metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×C4).47D28, C4.64(C2×D28), C4⋊C4.237D14, (C2×C28).473D4, C28.144(C2×D4), C4.24(D14⋊C4), (C2×Dic14)⋊11C4, C14.Q16⋊28C2, C28.66(C22×C4), (C22×C14).77D4, C42⋊C2.9D7, C28.48(C22⋊C4), (C2×C28).331C23, Dic14.27(C2×C4), (C22×C4).112D14, C23.55(C7⋊D4), C7⋊2(C23.38D4), C22.24(D14⋊C4), C2.2(D4.9D14), C14.106(C8.C22), (C22×C28).153C22, (C22×Dic14).12C2, (C2×Dic14).263C22, C4.53(C2×C4×D7), (C2×C4).45(C4×D7), (C2×C28).93(C2×C4), C2.19(C2×D14⋊C4), (C2×C7⋊C8).88C22, (C2×C14).460(C2×D4), C14.46(C2×C22⋊C4), C22.74(C2×C7⋊D4), (C2×C4).242(C7⋊D4), (C7×C4⋊C4).268C22, (C2×C4).431(C22×D7), (C2×C4.Dic7).19C2, (C2×C14).16(C22⋊C4), (C7×C42⋊C2).10C2, SmallGroup(448,538)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×C4).47D28
G = < a,b,c,d | a28=b2=c4=1, d2=a21, ab=ba, cac-1=a15, dad-1=a13, cbc-1=dbd-1=a14b, dcd-1=a7c-1 >
Subgroups: 628 in 150 conjugacy classes, 63 normal (23 characteristic)
C1, C2, C2, C2, C4, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, Q8, C23, C14, C14, C14, C42, C22⋊C4, C4⋊C4, C2×C8, M4(2), C22×C4, C22×C4, C2×Q8, Dic7, C28, C28, C28, C2×C14, C2×C14, C2×C14, Q8⋊C4, C42⋊C2, C2×M4(2), C22×Q8, C7⋊C8, Dic14, Dic14, C2×Dic7, C2×C28, C2×C28, C2×C28, C22×C14, C23.38D4, C2×C7⋊C8, C4.Dic7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C22×Dic7, C22×C28, C14.Q16, C2×C4.Dic7, C7×C42⋊C2, C22×Dic14, (C2×C4).47D28
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22⋊C4, C22×C4, C2×D4, D14, C2×C22⋊C4, C8.C22, C4×D7, D28, C7⋊D4, C22×D7, C23.38D4, D14⋊C4, C2×C4×D7, C2×D28, C2×C7⋊D4, C2×D14⋊C4, D4.9D14, (C2×C4).47D28
►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)
(1 212)(2 213)(3 214)(4 215)(5 216)(6 217)(7 218)(8 219)(9 220)(10 221)(11 222)(12 223)(13 224)(14 197)(15 198)(16 199)(17 200)(18 201)(19 202)(20 203)(21 204)(22 205)(23 206)(24 207)(25 208)(26 209)(27 210)(28 211)(29 196)(30 169)(31 170)(32 171)(33 172)(34 173)(35 174)(36 175)(37 176)(38 177)(39 178)(40 179)(41 180)(42 181)(43 182)(44 183)(45 184)(46 185)(47 186)(48 187)(49 188)(50 189)(51 190)(52 191)(53 192)(54 193)(55 194)(56 195)(57 129)(58 130)(59 131)(60 132)(61 133)(62 134)(63 135)(64 136)(65 137)(66 138)(67 139)(68 140)(69 113)(70 114)(71 115)(72 116)(73 117)(74 118)(75 119)(76 120)(77 121)(78 122)(79 123)(80 124)(81 125)(82 126)(83 127)(84 128)(85 162)(86 163)(87 164)(88 165)(89 166)(90 167)(91 168)(92 141)(93 142)(94 143)(95 144)(96 145)(97 146)(98 147)(99 148)(100 149)(101 150)(102 151)(103 152)(104 153)(105 154)(106 155)(107 156)(108 157)(109 158)(110 159)(111 160)(112 161)
(1 116 212 58)(2 131 213 73)(3 118 214 60)(4 133 215 75)(5 120 216 62)(6 135 217 77)(7 122 218 64)(8 137 219 79)(9 124 220 66)(10 139 221 81)(11 126 222 68)(12 113 223 83)(13 128 224 70)(14 115 197 57)(15 130 198 72)(16 117 199 59)(17 132 200 74)(18 119 201 61)(19 134 202 76)(20 121 203 63)(21 136 204 78)(22 123 205 65)(23 138 206 80)(24 125 207 67)(25 140 208 82)(26 127 209 69)(27 114 210 84)(28 129 211 71)(29 86 196 149)(30 101 169 164)(31 88 170 151)(32 103 171 166)(33 90 172 153)(34 105 173 168)(35 92 174 155)(36 107 175 142)(37 94 176 157)(38 109 177 144)(39 96 178 159)(40 111 179 146)(41 98 180 161)(42 85 181 148)(43 100 182 163)(44 87 183 150)(45 102 184 165)(46 89 185 152)(47 104 186 167)(48 91 187 154)(49 106 188 141)(50 93 189 156)(51 108 190 143)(52 95 191 158)(53 110 192 145)(54 97 193 160)(55 112 194 147)(56 99 195 162)
(1 107 22 100 15 93 8 86)(2 92 23 85 16 106 9 99)(3 105 24 98 17 91 10 112)(4 90 25 111 18 104 11 97)(5 103 26 96 19 89 12 110)(6 88 27 109 20 102 13 95)(7 101 28 94 21 87 14 108)(29 123 50 116 43 137 36 130)(30 136 51 129 44 122 37 115)(31 121 52 114 45 135 38 128)(32 134 53 127 46 120 39 113)(33 119 54 140 47 133 40 126)(34 132 55 125 48 118 41 139)(35 117 56 138 49 131 42 124)(57 169 78 190 71 183 64 176)(58 182 79 175 72 196 65 189)(59 195 80 188 73 181 66 174)(60 180 81 173 74 194 67 187)(61 193 82 186 75 179 68 172)(62 178 83 171 76 192 69 185)(63 191 84 184 77 177 70 170)(141 220 162 213 155 206 148 199)(142 205 163 198 156 219 149 212)(143 218 164 211 157 204 150 197)(144 203 165 224 158 217 151 210)(145 216 166 209 159 202 152 223)(146 201 167 222 160 215 153 208)(147 214 168 207 161 200 154 221)
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), (1,212)(2,213)(3,214)(4,215)(5,216)(6,217)(7,218)(8,219)(9,220)(10,221)(11,222)(12,223)(13,224)(14,197)(15,198)(16,199)(17,200)(18,201)(19,202)(20,203)(21,204)(22,205)(23,206)(24,207)(25,208)(26,209)(27,210)(28,211)(29,196)(30,169)(31,170)(32,171)(33,172)(34,173)(35,174)(36,175)(37,176)(38,177)(39,178)(40,179)(41,180)(42,181)(43,182)(44,183)(45,184)(46,185)(47,186)(48,187)(49,188)(50,189)(51,190)(52,191)(53,192)(54,193)(55,194)(56,195)(57,129)(58,130)(59,131)(60,132)(61,133)(62,134)(63,135)(64,136)(65,137)(66,138)(67,139)(68,140)(69,113)(70,114)(71,115)(72,116)(73,117)(74,118)(75,119)(76,120)(77,121)(78,122)(79,123)(80,124)(81,125)(82,126)(83,127)(84,128)(85,162)(86,163)(87,164)(88,165)(89,166)(90,167)(91,168)(92,141)(93,142)(94,143)(95,144)(96,145)(97,146)(98,147)(99,148)(100,149)(101,150)(102,151)(103,152)(104,153)(105,154)(106,155)(107,156)(108,157)(109,158)(110,159)(111,160)(112,161), (1,116,212,58)(2,131,213,73)(3,118,214,60)(4,133,215,75)(5,120,216,62)(6,135,217,77)(7,122,218,64)(8,137,219,79)(9,124,220,66)(10,139,221,81)(11,126,222,68)(12,113,223,83)(13,128,224,70)(14,115,197,57)(15,130,198,72)(16,117,199,59)(17,132,200,74)(18,119,201,61)(19,134,202,76)(20,121,203,63)(21,136,204,78)(22,123,205,65)(23,138,206,80)(24,125,207,67)(25,140,208,82)(26,127,209,69)(27,114,210,84)(28,129,211,71)(29,86,196,149)(30,101,169,164)(31,88,170,151)(32,103,171,166)(33,90,172,153)(34,105,173,168)(35,92,174,155)(36,107,175,142)(37,94,176,157)(38,109,177,144)(39,96,178,159)(40,111,179,146)(41,98,180,161)(42,85,181,148)(43,100,182,163)(44,87,183,150)(45,102,184,165)(46,89,185,152)(47,104,186,167)(48,91,187,154)(49,106,188,141)(50,93,189,156)(51,108,190,143)(52,95,191,158)(53,110,192,145)(54,97,193,160)(55,112,194,147)(56,99,195,162), (1,107,22,100,15,93,8,86)(2,92,23,85,16,106,9,99)(3,105,24,98,17,91,10,112)(4,90,25,111,18,104,11,97)(5,103,26,96,19,89,12,110)(6,88,27,109,20,102,13,95)(7,101,28,94,21,87,14,108)(29,123,50,116,43,137,36,130)(30,136,51,129,44,122,37,115)(31,121,52,114,45,135,38,128)(32,134,53,127,46,120,39,113)(33,119,54,140,47,133,40,126)(34,132,55,125,48,118,41,139)(35,117,56,138,49,131,42,124)(57,169,78,190,71,183,64,176)(58,182,79,175,72,196,65,189)(59,195,80,188,73,181,66,174)(60,180,81,173,74,194,67,187)(61,193,82,186,75,179,68,172)(62,178,83,171,76,192,69,185)(63,191,84,184,77,177,70,170)(141,220,162,213,155,206,148,199)(142,205,163,198,156,219,149,212)(143,218,164,211,157,204,150,197)(144,203,165,224,158,217,151,210)(145,216,166,209,159,202,152,223)(146,201,167,222,160,215,153,208)(147,214,168,207,161,200,154,221)>;
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), (1,212)(2,213)(3,214)(4,215)(5,216)(6,217)(7,218)(8,219)(9,220)(10,221)(11,222)(12,223)(13,224)(14,197)(15,198)(16,199)(17,200)(18,201)(19,202)(20,203)(21,204)(22,205)(23,206)(24,207)(25,208)(26,209)(27,210)(28,211)(29,196)(30,169)(31,170)(32,171)(33,172)(34,173)(35,174)(36,175)(37,176)(38,177)(39,178)(40,179)(41,180)(42,181)(43,182)(44,183)(45,184)(46,185)(47,186)(48,187)(49,188)(50,189)(51,190)(52,191)(53,192)(54,193)(55,194)(56,195)(57,129)(58,130)(59,131)(60,132)(61,133)(62,134)(63,135)(64,136)(65,137)(66,138)(67,139)(68,140)(69,113)(70,114)(71,115)(72,116)(73,117)(74,118)(75,119)(76,120)(77,121)(78,122)(79,123)(80,124)(81,125)(82,126)(83,127)(84,128)(85,162)(86,163)(87,164)(88,165)(89,166)(90,167)(91,168)(92,141)(93,142)(94,143)(95,144)(96,145)(97,146)(98,147)(99,148)(100,149)(101,150)(102,151)(103,152)(104,153)(105,154)(106,155)(107,156)(108,157)(109,158)(110,159)(111,160)(112,161), (1,116,212,58)(2,131,213,73)(3,118,214,60)(4,133,215,75)(5,120,216,62)(6,135,217,77)(7,122,218,64)(8,137,219,79)(9,124,220,66)(10,139,221,81)(11,126,222,68)(12,113,223,83)(13,128,224,70)(14,115,197,57)(15,130,198,72)(16,117,199,59)(17,132,200,74)(18,119,201,61)(19,134,202,76)(20,121,203,63)(21,136,204,78)(22,123,205,65)(23,138,206,80)(24,125,207,67)(25,140,208,82)(26,127,209,69)(27,114,210,84)(28,129,211,71)(29,86,196,149)(30,101,169,164)(31,88,170,151)(32,103,171,166)(33,90,172,153)(34,105,173,168)(35,92,174,155)(36,107,175,142)(37,94,176,157)(38,109,177,144)(39,96,178,159)(40,111,179,146)(41,98,180,161)(42,85,181,148)(43,100,182,163)(44,87,183,150)(45,102,184,165)(46,89,185,152)(47,104,186,167)(48,91,187,154)(49,106,188,141)(50,93,189,156)(51,108,190,143)(52,95,191,158)(53,110,192,145)(54,97,193,160)(55,112,194,147)(56,99,195,162), (1,107,22,100,15,93,8,86)(2,92,23,85,16,106,9,99)(3,105,24,98,17,91,10,112)(4,90,25,111,18,104,11,97)(5,103,26,96,19,89,12,110)(6,88,27,109,20,102,13,95)(7,101,28,94,21,87,14,108)(29,123,50,116,43,137,36,130)(30,136,51,129,44,122,37,115)(31,121,52,114,45,135,38,128)(32,134,53,127,46,120,39,113)(33,119,54,140,47,133,40,126)(34,132,55,125,48,118,41,139)(35,117,56,138,49,131,42,124)(57,169,78,190,71,183,64,176)(58,182,79,175,72,196,65,189)(59,195,80,188,73,181,66,174)(60,180,81,173,74,194,67,187)(61,193,82,186,75,179,68,172)(62,178,83,171,76,192,69,185)(63,191,84,184,77,177,70,170)(141,220,162,213,155,206,148,199)(142,205,163,198,156,219,149,212)(143,218,164,211,157,204,150,197)(144,203,165,224,158,217,151,210)(145,216,166,209,159,202,152,223)(146,201,167,222,160,215,153,208)(147,214,168,207,161,200,154,221) );
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)], [(1,212),(2,213),(3,214),(4,215),(5,216),(6,217),(7,218),(8,219),(9,220),(10,221),(11,222),(12,223),(13,224),(14,197),(15,198),(16,199),(17,200),(18,201),(19,202),(20,203),(21,204),(22,205),(23,206),(24,207),(25,208),(26,209),(27,210),(28,211),(29,196),(30,169),(31,170),(32,171),(33,172),(34,173),(35,174),(36,175),(37,176),(38,177),(39,178),(40,179),(41,180),(42,181),(43,182),(44,183),(45,184),(46,185),(47,186),(48,187),(49,188),(50,189),(51,190),(52,191),(53,192),(54,193),(55,194),(56,195),(57,129),(58,130),(59,131),(60,132),(61,133),(62,134),(63,135),(64,136),(65,137),(66,138),(67,139),(68,140),(69,113),(70,114),(71,115),(72,116),(73,117),(74,118),(75,119),(76,120),(77,121),(78,122),(79,123),(80,124),(81,125),(82,126),(83,127),(84,128),(85,162),(86,163),(87,164),(88,165),(89,166),(90,167),(91,168),(92,141),(93,142),(94,143),(95,144),(96,145),(97,146),(98,147),(99,148),(100,149),(101,150),(102,151),(103,152),(104,153),(105,154),(106,155),(107,156),(108,157),(109,158),(110,159),(111,160),(112,161)], [(1,116,212,58),(2,131,213,73),(3,118,214,60),(4,133,215,75),(5,120,216,62),(6,135,217,77),(7,122,218,64),(8,137,219,79),(9,124,220,66),(10,139,221,81),(11,126,222,68),(12,113,223,83),(13,128,224,70),(14,115,197,57),(15,130,198,72),(16,117,199,59),(17,132,200,74),(18,119,201,61),(19,134,202,76),(20,121,203,63),(21,136,204,78),(22,123,205,65),(23,138,206,80),(24,125,207,67),(25,140,208,82),(26,127,209,69),(27,114,210,84),(28,129,211,71),(29,86,196,149),(30,101,169,164),(31,88,170,151),(32,103,171,166),(33,90,172,153),(34,105,173,168),(35,92,174,155),(36,107,175,142),(37,94,176,157),(38,109,177,144),(39,96,178,159),(40,111,179,146),(41,98,180,161),(42,85,181,148),(43,100,182,163),(44,87,183,150),(45,102,184,165),(46,89,185,152),(47,104,186,167),(48,91,187,154),(49,106,188,141),(50,93,189,156),(51,108,190,143),(52,95,191,158),(53,110,192,145),(54,97,193,160),(55,112,194,147),(56,99,195,162)], [(1,107,22,100,15,93,8,86),(2,92,23,85,16,106,9,99),(3,105,24,98,17,91,10,112),(4,90,25,111,18,104,11,97),(5,103,26,96,19,89,12,110),(6,88,27,109,20,102,13,95),(7,101,28,94,21,87,14,108),(29,123,50,116,43,137,36,130),(30,136,51,129,44,122,37,115),(31,121,52,114,45,135,38,128),(32,134,53,127,46,120,39,113),(33,119,54,140,47,133,40,126),(34,132,55,125,48,118,41,139),(35,117,56,138,49,131,42,124),(57,169,78,190,71,183,64,176),(58,182,79,175,72,196,65,189),(59,195,80,188,73,181,66,174),(60,180,81,173,74,194,67,187),(61,193,82,186,75,179,68,172),(62,178,83,171,76,192,69,185),(63,191,84,184,77,177,70,170),(141,220,162,213,155,206,148,199),(142,205,163,198,156,219,149,212),(143,218,164,211,157,204,150,197),(144,203,165,224,158,217,151,210),(145,216,166,209,159,202,152,223),(146,201,167,222,160,215,153,208),(147,214,168,207,161,200,154,221)]])
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 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 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | - | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | D7 | D14 | D14 | C4×D7 | D28 | C7⋊D4 | C7⋊D4 | C8.C22 | D4.9D14 |
| kernel | (C2×C4).47D28 | C14.Q16 | C2×C4.Dic7 | C7×C42⋊C2 | C22×Dic14 | C2×Dic14 | C2×C28 | C22×C14 | C42⋊C2 | C4⋊C4 | C22×C4 | C2×C4 | C2×C4 | C2×C4 | C23 | C14 | C2 |
| # reps | 1 | 4 | 1 | 1 | 1 | 8 | 3 | 1 | 3 | 6 | 3 | 12 | 12 | 6 | 6 | 2 | 12 |
Matrix representation of (C2×C4).47D28 ►in GL6(𝔽113)
| 1 | 104 | 0 | 0 | 0 | 0 |
| 9 | 33 | 0 | 0 | 0 | 0 |
| 0 | 0 | 58 | 81 | 0 | 0 |
| 0 | 0 | 32 | 109 | 0 | 0 |
| 0 | 0 | 105 | 71 | 23 | 32 |
| 0 | 0 | 34 | 24 | 100 | 36 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 93 | 93 | 1 | 0 |
| 0 | 0 | 0 | 6 | 0 | 1 |
| 98 | 0 | 0 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 | 0 | 0 |
| 0 | 0 | 55 | 38 | 51 | 32 |
| 0 | 0 | 75 | 58 | 49 | 32 |
| 0 | 0 | 0 | 0 | 96 | 75 |
| 0 | 0 | 0 | 0 | 79 | 17 |
| 0 | 98 | 0 | 0 | 0 | 0 |
| 98 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 108 | 79 | 57 | 28 |
| 0 | 0 | 34 | 5 | 87 | 28 |
| 0 | 0 | 101 | 86 | 84 | 108 |
| 0 | 0 | 79 | 98 | 78 | 29 |
G:=sub<GL(6,GF(113))| [1,9,0,0,0,0,104,33,0,0,0,0,0,0,58,32,105,34,0,0,81,109,71,24,0,0,0,0,23,100,0,0,0,0,32,36],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,112,0,93,0,0,0,0,112,93,6,0,0,0,0,1,0,0,0,0,0,0,1],[98,0,0,0,0,0,0,98,0,0,0,0,0,0,55,75,0,0,0,0,38,58,0,0,0,0,51,49,96,79,0,0,32,32,75,17],[0,98,0,0,0,0,98,0,0,0,0,0,0,0,108,34,101,79,0,0,79,5,86,98,0,0,57,87,84,78,0,0,28,28,108,29] >;
(C2×C4).47D28 in GAP, Magma, Sage, TeX
(C_2\times C_4)._{47}D_{28} % in TeX
G:=Group("(C2xC4).47D28"); // GroupNames label
G:=SmallGroup(448,538);
// by ID
G=gap.SmallGroup(448,538);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,422,387,58,1684,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=b^2=c^4=1,d^2=a^21,a*b=b*a,c*a*c^-1=a^15,d*a*d^-1=a^13,c*b*c^-1=d*b*d^-1=a^14*b,d*c*d^-1=a^7*c^-1>;
// generators/relations