direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C28⋊1D4, C4⋊3(C2×D28), C28⋊4(C2×D4), (C2×C28)⋊8D4, C4⋊C4⋊38D14, D14⋊2(C2×D4), (C2×C4)⋊10D28, C14⋊2(C4⋊D4), (C22×D7)⋊10D4, (C22×D28)⋊7C2, C14.9(C22×D4), D14⋊C4⋊50C22, (C2×D28)⋊45C22, (C2×C14).50C24, C22.133(D4×D7), C2.11(C22×D28), C22.67(C2×D28), (C2×C28).487C23, (C22×C4).360D14, C22.84(C23×D7), C23.328(C22×D7), (C22×C14).399C23, (C22×C28).217C22, C22.36(Q8⋊2D7), (C2×Dic7).188C23, (C22×D7).156C23, (C23×D7).100C22, (C22×Dic7).213C22, C7⋊2(C2×C4⋊D4), C2.15(C2×D4×D7), (C2×C4⋊C4)⋊15D7, (C14×C4⋊C4)⋊12C2, (D7×C22×C4)⋊1C2, (C2×C4×D7)⋊55C22, (C2×D14⋊C4)⋊20C2, (C7×C4⋊C4)⋊46C22, C2.7(C2×Q8⋊2D7), C14.109(C2×C4○D4), (C2×C14).174(C2×D4), (C2×C4).141(C22×D7), (C2×C14).197(C4○D4), SmallGroup(448,959)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C28⋊1D4
G = < a,b,c,d | a2=b28=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=b15, dbd=b-1, dcd=c-1 >
Subgroups: 2500 in 426 conjugacy classes, 135 normal (21 characteristic)
C1, C2 [×3], C2 [×4], C2 [×8], C4 [×4], C4 [×6], C22, C22 [×6], C22 [×36], C7, C2×C4 [×10], C2×C4 [×16], D4 [×24], C23, C23 [×26], D7 [×8], C14 [×3], C14 [×4], C22⋊C4 [×8], C4⋊C4 [×4], C22×C4, C22×C4 [×2], C22×C4 [×9], C2×D4 [×24], C24 [×3], Dic7 [×2], C28 [×4], C28 [×4], D14 [×4], D14 [×32], C2×C14, C2×C14 [×6], C2×C22⋊C4 [×2], C2×C4⋊C4, C4⋊D4 [×8], C23×C4, C22×D4 [×3], C4×D7 [×8], D28 [×24], C2×Dic7 [×2], C2×Dic7 [×2], C2×C28 [×10], C2×C28 [×4], C22×D7 [×10], C22×D7 [×16], C22×C14, C2×C4⋊D4, D14⋊C4 [×8], C7×C4⋊C4 [×4], C2×C4×D7 [×4], C2×C4×D7 [×4], C2×D28 [×12], C2×D28 [×12], C22×Dic7, C22×C28, C22×C28 [×2], C23×D7, C23×D7 [×2], C28⋊1D4 [×8], C2×D14⋊C4 [×2], C14×C4⋊C4, D7×C22×C4, C22×D28, C22×D28 [×2], C2×C28⋊1D4
Quotients: C1, C2 [×15], C22 [×35], D4 [×8], C23 [×15], D7, C2×D4 [×12], C4○D4 [×2], C24, D14 [×7], C4⋊D4 [×4], C22×D4 [×2], C2×C4○D4, D28 [×4], C22×D7 [×7], C2×C4⋊D4, C2×D28 [×6], D4×D7 [×2], Q8⋊2D7 [×2], C23×D7, C28⋊1D4 [×4], C22×D28, C2×D4×D7, C2×Q8⋊2D7, C2×C28⋊1D4
►On 224 points
Generators in S224
(1 204)(2 205)(3 206)(4 207)(5 208)(6 209)(7 210)(8 211)(9 212)(10 213)(11 214)(12 215)(13 216)(14 217)(15 218)(16 219)(17 220)(18 221)(19 222)(20 223)(21 224)(22 197)(23 198)(24 199)(25 200)(26 201)(27 202)(28 203)(29 149)(30 150)(31 151)(32 152)(33 153)(34 154)(35 155)(36 156)(37 157)(38 158)(39 159)(40 160)(41 161)(42 162)(43 163)(44 164)(45 165)(46 166)(47 167)(48 168)(49 141)(50 142)(51 143)(52 144)(53 145)(54 146)(55 147)(56 148)(57 138)(58 139)(59 140)(60 113)(61 114)(62 115)(63 116)(64 117)(65 118)(66 119)(67 120)(68 121)(69 122)(70 123)(71 124)(72 125)(73 126)(74 127)(75 128)(76 129)(77 130)(78 131)(79 132)(80 133)(81 134)(82 135)(83 136)(84 137)(85 186)(86 187)(87 188)(88 189)(89 190)(90 191)(91 192)(92 193)(93 194)(94 195)(95 196)(96 169)(97 170)(98 171)(99 172)(100 173)(101 174)(102 175)(103 176)(104 177)(105 178)(106 179)(107 180)(108 181)(109 182)(110 183)(111 184)(112 185)
(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)
(1 153 114 187)(2 168 115 174)(3 155 116 189)(4 142 117 176)(5 157 118 191)(6 144 119 178)(7 159 120 193)(8 146 121 180)(9 161 122 195)(10 148 123 182)(11 163 124 169)(12 150 125 184)(13 165 126 171)(14 152 127 186)(15 167 128 173)(16 154 129 188)(17 141 130 175)(18 156 131 190)(19 143 132 177)(20 158 133 192)(21 145 134 179)(22 160 135 194)(23 147 136 181)(24 162 137 196)(25 149 138 183)(26 164 139 170)(27 151 140 185)(28 166 113 172)(29 57 110 200)(30 72 111 215)(31 59 112 202)(32 74 85 217)(33 61 86 204)(34 76 87 219)(35 63 88 206)(36 78 89 221)(37 65 90 208)(38 80 91 223)(39 67 92 210)(40 82 93 197)(41 69 94 212)(42 84 95 199)(43 71 96 214)(44 58 97 201)(45 73 98 216)(46 60 99 203)(47 75 100 218)(48 62 101 205)(49 77 102 220)(50 64 103 207)(51 79 104 222)(52 66 105 209)(53 81 106 224)(54 68 107 211)(55 83 108 198)(56 70 109 213)
(1 187)(2 186)(3 185)(4 184)(5 183)(6 182)(7 181)(8 180)(9 179)(10 178)(11 177)(12 176)(13 175)(14 174)(15 173)(16 172)(17 171)(18 170)(19 169)(20 196)(21 195)(22 194)(23 193)(24 192)(25 191)(26 190)(27 189)(28 188)(29 65)(30 64)(31 63)(32 62)(33 61)(34 60)(35 59)(36 58)(37 57)(38 84)(39 83)(40 82)(41 81)(42 80)(43 79)(44 78)(45 77)(46 76)(47 75)(48 74)(49 73)(50 72)(51 71)(52 70)(53 69)(54 68)(55 67)(56 66)(85 205)(86 204)(87 203)(88 202)(89 201)(90 200)(91 199)(92 198)(93 197)(94 224)(95 223)(96 222)(97 221)(98 220)(99 219)(100 218)(101 217)(102 216)(103 215)(104 214)(105 213)(106 212)(107 211)(108 210)(109 209)(110 208)(111 207)(112 206)(113 154)(114 153)(115 152)(116 151)(117 150)(118 149)(119 148)(120 147)(121 146)(122 145)(123 144)(124 143)(125 142)(126 141)(127 168)(128 167)(129 166)(130 165)(131 164)(132 163)(133 162)(134 161)(135 160)(136 159)(137 158)(138 157)(139 156)(140 155)
G:=sub<Sym(224)| (1,204)(2,205)(3,206)(4,207)(5,208)(6,209)(7,210)(8,211)(9,212)(10,213)(11,214)(12,215)(13,216)(14,217)(15,218)(16,219)(17,220)(18,221)(19,222)(20,223)(21,224)(22,197)(23,198)(24,199)(25,200)(26,201)(27,202)(28,203)(29,149)(30,150)(31,151)(32,152)(33,153)(34,154)(35,155)(36,156)(37,157)(38,158)(39,159)(40,160)(41,161)(42,162)(43,163)(44,164)(45,165)(46,166)(47,167)(48,168)(49,141)(50,142)(51,143)(52,144)(53,145)(54,146)(55,147)(56,148)(57,138)(58,139)(59,140)(60,113)(61,114)(62,115)(63,116)(64,117)(65,118)(66,119)(67,120)(68,121)(69,122)(70,123)(71,124)(72,125)(73,126)(74,127)(75,128)(76,129)(77,130)(78,131)(79,132)(80,133)(81,134)(82,135)(83,136)(84,137)(85,186)(86,187)(87,188)(88,189)(89,190)(90,191)(91,192)(92,193)(93,194)(94,195)(95,196)(96,169)(97,170)(98,171)(99,172)(100,173)(101,174)(102,175)(103,176)(104,177)(105,178)(106,179)(107,180)(108,181)(109,182)(110,183)(111,184)(112,185), (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), (1,153,114,187)(2,168,115,174)(3,155,116,189)(4,142,117,176)(5,157,118,191)(6,144,119,178)(7,159,120,193)(8,146,121,180)(9,161,122,195)(10,148,123,182)(11,163,124,169)(12,150,125,184)(13,165,126,171)(14,152,127,186)(15,167,128,173)(16,154,129,188)(17,141,130,175)(18,156,131,190)(19,143,132,177)(20,158,133,192)(21,145,134,179)(22,160,135,194)(23,147,136,181)(24,162,137,196)(25,149,138,183)(26,164,139,170)(27,151,140,185)(28,166,113,172)(29,57,110,200)(30,72,111,215)(31,59,112,202)(32,74,85,217)(33,61,86,204)(34,76,87,219)(35,63,88,206)(36,78,89,221)(37,65,90,208)(38,80,91,223)(39,67,92,210)(40,82,93,197)(41,69,94,212)(42,84,95,199)(43,71,96,214)(44,58,97,201)(45,73,98,216)(46,60,99,203)(47,75,100,218)(48,62,101,205)(49,77,102,220)(50,64,103,207)(51,79,104,222)(52,66,105,209)(53,81,106,224)(54,68,107,211)(55,83,108,198)(56,70,109,213), (1,187)(2,186)(3,185)(4,184)(5,183)(6,182)(7,181)(8,180)(9,179)(10,178)(11,177)(12,176)(13,175)(14,174)(15,173)(16,172)(17,171)(18,170)(19,169)(20,196)(21,195)(22,194)(23,193)(24,192)(25,191)(26,190)(27,189)(28,188)(29,65)(30,64)(31,63)(32,62)(33,61)(34,60)(35,59)(36,58)(37,57)(38,84)(39,83)(40,82)(41,81)(42,80)(43,79)(44,78)(45,77)(46,76)(47,75)(48,74)(49,73)(50,72)(51,71)(52,70)(53,69)(54,68)(55,67)(56,66)(85,205)(86,204)(87,203)(88,202)(89,201)(90,200)(91,199)(92,198)(93,197)(94,224)(95,223)(96,222)(97,221)(98,220)(99,219)(100,218)(101,217)(102,216)(103,215)(104,214)(105,213)(106,212)(107,211)(108,210)(109,209)(110,208)(111,207)(112,206)(113,154)(114,153)(115,152)(116,151)(117,150)(118,149)(119,148)(120,147)(121,146)(122,145)(123,144)(124,143)(125,142)(126,141)(127,168)(128,167)(129,166)(130,165)(131,164)(132,163)(133,162)(134,161)(135,160)(136,159)(137,158)(138,157)(139,156)(140,155)>;
G:=Group( (1,204)(2,205)(3,206)(4,207)(5,208)(6,209)(7,210)(8,211)(9,212)(10,213)(11,214)(12,215)(13,216)(14,217)(15,218)(16,219)(17,220)(18,221)(19,222)(20,223)(21,224)(22,197)(23,198)(24,199)(25,200)(26,201)(27,202)(28,203)(29,149)(30,150)(31,151)(32,152)(33,153)(34,154)(35,155)(36,156)(37,157)(38,158)(39,159)(40,160)(41,161)(42,162)(43,163)(44,164)(45,165)(46,166)(47,167)(48,168)(49,141)(50,142)(51,143)(52,144)(53,145)(54,146)(55,147)(56,148)(57,138)(58,139)(59,140)(60,113)(61,114)(62,115)(63,116)(64,117)(65,118)(66,119)(67,120)(68,121)(69,122)(70,123)(71,124)(72,125)(73,126)(74,127)(75,128)(76,129)(77,130)(78,131)(79,132)(80,133)(81,134)(82,135)(83,136)(84,137)(85,186)(86,187)(87,188)(88,189)(89,190)(90,191)(91,192)(92,193)(93,194)(94,195)(95,196)(96,169)(97,170)(98,171)(99,172)(100,173)(101,174)(102,175)(103,176)(104,177)(105,178)(106,179)(107,180)(108,181)(109,182)(110,183)(111,184)(112,185), (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), (1,153,114,187)(2,168,115,174)(3,155,116,189)(4,142,117,176)(5,157,118,191)(6,144,119,178)(7,159,120,193)(8,146,121,180)(9,161,122,195)(10,148,123,182)(11,163,124,169)(12,150,125,184)(13,165,126,171)(14,152,127,186)(15,167,128,173)(16,154,129,188)(17,141,130,175)(18,156,131,190)(19,143,132,177)(20,158,133,192)(21,145,134,179)(22,160,135,194)(23,147,136,181)(24,162,137,196)(25,149,138,183)(26,164,139,170)(27,151,140,185)(28,166,113,172)(29,57,110,200)(30,72,111,215)(31,59,112,202)(32,74,85,217)(33,61,86,204)(34,76,87,219)(35,63,88,206)(36,78,89,221)(37,65,90,208)(38,80,91,223)(39,67,92,210)(40,82,93,197)(41,69,94,212)(42,84,95,199)(43,71,96,214)(44,58,97,201)(45,73,98,216)(46,60,99,203)(47,75,100,218)(48,62,101,205)(49,77,102,220)(50,64,103,207)(51,79,104,222)(52,66,105,209)(53,81,106,224)(54,68,107,211)(55,83,108,198)(56,70,109,213), (1,187)(2,186)(3,185)(4,184)(5,183)(6,182)(7,181)(8,180)(9,179)(10,178)(11,177)(12,176)(13,175)(14,174)(15,173)(16,172)(17,171)(18,170)(19,169)(20,196)(21,195)(22,194)(23,193)(24,192)(25,191)(26,190)(27,189)(28,188)(29,65)(30,64)(31,63)(32,62)(33,61)(34,60)(35,59)(36,58)(37,57)(38,84)(39,83)(40,82)(41,81)(42,80)(43,79)(44,78)(45,77)(46,76)(47,75)(48,74)(49,73)(50,72)(51,71)(52,70)(53,69)(54,68)(55,67)(56,66)(85,205)(86,204)(87,203)(88,202)(89,201)(90,200)(91,199)(92,198)(93,197)(94,224)(95,223)(96,222)(97,221)(98,220)(99,219)(100,218)(101,217)(102,216)(103,215)(104,214)(105,213)(106,212)(107,211)(108,210)(109,209)(110,208)(111,207)(112,206)(113,154)(114,153)(115,152)(116,151)(117,150)(118,149)(119,148)(120,147)(121,146)(122,145)(123,144)(124,143)(125,142)(126,141)(127,168)(128,167)(129,166)(130,165)(131,164)(132,163)(133,162)(134,161)(135,160)(136,159)(137,158)(138,157)(139,156)(140,155) );
G=PermutationGroup([(1,204),(2,205),(3,206),(4,207),(5,208),(6,209),(7,210),(8,211),(9,212),(10,213),(11,214),(12,215),(13,216),(14,217),(15,218),(16,219),(17,220),(18,221),(19,222),(20,223),(21,224),(22,197),(23,198),(24,199),(25,200),(26,201),(27,202),(28,203),(29,149),(30,150),(31,151),(32,152),(33,153),(34,154),(35,155),(36,156),(37,157),(38,158),(39,159),(40,160),(41,161),(42,162),(43,163),(44,164),(45,165),(46,166),(47,167),(48,168),(49,141),(50,142),(51,143),(52,144),(53,145),(54,146),(55,147),(56,148),(57,138),(58,139),(59,140),(60,113),(61,114),(62,115),(63,116),(64,117),(65,118),(66,119),(67,120),(68,121),(69,122),(70,123),(71,124),(72,125),(73,126),(74,127),(75,128),(76,129),(77,130),(78,131),(79,132),(80,133),(81,134),(82,135),(83,136),(84,137),(85,186),(86,187),(87,188),(88,189),(89,190),(90,191),(91,192),(92,193),(93,194),(94,195),(95,196),(96,169),(97,170),(98,171),(99,172),(100,173),(101,174),(102,175),(103,176),(104,177),(105,178),(106,179),(107,180),(108,181),(109,182),(110,183),(111,184),(112,185)], [(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)], [(1,153,114,187),(2,168,115,174),(3,155,116,189),(4,142,117,176),(5,157,118,191),(6,144,119,178),(7,159,120,193),(8,146,121,180),(9,161,122,195),(10,148,123,182),(11,163,124,169),(12,150,125,184),(13,165,126,171),(14,152,127,186),(15,167,128,173),(16,154,129,188),(17,141,130,175),(18,156,131,190),(19,143,132,177),(20,158,133,192),(21,145,134,179),(22,160,135,194),(23,147,136,181),(24,162,137,196),(25,149,138,183),(26,164,139,170),(27,151,140,185),(28,166,113,172),(29,57,110,200),(30,72,111,215),(31,59,112,202),(32,74,85,217),(33,61,86,204),(34,76,87,219),(35,63,88,206),(36,78,89,221),(37,65,90,208),(38,80,91,223),(39,67,92,210),(40,82,93,197),(41,69,94,212),(42,84,95,199),(43,71,96,214),(44,58,97,201),(45,73,98,216),(46,60,99,203),(47,75,100,218),(48,62,101,205),(49,77,102,220),(50,64,103,207),(51,79,104,222),(52,66,105,209),(53,81,106,224),(54,68,107,211),(55,83,108,198),(56,70,109,213)], [(1,187),(2,186),(3,185),(4,184),(5,183),(6,182),(7,181),(8,180),(9,179),(10,178),(11,177),(12,176),(13,175),(14,174),(15,173),(16,172),(17,171),(18,170),(19,169),(20,196),(21,195),(22,194),(23,193),(24,192),(25,191),(26,190),(27,189),(28,188),(29,65),(30,64),(31,63),(32,62),(33,61),(34,60),(35,59),(36,58),(37,57),(38,84),(39,83),(40,82),(41,81),(42,80),(43,79),(44,78),(45,77),(46,76),(47,75),(48,74),(49,73),(50,72),(51,71),(52,70),(53,69),(54,68),(55,67),(56,66),(85,205),(86,204),(87,203),(88,202),(89,201),(90,200),(91,199),(92,198),(93,197),(94,224),(95,223),(96,222),(97,221),(98,220),(99,219),(100,218),(101,217),(102,216),(103,215),(104,214),(105,213),(106,212),(107,211),(108,210),(109,209),(110,208),(111,207),(112,206),(113,154),(114,153),(115,152),(116,151),(117,150),(118,149),(119,148),(120,147),(121,146),(122,145),(123,144),(124,143),(125,142),(126,141),(127,168),(128,167),(129,166),(130,165),(131,164),(132,163),(133,162),(134,161),(135,160),(136,159),(137,158),(138,157),(139,156),(140,155)])
88 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 2L | 2M | 2N | 2O | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 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 |
| size | 1 | 1 | ··· | 1 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | C4○D4 | D14 | D14 | D28 | D4×D7 | Q8⋊2D7 |
| kernel | C2×C28⋊1D4 | C28⋊1D4 | C2×D14⋊C4 | C14×C4⋊C4 | D7×C22×C4 | C22×D28 | C2×C28 | C22×D7 | C2×C4⋊C4 | C2×C14 | C4⋊C4 | C22×C4 | C2×C4 | C22 | C22 |
| # reps | 1 | 8 | 2 | 1 | 1 | 3 | 4 | 4 | 3 | 4 | 12 | 9 | 24 | 6 | 6 |
Matrix representation of C2×C28⋊1D4 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 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 |
| 21 | 3 | 0 | 0 | 0 | 0 |
| 26 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 18 | 0 | 0 |
| 0 | 0 | 11 | 2 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 3 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[21,26,0,0,0,0,3,1,0,0,0,0,0,0,27,11,0,0,0,0,18,2,0,0,0,0,0,0,12,0,0,0,0,0,0,17],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,28,0,0,0,0,1,0],[1,3,0,0,0,0,0,28,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0] >;
C2×C28⋊1D4 in GAP, Magma, Sage, TeX
C_2\times C_{28}\rtimes_1D_4 % in TeX
G:=Group("C2xC28:1D4"); // GroupNames label
G:=SmallGroup(448,959);
// by ID
G=gap.SmallGroup(448,959);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,184,675,297,80,18822]);
// 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=b^15,d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations