,167,207,173), (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), (1,64,218,38)(2,37,219,63)(3,62,220,36)(4,35,221,61)(5,60,222,34)(6,33,223,59)(7,58,224,32)(8,31,197,57)(9,84,198,30)(10,29,199,83)(11,82,200,56)(12,55,201,81)(13,80,202,54)(14,53,203,79)(15,78,204,52)(16,51,205,77)(17,76,206,50)(18,49,207,75)(19,74,208,48)(20,47,209,73)(21,72,210,46)(22,45,211,71)(23,70,212,44)(24,43,213,69)(25,68,214,42)(26,41,215,67)(27,66,216,40)(28,39,217,65)(85,123,181,152)(86,151,182,122)(87,121,183,150)(88,149,184,120)(89,119,185,148)(90,147,186,118)(91,117,187,146)(92,145,188,116)(93,115,189,144)(94,143,190,114)(95,113,191,142)(96,141,192,140)(97,139,193,168)(98,167,194,138)(99,137,195,166)(100,165,196,136)(101,135,169,164)(102,163,170,134)(103,133,171,162)(104,161,172,132)(105,131,173,160)(106,159,174,130)(107,129,175,158)(108,157,176,128)(109,127,177,156)(110,155,178,126)(111,125,179,154)(112,153,180,124) );
G=PermutationGroup([[(1,39),(2,40),(3,41),(4,42),(5,43),(6,44),(7,45),(8,46),(9,47),(10,48),(11,49),(12,50),(13,51),(14,52),(15,53),(16,54),(17,55),(18,56),(19,29),(20,30),(21,31),(22,32),(23,33),(24,34),(25,35),(26,36),(27,37),(28,38),(57,210),(58,211),(59,212),(60,213),(61,214),(62,215),(63,216),(64,217),(65,218),(66,219),(67,220),(68,221),(69,222),(70,223),(71,224),(72,197),(73,198),(74,199),(75,200),(76,201),(77,202),(78,203),(79,204),(80,205),(81,206),(82,207),(83,208),(84,209),(85,147),(86,148),(87,149),(88,150),(89,151),(90,152),(91,153),(92,154),(93,155),(94,156),(95,157),(96,158),(97,159),(98,160),(99,161),(100,162),(101,163),(102,164),(103,165),(104,166),(105,167),(106,168),(107,141),(108,142),(109,143),(110,144),(111,145),(112,146),(113,176),(114,177),(115,178),(116,179),(117,180),(118,181),(119,182),(120,183),(121,184),(122,185),(123,186),(124,187),(125,188),(126,189),(127,190),(128,191),(129,192),(130,193),(131,194),(132,195),(133,196),(134,169),(135,170),(136,171),(137,172),(138,173),(139,174),(140,175)], [(1,150,65,184),(2,89,66,122),(3,152,67,186),(4,91,68,124),(5,154,69,188),(6,93,70,126),(7,156,71,190),(8,95,72,128),(9,158,73,192),(10,97,74,130),(11,160,75,194),(12,99,76,132),(13,162,77,196),(14,101,78,134),(15,164,79,170),(16,103,80,136),(17,166,81,172),(18,105,82,138),(19,168,83,174),(20,107,84,140),(21,142,57,176),(22,109,58,114),(23,144,59,178),(24,111,60,116),(25,146,61,180),(26,85,62,118),(27,148,63,182),(28,87,64,120),(29,106,208,139),(30,141,209,175),(31,108,210,113),(32,143,211,177),(33,110,212,115),(34,145,213,179),(35,112,214,117),(36,147,215,181),(37,86,216,119),(38,149,217,183),(39,88,218,121),(40,151,219,185),(41,90,220,123),(42,153,221,187),(43,92,222,125),(44,155,223,189),(45,94,224,127),(46,157,197,191),(47,96,198,129),(48,159,199,193),(49,98,200,131),(50,161,201,195),(51,100,202,133),(52,163,203,169),(53,102,204,135),(54,165,205,171),(55,104,206,137),(56,167,207,173)], [(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)], [(1,64,218,38),(2,37,219,63),(3,62,220,36),(4,35,221,61),(5,60,222,34),(6,33,223,59),(7,58,224,32),(8,31,197,57),(9,84,198,30),(10,29,199,83),(11,82,200,56),(12,55,201,81),(13,80,202,54),(14,53,203,79),(15,78,204,52),(16,51,205,77),(17,76,206,50),(18,49,207,75),(19,74,208,48),(20,47,209,73),(21,72,210,46),(22,45,211,71),(23,70,212,44),(24,43,213,69),(25,68,214,42),(26,41,215,67),(27,66,216,40),(28,39,217,65),(85,123,181,152),(86,151,182,122),(87,121,183,150),(88,149,184,120),(89,119,185,148),(90,147,186,118),(91,117,187,146),(92,145,188,116),(93,115,189,144),(94,143,190,114),(95,113,191,142),(96,141,192,140),(97,139,193,168),(98,167,194,138),(99,137,195,166),(100,165,196,136),(101,135,169,164),(102,163,170,134),(103,133,171,162),(104,161,172,132),(105,131,173,160),(106,159,174,130),(107,129,175,158),(108,157,176,128),(109,127,177,156),(110,155,178,126),(111,125,179,154),(112,153,180,124)]])
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 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | - | + | ||
| image | C1 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | C4○D4 | D14 | D28 | C4○D28 | D4×D7 | D4⋊2D7 | Q8⋊2D7 |
| kernel | (C2×C4).21D28 | C14.C42 | C7×C2.C42 | C2×C4⋊Dic7 | C2×D14⋊C4 | C2×C28 | C22×D7 | C2.C42 | C2×C14 | C22×C4 | C2×C4 | C22 | C22 | C22 | C22 |
| # reps | 1 | 2 | 1 | 1 | 3 | 2 | 2 | 3 | 10 | 9 | 12 | 24 | 3 | 6 | 3 |
Matrix representation of (C2×C4).21D28 ►in GL6(𝔽29)
| 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 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 16 | 24 | 0 | 0 | 0 | 0 |
| 5 | 13 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 11 | 0 | 0 |
| 0 | 0 | 7 | 26 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 16 | 12 |
| 22 | 3 | 0 | 0 | 0 | 0 |
| 26 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 22 | 0 | 0 |
| 0 | 0 | 14 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 21 | 17 |
| 0 | 0 | 0 | 0 | 3 | 8 |
| 22 | 3 | 0 | 0 | 0 | 0 |
| 22 | 7 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 9 | 0 | 0 |
| 0 | 0 | 10 | 24 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 12 |
| 0 | 0 | 0 | 0 | 2 | 21 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[16,5,0,0,0,0,24,13,0,0,0,0,0,0,3,7,0,0,0,0,11,26,0,0,0,0,0,0,17,16,0,0,0,0,0,12],[22,26,0,0,0,0,3,18,0,0,0,0,0,0,19,14,0,0,0,0,22,7,0,0,0,0,0,0,21,3,0,0,0,0,17,8],[22,22,0,0,0,0,3,7,0,0,0,0,0,0,5,10,0,0,0,0,9,24,0,0,0,0,0,0,8,2,0,0,0,0,12,21] >;
(C2×C4).21D28 in GAP, Magma, Sage, TeX
(C_2\times C_4)._{21}D_{28} % in TeX
G:=Group("(C2xC4).21D28"); // GroupNames label
G:=SmallGroup(448,208);
// by ID
G=gap.SmallGroup(448,208);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,64,254,387,100,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^4=c^28=1,d^2=a*b^2,c*b*c^-1=a*b=b*a,a*c=c*a,a*d=d*a,d*b*d^-1=b^-1,d*c*d^-1=a*b^2*c^-1>;
// generators/relations