direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C28⋊7D4, C23⋊4D28, C24.71D14, (C2×C28)⋊37D4, C28⋊15(C2×D4), (C23×C4)⋊5D7, (C23×C28)⋊8C2, C22⋊2(C2×D28), C14⋊3(C4⋊D4), (C22×C4)⋊44D14, (C22×C14)⋊15D4, D14⋊C4⋊42C22, (C22×D28)⋊12C2, (C2×D28)⋊50C22, C4⋊Dic7⋊64C22, C2.33(C22×D28), (C2×C14).288C24, (C2×C28).705C23, (C22×C28)⋊60C22, C14.134(C22×D4), C22.83(C4○D28), (C23×D7).75C22, C22.303(C23×D7), C23.234(C22×D7), (C23×C14).110C22, (C22×C14).417C23, (C2×Dic7).150C23, (C22×D7).126C23, (C22×Dic7).162C22, C7⋊4(C2×C4⋊D4), C4⋊4(C2×C7⋊D4), (C2×C14)⋊11(C2×D4), (C2×D14⋊C4)⋊14C2, (C2×C4)⋊16(C7⋊D4), (C2×C4⋊Dic7)⋊29C2, C14.63(C2×C4○D4), C2.71(C2×C4○D28), C2.7(C22×C7⋊D4), (C2×C7⋊D4)⋊42C22, (C22×C7⋊D4)⋊11C2, (C2×C4).658(C22×D7), C22.104(C2×C7⋊D4), (C2×C14).114(C4○D4), SmallGroup(448,1243)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C28⋊7D4
G = < a,b,c,d | a2=b28=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=dbd=b-1, dcd=c-1 >
Subgroups: 2116 in 426 conjugacy classes, 143 normal (23 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, C23, C23, C23, D7, C14, C14, C14, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×D4, C24, C24, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C14, C2×C22⋊C4, C2×C4⋊C4, C4⋊D4, C23×C4, C22×D4, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C22×C14, C22×C14, C2×C4⋊D4, C4⋊Dic7, D14⋊C4, C2×D28, C2×D28, C22×Dic7, C2×C7⋊D4, C2×C7⋊D4, C22×C28, C22×C28, C22×C28, C23×D7, C23×C14, C2×C4⋊Dic7, C2×D14⋊C4, C28⋊7D4, C22×D28, C22×C7⋊D4, C23×C28, C2×C28⋊7D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C4⋊D4, C22×D4, C2×C4○D4, D28, C7⋊D4, C22×D7, C2×C4⋊D4, C2×D28, C4○D28, C2×C7⋊D4, C23×D7, C28⋊7D4, C22×D28, C2×C4○D28, C22×C7⋊D4, C2×C28⋊7D4
►On 224 points
Generators in S224
(1 163)(2 164)(3 165)(4 166)(5 167)(6 168)(7 141)(8 142)(9 143)(10 144)(11 145)(12 146)(13 147)(14 148)(15 149)(16 150)(17 151)(18 152)(19 153)(20 154)(21 155)(22 156)(23 157)(24 158)(25 159)(26 160)(27 161)(28 162)(29 76)(30 77)(31 78)(32 79)(33 80)(34 81)(35 82)(36 83)(37 84)(38 57)(39 58)(40 59)(41 60)(42 61)(43 62)(44 63)(45 64)(46 65)(47 66)(48 67)(49 68)(50 69)(51 70)(52 71)(53 72)(54 73)(55 74)(56 75)(85 174)(86 175)(87 176)(88 177)(89 178)(90 179)(91 180)(92 181)(93 182)(94 183)(95 184)(96 185)(97 186)(98 187)(99 188)(100 189)(101 190)(102 191)(103 192)(104 193)(105 194)(106 195)(107 196)(108 169)(109 170)(110 171)(111 172)(112 173)(113 203)(114 204)(115 205)(116 206)(117 207)(118 208)(119 209)(120 210)(121 211)(122 212)(123 213)(124 214)(125 215)(126 216)(127 217)(128 218)(129 219)(130 220)(131 221)(132 222)(133 223)(134 224)(135 197)(136 198)(137 199)(138 200)(139 201)(140 202)
(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 93 120 75)(2 92 121 74)(3 91 122 73)(4 90 123 72)(5 89 124 71)(6 88 125 70)(7 87 126 69)(8 86 127 68)(9 85 128 67)(10 112 129 66)(11 111 130 65)(12 110 131 64)(13 109 132 63)(14 108 133 62)(15 107 134 61)(16 106 135 60)(17 105 136 59)(18 104 137 58)(19 103 138 57)(20 102 139 84)(21 101 140 83)(22 100 113 82)(23 99 114 81)(24 98 115 80)(25 97 116 79)(26 96 117 78)(27 95 118 77)(28 94 119 76)(29 162 183 209)(30 161 184 208)(31 160 185 207)(32 159 186 206)(33 158 187 205)(34 157 188 204)(35 156 189 203)(36 155 190 202)(37 154 191 201)(38 153 192 200)(39 152 193 199)(40 151 194 198)(41 150 195 197)(42 149 196 224)(43 148 169 223)(44 147 170 222)(45 146 171 221)(46 145 172 220)(47 144 173 219)(48 143 174 218)(49 142 175 217)(50 141 176 216)(51 168 177 215)(52 167 178 214)(53 166 179 213)(54 165 180 212)(55 164 181 211)(56 163 182 210)
(1 61)(2 60)(3 59)(4 58)(5 57)(6 84)(7 83)(8 82)(9 81)(10 80)(11 79)(12 78)(13 77)(14 76)(15 75)(16 74)(17 73)(18 72)(19 71)(20 70)(21 69)(22 68)(23 67)(24 66)(25 65)(26 64)(27 63)(28 62)(29 148)(30 147)(31 146)(32 145)(33 144)(34 143)(35 142)(36 141)(37 168)(38 167)(39 166)(40 165)(41 164)(42 163)(43 162)(44 161)(45 160)(46 159)(47 158)(48 157)(49 156)(50 155)(51 154)(52 153)(53 152)(54 151)(55 150)(56 149)(85 114)(86 113)(87 140)(88 139)(89 138)(90 137)(91 136)(92 135)(93 134)(94 133)(95 132)(96 131)(97 130)(98 129)(99 128)(100 127)(101 126)(102 125)(103 124)(104 123)(105 122)(106 121)(107 120)(108 119)(109 118)(110 117)(111 116)(112 115)(169 209)(170 208)(171 207)(172 206)(173 205)(174 204)(175 203)(176 202)(177 201)(178 200)(179 199)(180 198)(181 197)(182 224)(183 223)(184 222)(185 221)(186 220)(187 219)(188 218)(189 217)(190 216)(191 215)(192 214)(193 213)(194 212)(195 211)(196 210)
G:=sub<Sym(224)| (1,163)(2,164)(3,165)(4,166)(5,167)(6,168)(7,141)(8,142)(9,143)(10,144)(11,145)(12,146)(13,147)(14,148)(15,149)(16,150)(17,151)(18,152)(19,153)(20,154)(21,155)(22,156)(23,157)(24,158)(25,159)(26,160)(27,161)(28,162)(29,76)(30,77)(31,78)(32,79)(33,80)(34,81)(35,82)(36,83)(37,84)(38,57)(39,58)(40,59)(41,60)(42,61)(43,62)(44,63)(45,64)(46,65)(47,66)(48,67)(49,68)(50,69)(51,70)(52,71)(53,72)(54,73)(55,74)(56,75)(85,174)(86,175)(87,176)(88,177)(89,178)(90,179)(91,180)(92,181)(93,182)(94,183)(95,184)(96,185)(97,186)(98,187)(99,188)(100,189)(101,190)(102,191)(103,192)(104,193)(105,194)(106,195)(107,196)(108,169)(109,170)(110,171)(111,172)(112,173)(113,203)(114,204)(115,205)(116,206)(117,207)(118,208)(119,209)(120,210)(121,211)(122,212)(123,213)(124,214)(125,215)(126,216)(127,217)(128,218)(129,219)(130,220)(131,221)(132,222)(133,223)(134,224)(135,197)(136,198)(137,199)(138,200)(139,201)(140,202), (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), (1,93,120,75)(2,92,121,74)(3,91,122,73)(4,90,123,72)(5,89,124,71)(6,88,125,70)(7,87,126,69)(8,86,127,68)(9,85,128,67)(10,112,129,66)(11,111,130,65)(12,110,131,64)(13,109,132,63)(14,108,133,62)(15,107,134,61)(16,106,135,60)(17,105,136,59)(18,104,137,58)(19,103,138,57)(20,102,139,84)(21,101,140,83)(22,100,113,82)(23,99,114,81)(24,98,115,80)(25,97,116,79)(26,96,117,78)(27,95,118,77)(28,94,119,76)(29,162,183,209)(30,161,184,208)(31,160,185,207)(32,159,186,206)(33,158,187,205)(34,157,188,204)(35,156,189,203)(36,155,190,202)(37,154,191,201)(38,153,192,200)(39,152,193,199)(40,151,194,198)(41,150,195,197)(42,149,196,224)(43,148,169,223)(44,147,170,222)(45,146,171,221)(46,145,172,220)(47,144,173,219)(48,143,174,218)(49,142,175,217)(50,141,176,216)(51,168,177,215)(52,167,178,214)(53,166,179,213)(54,165,180,212)(55,164,181,211)(56,163,182,210), (1,61)(2,60)(3,59)(4,58)(5,57)(6,84)(7,83)(8,82)(9,81)(10,80)(11,79)(12,78)(13,77)(14,76)(15,75)(16,74)(17,73)(18,72)(19,71)(20,70)(21,69)(22,68)(23,67)(24,66)(25,65)(26,64)(27,63)(28,62)(29,148)(30,147)(31,146)(32,145)(33,144)(34,143)(35,142)(36,141)(37,168)(38,167)(39,166)(40,165)(41,164)(42,163)(43,162)(44,161)(45,160)(46,159)(47,158)(48,157)(49,156)(50,155)(51,154)(52,153)(53,152)(54,151)(55,150)(56,149)(85,114)(86,113)(87,140)(88,139)(89,138)(90,137)(91,136)(92,135)(93,134)(94,133)(95,132)(96,131)(97,130)(98,129)(99,128)(100,127)(101,126)(102,125)(103,124)(104,123)(105,122)(106,121)(107,120)(108,119)(109,118)(110,117)(111,116)(112,115)(169,209)(170,208)(171,207)(172,206)(173,205)(174,204)(175,203)(176,202)(177,201)(178,200)(179,199)(180,198)(181,197)(182,224)(183,223)(184,222)(185,221)(186,220)(187,219)(188,218)(189,217)(190,216)(191,215)(192,214)(193,213)(194,212)(195,211)(196,210)>;
G:=Group( (1,163)(2,164)(3,165)(4,166)(5,167)(6,168)(7,141)(8,142)(9,143)(10,144)(11,145)(12,146)(13,147)(14,148)(15,149)(16,150)(17,151)(18,152)(19,153)(20,154)(21,155)(22,156)(23,157)(24,158)(25,159)(26,160)(27,161)(28,162)(29,76)(30,77)(31,78)(32,79)(33,80)(34,81)(35,82)(36,83)(37,84)(38,57)(39,58)(40,59)(41,60)(42,61)(43,62)(44,63)(45,64)(46,65)(47,66)(48,67)(49,68)(50,69)(51,70)(52,71)(53,72)(54,73)(55,74)(56,75)(85,174)(86,175)(87,176)(88,177)(89,178)(90,179)(91,180)(92,181)(93,182)(94,183)(95,184)(96,185)(97,186)(98,187)(99,188)(100,189)(101,190)(102,191)(103,192)(104,193)(105,194)(106,195)(107,196)(108,169)(109,170)(110,171)(111,172)(112,173)(113,203)(114,204)(115,205)(116,206)(117,207)(118,208)(119,209)(120,210)(121,211)(122,212)(123,213)(124,214)(125,215)(126,216)(127,217)(128,218)(129,219)(130,220)(131,221)(132,222)(133,223)(134,224)(135,197)(136,198)(137,199)(138,200)(139,201)(140,202), (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), (1,93,120,75)(2,92,121,74)(3,91,122,73)(4,90,123,72)(5,89,124,71)(6,88,125,70)(7,87,126,69)(8,86,127,68)(9,85,128,67)(10,112,129,66)(11,111,130,65)(12,110,131,64)(13,109,132,63)(14,108,133,62)(15,107,134,61)(16,106,135,60)(17,105,136,59)(18,104,137,58)(19,103,138,57)(20,102,139,84)(21,101,140,83)(22,100,113,82)(23,99,114,81)(24,98,115,80)(25,97,116,79)(26,96,117,78)(27,95,118,77)(28,94,119,76)(29,162,183,209)(30,161,184,208)(31,160,185,207)(32,159,186,206)(33,158,187,205)(34,157,188,204)(35,156,189,203)(36,155,190,202)(37,154,191,201)(38,153,192,200)(39,152,193,199)(40,151,194,198)(41,150,195,197)(42,149,196,224)(43,148,169,223)(44,147,170,222)(45,146,171,221)(46,145,172,220)(47,144,173,219)(48,143,174,218)(49,142,175,217)(50,141,176,216)(51,168,177,215)(52,167,178,214)(53,166,179,213)(54,165,180,212)(55,164,181,211)(56,163,182,210), (1,61)(2,60)(3,59)(4,58)(5,57)(6,84)(7,83)(8,82)(9,81)(10,80)(11,79)(12,78)(13,77)(14,76)(15,75)(16,74)(17,73)(18,72)(19,71)(20,70)(21,69)(22,68)(23,67)(24,66)(25,65)(26,64)(27,63)(28,62)(29,148)(30,147)(31,146)(32,145)(33,144)(34,143)(35,142)(36,141)(37,168)(38,167)(39,166)(40,165)(41,164)(42,163)(43,162)(44,161)(45,160)(46,159)(47,158)(48,157)(49,156)(50,155)(51,154)(52,153)(53,152)(54,151)(55,150)(56,149)(85,114)(86,113)(87,140)(88,139)(89,138)(90,137)(91,136)(92,135)(93,134)(94,133)(95,132)(96,131)(97,130)(98,129)(99,128)(100,127)(101,126)(102,125)(103,124)(104,123)(105,122)(106,121)(107,120)(108,119)(109,118)(110,117)(111,116)(112,115)(169,209)(170,208)(171,207)(172,206)(173,205)(174,204)(175,203)(176,202)(177,201)(178,200)(179,199)(180,198)(181,197)(182,224)(183,223)(184,222)(185,221)(186,220)(187,219)(188,218)(189,217)(190,216)(191,215)(192,214)(193,213)(194,212)(195,211)(196,210) );
G=PermutationGroup([[(1,163),(2,164),(3,165),(4,166),(5,167),(6,168),(7,141),(8,142),(9,143),(10,144),(11,145),(12,146),(13,147),(14,148),(15,149),(16,150),(17,151),(18,152),(19,153),(20,154),(21,155),(22,156),(23,157),(24,158),(25,159),(26,160),(27,161),(28,162),(29,76),(30,77),(31,78),(32,79),(33,80),(34,81),(35,82),(36,83),(37,84),(38,57),(39,58),(40,59),(41,60),(42,61),(43,62),(44,63),(45,64),(46,65),(47,66),(48,67),(49,68),(50,69),(51,70),(52,71),(53,72),(54,73),(55,74),(56,75),(85,174),(86,175),(87,176),(88,177),(89,178),(90,179),(91,180),(92,181),(93,182),(94,183),(95,184),(96,185),(97,186),(98,187),(99,188),(100,189),(101,190),(102,191),(103,192),(104,193),(105,194),(106,195),(107,196),(108,169),(109,170),(110,171),(111,172),(112,173),(113,203),(114,204),(115,205),(116,206),(117,207),(118,208),(119,209),(120,210),(121,211),(122,212),(123,213),(124,214),(125,215),(126,216),(127,217),(128,218),(129,219),(130,220),(131,221),(132,222),(133,223),(134,224),(135,197),(136,198),(137,199),(138,200),(139,201),(140,202)], [(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)], [(1,93,120,75),(2,92,121,74),(3,91,122,73),(4,90,123,72),(5,89,124,71),(6,88,125,70),(7,87,126,69),(8,86,127,68),(9,85,128,67),(10,112,129,66),(11,111,130,65),(12,110,131,64),(13,109,132,63),(14,108,133,62),(15,107,134,61),(16,106,135,60),(17,105,136,59),(18,104,137,58),(19,103,138,57),(20,102,139,84),(21,101,140,83),(22,100,113,82),(23,99,114,81),(24,98,115,80),(25,97,116,79),(26,96,117,78),(27,95,118,77),(28,94,119,76),(29,162,183,209),(30,161,184,208),(31,160,185,207),(32,159,186,206),(33,158,187,205),(34,157,188,204),(35,156,189,203),(36,155,190,202),(37,154,191,201),(38,153,192,200),(39,152,193,199),(40,151,194,198),(41,150,195,197),(42,149,196,224),(43,148,169,223),(44,147,170,222),(45,146,171,221),(46,145,172,220),(47,144,173,219),(48,143,174,218),(49,142,175,217),(50,141,176,216),(51,168,177,215),(52,167,178,214),(53,166,179,213),(54,165,180,212),(55,164,181,211),(56,163,182,210)], [(1,61),(2,60),(3,59),(4,58),(5,57),(6,84),(7,83),(8,82),(9,81),(10,80),(11,79),(12,78),(13,77),(14,76),(15,75),(16,74),(17,73),(18,72),(19,71),(20,70),(21,69),(22,68),(23,67),(24,66),(25,65),(26,64),(27,63),(28,62),(29,148),(30,147),(31,146),(32,145),(33,144),(34,143),(35,142),(36,141),(37,168),(38,167),(39,166),(40,165),(41,164),(42,163),(43,162),(44,161),(45,160),(46,159),(47,158),(48,157),(49,156),(50,155),(51,154),(52,153),(53,152),(54,151),(55,150),(56,149),(85,114),(86,113),(87,140),(88,139),(89,138),(90,137),(91,136),(92,135),(93,134),(94,133),(95,132),(96,131),(97,130),(98,129),(99,128),(100,127),(101,126),(102,125),(103,124),(104,123),(105,122),(106,121),(107,120),(108,119),(109,118),(110,117),(111,116),(112,115),(169,209),(170,208),(171,207),(172,206),(173,205),(174,204),(175,203),(176,202),(177,201),(178,200),(179,199),(180,198),(181,197),(182,224),(183,223),(184,222),(185,221),(186,220),(187,219),(188,218),(189,217),(190,216),(191,215),(192,214),(193,213),(194,212),(195,211),(196,210)]])
124 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 2L | 2M | 2N | 2O | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 7A | 7B | 7C | 14A | ··· | 14AS | 28A | ··· | 28AV |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
124 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | C4○D4 | D14 | D14 | C7⋊D4 | D28 | C4○D28 |
| kernel | C2×C28⋊7D4 | C2×C4⋊Dic7 | C2×D14⋊C4 | C28⋊7D4 | C22×D28 | C22×C7⋊D4 | C23×C28 | C2×C28 | C22×C14 | C23×C4 | C2×C14 | C22×C4 | C24 | C2×C4 | C23 | C22 |
| # reps | 1 | 1 | 2 | 8 | 1 | 2 | 1 | 4 | 4 | 3 | 4 | 18 | 3 | 24 | 24 | 24 |
Matrix representation of C2×C28⋊7D4 ►in GL5(𝔽29)
| 28 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 19 | 0 | 0 | 0 |
| 0 | 28 | 26 | 0 | 0 |
| 0 | 0 | 0 | 21 | 25 |
| 0 | 0 | 0 | 4 | 20 |
| 28 | 0 | 0 | 0 | 0 |
| 0 | 28 | 7 | 0 | 0 |
| 0 | 8 | 1 | 0 | 0 |
| 0 | 0 | 0 | 25 | 9 |
| 0 | 0 | 0 | 8 | 4 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 22 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 4 | 20 |
| 0 | 0 | 0 | 21 | 25 |
G:=sub<GL(5,GF(29))| [28,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,19,28,0,0,0,0,26,0,0,0,0,0,21,4,0,0,0,25,20],[28,0,0,0,0,0,28,8,0,0,0,7,1,0,0,0,0,0,25,8,0,0,0,9,4],[1,0,0,0,0,0,1,0,0,0,0,22,28,0,0,0,0,0,4,21,0,0,0,20,25] >;
C2×C28⋊7D4 in GAP, Magma, Sage, TeX
C_2\times C_{28}\rtimes_7D_4 % in TeX
G:=Group("C2xC28:7D4"); // GroupNames label
G:=SmallGroup(448,1243);
// by ID
G=gap.SmallGroup(448,1243);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,758,184,675,18822]);
// 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=d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations