direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×D28.2C4, C56.71C23, C28.67C24, (C2×C8)⋊37D14, C14⋊1(C8○D4), C4○D28.7C4, (C22×C8)⋊13D7, C7⋊C8.31C23, (C22×C56)⋊19C2, (C2×C56)⋊49C22, (C2×D28).19C4, D28.30(C2×C4), (C8×D7)⋊19C22, C8.65(C22×D7), C4.66(C23×D7), C23.39(C4×D7), C8⋊D7⋊21C22, C14.30(C23×C4), (C4×D7).34C23, (C2×C28).880C23, C28.121(C22×C4), (C2×Dic14).19C4, Dic14.32(C2×C4), C4○D28.58C22, D14.12(C22×C4), (C22×C4).441D14, C4.Dic7⋊39C22, Dic7.12(C22×C4), (C22×C28).544C22, C7⋊1(C2×C8○D4), (D7×C2×C8)⋊25C2, C4.121(C2×C4×D7), C7⋊D4.5(C2×C4), (C2×C8⋊D7)⋊29C2, C22.11(C2×C4×D7), C2.31(D7×C22×C4), (C4×D7).23(C2×C4), (C2×C4).119(C4×D7), (C2×C7⋊D4).17C4, (C2×C28).236(C2×C4), (C2×C4○D28).27C2, (C2×C7⋊C8).327C22, (C2×C4.Dic7)⋊33C2, (C2×C4×D7).302C22, (C2×Dic7).71(C2×C4), (C22×D7).45(C2×C4), (C2×C4).824(C22×D7), (C22×C14).103(C2×C4), (C2×C14).156(C22×C4), SmallGroup(448,1191)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×D28.2C4
G = < a,b,c,d | a2=b28=c2=1, d4=b14, ab=ba, ac=ca, ad=da, cbc=b-1, bd=db, cd=dc >
Subgroups: 932 in 266 conjugacy classes, 151 normal (29 characteristic)
C1, C2, C2, C2, C4, C4, C4, C22, C22, C22, C7, C8, C8, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C14, C2×C8, C2×C8, C2×C8, M4(2), C22×C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C14, C22×C8, C22×C8, C2×M4(2), C8○D4, C2×C4○D4, C7⋊C8, C56, Dic14, C4×D7, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C22×D7, C22×C14, C2×C8○D4, C8×D7, C8⋊D7, C2×C7⋊C8, C4.Dic7, C2×C56, C2×C56, C2×Dic14, C2×C4×D7, C2×D28, C4○D28, C2×C7⋊D4, C22×C28, D7×C2×C8, C2×C8⋊D7, D28.2C4, C2×C4.Dic7, C22×C56, C2×C4○D28, C2×D28.2C4
Quotients: C1, C2, C4, C22, C2×C4, C23, D7, C22×C4, C24, D14, C8○D4, C23×C4, C4×D7, C22×D7, C2×C8○D4, C2×C4×D7, C23×D7, D28.2C4, D7×C22×C4, C2×D28.2C4
►On 224 points
Generators in S224
(1 51)(2 52)(3 53)(4 54)(5 55)(6 56)(7 29)(8 30)(9 31)(10 32)(11 33)(12 34)(13 35)(14 36)(15 37)(16 38)(17 39)(18 40)(19 41)(20 42)(21 43)(22 44)(23 45)(24 46)(25 47)(26 48)(27 49)(28 50)(57 179)(58 180)(59 181)(60 182)(61 183)(62 184)(63 185)(64 186)(65 187)(66 188)(67 189)(68 190)(69 191)(70 192)(71 193)(72 194)(73 195)(74 196)(75 169)(76 170)(77 171)(78 172)(79 173)(80 174)(81 175)(82 176)(83 177)(84 178)(85 219)(86 220)(87 221)(88 222)(89 223)(90 224)(91 197)(92 198)(93 199)(94 200)(95 201)(96 202)(97 203)(98 204)(99 205)(100 206)(101 207)(102 208)(103 209)(104 210)(105 211)(106 212)(107 213)(108 214)(109 215)(110 216)(111 217)(112 218)(113 154)(114 155)(115 156)(116 157)(117 158)(118 159)(119 160)(120 161)(121 162)(122 163)(123 164)(124 165)(125 166)(126 167)(127 168)(128 141)(129 142)(130 143)(131 144)(132 145)(133 146)(134 147)(135 148)(136 149)(137 150)(138 151)(139 152)(140 153)
(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 28)(2 27)(3 26)(4 25)(5 24)(6 23)(7 22)(8 21)(9 20)(10 19)(11 18)(12 17)(13 16)(14 15)(29 44)(30 43)(31 42)(32 41)(33 40)(34 39)(35 38)(36 37)(45 56)(46 55)(47 54)(48 53)(49 52)(50 51)(57 84)(58 83)(59 82)(60 81)(61 80)(62 79)(63 78)(64 77)(65 76)(66 75)(67 74)(68 73)(69 72)(70 71)(85 94)(86 93)(87 92)(88 91)(89 90)(95 112)(96 111)(97 110)(98 109)(99 108)(100 107)(101 106)(102 105)(103 104)(113 130)(114 129)(115 128)(116 127)(117 126)(118 125)(119 124)(120 123)(121 122)(131 140)(132 139)(133 138)(134 137)(135 136)(141 156)(142 155)(143 154)(144 153)(145 152)(146 151)(147 150)(148 149)(157 168)(158 167)(159 166)(160 165)(161 164)(162 163)(169 188)(170 187)(171 186)(172 185)(173 184)(174 183)(175 182)(176 181)(177 180)(178 179)(189 196)(190 195)(191 194)(192 193)(197 222)(198 221)(199 220)(200 219)(201 218)(202 217)(203 216)(204 215)(205 214)(206 213)(207 212)(208 211)(209 210)(223 224)
(1 122 104 71 15 136 90 57)(2 123 105 72 16 137 91 58)(3 124 106 73 17 138 92 59)(4 125 107 74 18 139 93 60)(5 126 108 75 19 140 94 61)(6 127 109 76 20 113 95 62)(7 128 110 77 21 114 96 63)(8 129 111 78 22 115 97 64)(9 130 112 79 23 116 98 65)(10 131 85 80 24 117 99 66)(11 132 86 81 25 118 100 67)(12 133 87 82 26 119 101 68)(13 134 88 83 27 120 102 69)(14 135 89 84 28 121 103 70)(29 141 216 171 43 155 202 185)(30 142 217 172 44 156 203 186)(31 143 218 173 45 157 204 187)(32 144 219 174 46 158 205 188)(33 145 220 175 47 159 206 189)(34 146 221 176 48 160 207 190)(35 147 222 177 49 161 208 191)(36 148 223 178 50 162 209 192)(37 149 224 179 51 163 210 193)(38 150 197 180 52 164 211 194)(39 151 198 181 53 165 212 195)(40 152 199 182 54 166 213 196)(41 153 200 183 55 167 214 169)(42 154 201 184 56 168 215 170)
G:=sub<Sym(224)| (1,51)(2,52)(3,53)(4,54)(5,55)(6,56)(7,29)(8,30)(9,31)(10,32)(11,33)(12,34)(13,35)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(23,45)(24,46)(25,47)(26,48)(27,49)(28,50)(57,179)(58,180)(59,181)(60,182)(61,183)(62,184)(63,185)(64,186)(65,187)(66,188)(67,189)(68,190)(69,191)(70,192)(71,193)(72,194)(73,195)(74,196)(75,169)(76,170)(77,171)(78,172)(79,173)(80,174)(81,175)(82,176)(83,177)(84,178)(85,219)(86,220)(87,221)(88,222)(89,223)(90,224)(91,197)(92,198)(93,199)(94,200)(95,201)(96,202)(97,203)(98,204)(99,205)(100,206)(101,207)(102,208)(103,209)(104,210)(105,211)(106,212)(107,213)(108,214)(109,215)(110,216)(111,217)(112,218)(113,154)(114,155)(115,156)(116,157)(117,158)(118,159)(119,160)(120,161)(121,162)(122,163)(123,164)(124,165)(125,166)(126,167)(127,168)(128,141)(129,142)(130,143)(131,144)(132,145)(133,146)(134,147)(135,148)(136,149)(137,150)(138,151)(139,152)(140,153), (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), (1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)(57,84)(58,83)(59,82)(60,81)(61,80)(62,79)(63,78)(64,77)(65,76)(66,75)(67,74)(68,73)(69,72)(70,71)(85,94)(86,93)(87,92)(88,91)(89,90)(95,112)(96,111)(97,110)(98,109)(99,108)(100,107)(101,106)(102,105)(103,104)(113,130)(114,129)(115,128)(116,127)(117,126)(118,125)(119,124)(120,123)(121,122)(131,140)(132,139)(133,138)(134,137)(135,136)(141,156)(142,155)(143,154)(144,153)(145,152)(146,151)(147,150)(148,149)(157,168)(158,167)(159,166)(160,165)(161,164)(162,163)(169,188)(170,187)(171,186)(172,185)(173,184)(174,183)(175,182)(176,181)(177,180)(178,179)(189,196)(190,195)(191,194)(192,193)(197,222)(198,221)(199,220)(200,219)(201,218)(202,217)(203,216)(204,215)(205,214)(206,213)(207,212)(208,211)(209,210)(223,224), (1,122,104,71,15,136,90,57)(2,123,105,72,16,137,91,58)(3,124,106,73,17,138,92,59)(4,125,107,74,18,139,93,60)(5,126,108,75,19,140,94,61)(6,127,109,76,20,113,95,62)(7,128,110,77,21,114,96,63)(8,129,111,78,22,115,97,64)(9,130,112,79,23,116,98,65)(10,131,85,80,24,117,99,66)(11,132,86,81,25,118,100,67)(12,133,87,82,26,119,101,68)(13,134,88,83,27,120,102,69)(14,135,89,84,28,121,103,70)(29,141,216,171,43,155,202,185)(30,142,217,172,44,156,203,186)(31,143,218,173,45,157,204,187)(32,144,219,174,46,158,205,188)(33,145,220,175,47,159,206,189)(34,146,221,176,48,160,207,190)(35,147,222,177,49,161,208,191)(36,148,223,178,50,162,209,192)(37,149,224,179,51,163,210,193)(38,150,197,180,52,164,211,194)(39,151,198,181,53,165,212,195)(40,152,199,182,54,166,213,196)(41,153,200,183,55,167,214,169)(42,154,201,184,56,168,215,170)>;
G:=Group( (1,51)(2,52)(3,53)(4,54)(5,55)(6,56)(7,29)(8,30)(9,31)(10,32)(11,33)(12,34)(13,35)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(23,45)(24,46)(25,47)(26,48)(27,49)(28,50)(57,179)(58,180)(59,181)(60,182)(61,183)(62,184)(63,185)(64,186)(65,187)(66,188)(67,189)(68,190)(69,191)(70,192)(71,193)(72,194)(73,195)(74,196)(75,169)(76,170)(77,171)(78,172)(79,173)(80,174)(81,175)(82,176)(83,177)(84,178)(85,219)(86,220)(87,221)(88,222)(89,223)(90,224)(91,197)(92,198)(93,199)(94,200)(95,201)(96,202)(97,203)(98,204)(99,205)(100,206)(101,207)(102,208)(103,209)(104,210)(105,211)(106,212)(107,213)(108,214)(109,215)(110,216)(111,217)(112,218)(113,154)(114,155)(115,156)(116,157)(117,158)(118,159)(119,160)(120,161)(121,162)(122,163)(123,164)(124,165)(125,166)(126,167)(127,168)(128,141)(129,142)(130,143)(131,144)(132,145)(133,146)(134,147)(135,148)(136,149)(137,150)(138,151)(139,152)(140,153), (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), (1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)(57,84)(58,83)(59,82)(60,81)(61,80)(62,79)(63,78)(64,77)(65,76)(66,75)(67,74)(68,73)(69,72)(70,71)(85,94)(86,93)(87,92)(88,91)(89,90)(95,112)(96,111)(97,110)(98,109)(99,108)(100,107)(101,106)(102,105)(103,104)(113,130)(114,129)(115,128)(116,127)(117,126)(118,125)(119,124)(120,123)(121,122)(131,140)(132,139)(133,138)(134,137)(135,136)(141,156)(142,155)(143,154)(144,153)(145,152)(146,151)(147,150)(148,149)(157,168)(158,167)(159,166)(160,165)(161,164)(162,163)(169,188)(170,187)(171,186)(172,185)(173,184)(174,183)(175,182)(176,181)(177,180)(178,179)(189,196)(190,195)(191,194)(192,193)(197,222)(198,221)(199,220)(200,219)(201,218)(202,217)(203,216)(204,215)(205,214)(206,213)(207,212)(208,211)(209,210)(223,224), (1,122,104,71,15,136,90,57)(2,123,105,72,16,137,91,58)(3,124,106,73,17,138,92,59)(4,125,107,74,18,139,93,60)(5,126,108,75,19,140,94,61)(6,127,109,76,20,113,95,62)(7,128,110,77,21,114,96,63)(8,129,111,78,22,115,97,64)(9,130,112,79,23,116,98,65)(10,131,85,80,24,117,99,66)(11,132,86,81,25,118,100,67)(12,133,87,82,26,119,101,68)(13,134,88,83,27,120,102,69)(14,135,89,84,28,121,103,70)(29,141,216,171,43,155,202,185)(30,142,217,172,44,156,203,186)(31,143,218,173,45,157,204,187)(32,144,219,174,46,158,205,188)(33,145,220,175,47,159,206,189)(34,146,221,176,48,160,207,190)(35,147,222,177,49,161,208,191)(36,148,223,178,50,162,209,192)(37,149,224,179,51,163,210,193)(38,150,197,180,52,164,211,194)(39,151,198,181,53,165,212,195)(40,152,199,182,54,166,213,196)(41,153,200,183,55,167,214,169)(42,154,201,184,56,168,215,170) );
G=PermutationGroup([[(1,51),(2,52),(3,53),(4,54),(5,55),(6,56),(7,29),(8,30),(9,31),(10,32),(11,33),(12,34),(13,35),(14,36),(15,37),(16,38),(17,39),(18,40),(19,41),(20,42),(21,43),(22,44),(23,45),(24,46),(25,47),(26,48),(27,49),(28,50),(57,179),(58,180),(59,181),(60,182),(61,183),(62,184),(63,185),(64,186),(65,187),(66,188),(67,189),(68,190),(69,191),(70,192),(71,193),(72,194),(73,195),(74,196),(75,169),(76,170),(77,171),(78,172),(79,173),(80,174),(81,175),(82,176),(83,177),(84,178),(85,219),(86,220),(87,221),(88,222),(89,223),(90,224),(91,197),(92,198),(93,199),(94,200),(95,201),(96,202),(97,203),(98,204),(99,205),(100,206),(101,207),(102,208),(103,209),(104,210),(105,211),(106,212),(107,213),(108,214),(109,215),(110,216),(111,217),(112,218),(113,154),(114,155),(115,156),(116,157),(117,158),(118,159),(119,160),(120,161),(121,162),(122,163),(123,164),(124,165),(125,166),(126,167),(127,168),(128,141),(129,142),(130,143),(131,144),(132,145),(133,146),(134,147),(135,148),(136,149),(137,150),(138,151),(139,152),(140,153)], [(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)], [(1,28),(2,27),(3,26),(4,25),(5,24),(6,23),(7,22),(8,21),(9,20),(10,19),(11,18),(12,17),(13,16),(14,15),(29,44),(30,43),(31,42),(32,41),(33,40),(34,39),(35,38),(36,37),(45,56),(46,55),(47,54),(48,53),(49,52),(50,51),(57,84),(58,83),(59,82),(60,81),(61,80),(62,79),(63,78),(64,77),(65,76),(66,75),(67,74),(68,73),(69,72),(70,71),(85,94),(86,93),(87,92),(88,91),(89,90),(95,112),(96,111),(97,110),(98,109),(99,108),(100,107),(101,106),(102,105),(103,104),(113,130),(114,129),(115,128),(116,127),(117,126),(118,125),(119,124),(120,123),(121,122),(131,140),(132,139),(133,138),(134,137),(135,136),(141,156),(142,155),(143,154),(144,153),(145,152),(146,151),(147,150),(148,149),(157,168),(158,167),(159,166),(160,165),(161,164),(162,163),(169,188),(170,187),(171,186),(172,185),(173,184),(174,183),(175,182),(176,181),(177,180),(178,179),(189,196),(190,195),(191,194),(192,193),(197,222),(198,221),(199,220),(200,219),(201,218),(202,217),(203,216),(204,215),(205,214),(206,213),(207,212),(208,211),(209,210),(223,224)], [(1,122,104,71,15,136,90,57),(2,123,105,72,16,137,91,58),(3,124,106,73,17,138,92,59),(4,125,107,74,18,139,93,60),(5,126,108,75,19,140,94,61),(6,127,109,76,20,113,95,62),(7,128,110,77,21,114,96,63),(8,129,111,78,22,115,97,64),(9,130,112,79,23,116,98,65),(10,131,85,80,24,117,99,66),(11,132,86,81,25,118,100,67),(12,133,87,82,26,119,101,68),(13,134,88,83,27,120,102,69),(14,135,89,84,28,121,103,70),(29,141,216,171,43,155,202,185),(30,142,217,172,44,156,203,186),(31,143,218,173,45,157,204,187),(32,144,219,174,46,158,205,188),(33,145,220,175,47,159,206,189),(34,146,221,176,48,160,207,190),(35,147,222,177,49,161,208,191),(36,148,223,178,50,162,209,192),(37,149,224,179,51,163,210,193),(38,150,197,180,52,164,211,194),(39,151,198,181,53,165,212,195),(40,152,199,182,54,166,213,196),(41,153,200,183,55,167,214,169),(42,154,201,184,56,168,215,170)]])
136 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 7A | 7B | 7C | 8A | ··· | 8H | 8I | 8J | 8K | 8L | 8M | ··· | 8T | 14A | ··· | 14U | 28A | ··· | 28X | 56A | ··· | 56AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 8 | 8 | 8 | 8 | 8 | ··· | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 14 | 14 | 14 | 14 | 1 | 1 | 1 | 1 | 2 | 2 | 14 | 14 | 14 | 14 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 14 | ··· | 14 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
136 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | ||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | C4 | C4 | C4 | D7 | D14 | D14 | C8○D4 | C4×D7 | C4×D7 | D28.2C4 |
| kernel | C2×D28.2C4 | D7×C2×C8 | C2×C8⋊D7 | D28.2C4 | C2×C4.Dic7 | C22×C56 | C2×C4○D28 | C2×Dic14 | C2×D28 | C4○D28 | C2×C7⋊D4 | C22×C8 | C2×C8 | C22×C4 | C14 | C2×C4 | C23 | C2 |
| # reps | 1 | 2 | 2 | 8 | 1 | 1 | 1 | 2 | 2 | 8 | 4 | 3 | 18 | 3 | 8 | 18 | 6 | 48 |
Matrix representation of C2×D28.2C4 ►in GL4(𝔽113) generated by
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 10 | 24 | 0 | 0 |
| 89 | 112 | 0 | 0 |
| 0 | 0 | 78 | 32 |
| 0 | 0 | 49 | 94 |
| 112 | 0 | 0 | 0 |
| 24 | 1 | 0 | 0 |
| 0 | 0 | 47 | 38 |
| 0 | 0 | 43 | 66 |
| 98 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 44 | 0 |
| 0 | 0 | 0 | 44 |
G:=sub<GL(4,GF(113))| [112,0,0,0,0,112,0,0,0,0,1,0,0,0,0,1],[10,89,0,0,24,112,0,0,0,0,78,49,0,0,32,94],[112,24,0,0,0,1,0,0,0,0,47,43,0,0,38,66],[98,0,0,0,0,98,0,0,0,0,44,0,0,0,0,44] >;
C2×D28.2C4 in GAP, Magma, Sage, TeX
C_2\times D_{28}._2C_4 % in TeX
G:=Group("C2xD28.2C4"); // GroupNames label
G:=SmallGroup(448,1191);
// by ID
G=gap.SmallGroup(448,1191);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,758,80,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^28=c^2=1,d^4=b^14,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c=b^-1,b*d=d*b,c*d=d*c>;
// generators/relations