metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4⋊1(D14⋊C4), (C2×D28)⋊10C4, C14.59(C4×D4), C28⋊2(C22⋊C4), (C2×Dic7)⋊11D4, (C2×C28).142D4, (C2×C4).144D28, C2.3(C28⋊D4), C2.5(C4⋊D28), C22.111(D4×D7), C22.48(C2×D28), C14.15(C4⋊1D4), C14.54(C4⋊D4), (C22×D28).11C2, (C22×C4).335D14, C2.18(D28⋊C4), C2.2(C28.23D4), C14.51(C4.4D4), C7⋊3(C24.3C22), (C23×D7).18C22, C23.296(C22×D7), (C22×C28).144C22, (C22×C14).352C23, C22.28(Q8⋊2D7), (C22×Dic7).192C22, (C2×C4⋊C4)⋊6D7, (C14×C4⋊C4)⋊6C2, (C2×C4×Dic7)⋊1C2, (C2×C4).79(C4×D7), (C2×D14⋊C4)⋊10C2, (C2×C28).86(C2×C4), C2.16(C2×D14⋊C4), C22.137(C2×C4×D7), (C2×C14).452(C2×D4), C14.43(C2×C22⋊C4), C22.67(C2×C7⋊D4), (C2×C4).129(C7⋊D4), (C22×D7).21(C2×C4), (C2×C14).189(C4○D4), (C2×C14).120(C22×C4), SmallGroup(448,522)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×D28)⋊10C4
G = < a,b,c,d | a2=b28=c2=d4=1, ab=ba, dcd-1=ac=ca, ad=da, cbc=b-1, dbd-1=b15 >
Subgroups: 1540 in 258 conjugacy classes, 83 normal (23 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×D4, C24, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C42, C2×C22⋊C4, C2×C4⋊C4, C22×D4, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C24.3C22, C4×Dic7, D14⋊C4, C7×C4⋊C4, C2×D28, C2×D28, C22×Dic7, C22×C28, C22×C28, C23×D7, C2×C4×Dic7, C2×D14⋊C4, C14×C4⋊C4, C22×D28, (C2×D28)⋊10C4
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22⋊C4, C22×C4, C2×D4, C4○D4, D14, C2×C22⋊C4, C4×D4, C4⋊D4, C4.4D4, C4⋊1D4, C4×D7, D28, C7⋊D4, C22×D7, C24.3C22, D14⋊C4, C2×C4×D7, C2×D28, D4×D7, Q8⋊2D7, C2×C7⋊D4, D28⋊C4, C4⋊D28, C2×D14⋊C4, C28⋊D4, C28.23D4, (C2×D28)⋊10C4
►On 224 points
Generators in S224
(1 216)(2 217)(3 218)(4 219)(5 220)(6 221)(7 222)(8 223)(9 224)(10 197)(11 198)(12 199)(13 200)(14 201)(15 202)(16 203)(17 204)(18 205)(19 206)(20 207)(21 208)(22 209)(23 210)(24 211)(25 212)(26 213)(27 214)(28 215)(29 69)(30 70)(31 71)(32 72)(33 73)(34 74)(35 75)(36 76)(37 77)(38 78)(39 79)(40 80)(41 81)(42 82)(43 83)(44 84)(45 57)(46 58)(47 59)(48 60)(49 61)(50 62)(51 63)(52 64)(53 65)(54 66)(55 67)(56 68)(85 181)(86 182)(87 183)(88 184)(89 185)(90 186)(91 187)(92 188)(93 189)(94 190)(95 191)(96 192)(97 193)(98 194)(99 195)(100 196)(101 169)(102 170)(103 171)(104 172)(105 173)(106 174)(107 175)(108 176)(109 177)(110 178)(111 179)(112 180)(113 157)(114 158)(115 159)(116 160)(117 161)(118 162)(119 163)(120 164)(121 165)(122 166)(123 167)(124 168)(125 141)(126 142)(127 143)(128 144)(129 145)(130 146)(131 147)(132 148)(133 149)(134 150)(135 151)(136 152)(137 153)(138 154)(139 155)(140 156)
(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)
(1 185)(2 184)(3 183)(4 182)(5 181)(6 180)(7 179)(8 178)(9 177)(10 176)(11 175)(12 174)(13 173)(14 172)(15 171)(16 170)(17 169)(18 196)(19 195)(20 194)(21 193)(22 192)(23 191)(24 190)(25 189)(26 188)(27 187)(28 186)(29 158)(30 157)(31 156)(32 155)(33 154)(34 153)(35 152)(36 151)(37 150)(38 149)(39 148)(40 147)(41 146)(42 145)(43 144)(44 143)(45 142)(46 141)(47 168)(48 167)(49 166)(50 165)(51 164)(52 163)(53 162)(54 161)(55 160)(56 159)(57 126)(58 125)(59 124)(60 123)(61 122)(62 121)(63 120)(64 119)(65 118)(66 117)(67 116)(68 115)(69 114)(70 113)(71 140)(72 139)(73 138)(74 137)(75 136)(76 135)(77 134)(78 133)(79 132)(80 131)(81 130)(82 129)(83 128)(84 127)(85 220)(86 219)(87 218)(88 217)(89 216)(90 215)(91 214)(92 213)(93 212)(94 211)(95 210)(96 209)(97 208)(98 207)(99 206)(100 205)(101 204)(102 203)(103 202)(104 201)(105 200)(106 199)(107 198)(108 197)(109 224)(110 223)(111 222)(112 221)
(1 141 179 80)(2 156 180 67)(3 143 181 82)(4 158 182 69)(5 145 183 84)(6 160 184 71)(7 147 185 58)(8 162 186 73)(9 149 187 60)(10 164 188 75)(11 151 189 62)(12 166 190 77)(13 153 191 64)(14 168 192 79)(15 155 193 66)(16 142 194 81)(17 157 195 68)(18 144 196 83)(19 159 169 70)(20 146 170 57)(21 161 171 72)(22 148 172 59)(23 163 173 74)(24 150 174 61)(25 165 175 76)(26 152 176 63)(27 167 177 78)(28 154 178 65)(29 219 114 86)(30 206 115 101)(31 221 116 88)(32 208 117 103)(33 223 118 90)(34 210 119 105)(35 197 120 92)(36 212 121 107)(37 199 122 94)(38 214 123 109)(39 201 124 96)(40 216 125 111)(41 203 126 98)(42 218 127 85)(43 205 128 100)(44 220 129 87)(45 207 130 102)(46 222 131 89)(47 209 132 104)(48 224 133 91)(49 211 134 106)(50 198 135 93)(51 213 136 108)(52 200 137 95)(53 215 138 110)(54 202 139 97)(55 217 140 112)(56 204 113 99)
G:=sub<Sym(224)| (1,216)(2,217)(3,218)(4,219)(5,220)(6,221)(7,222)(8,223)(9,224)(10,197)(11,198)(12,199)(13,200)(14,201)(15,202)(16,203)(17,204)(18,205)(19,206)(20,207)(21,208)(22,209)(23,210)(24,211)(25,212)(26,213)(27,214)(28,215)(29,69)(30,70)(31,71)(32,72)(33,73)(34,74)(35,75)(36,76)(37,77)(38,78)(39,79)(40,80)(41,81)(42,82)(43,83)(44,84)(45,57)(46,58)(47,59)(48,60)(49,61)(50,62)(51,63)(52,64)(53,65)(54,66)(55,67)(56,68)(85,181)(86,182)(87,183)(88,184)(89,185)(90,186)(91,187)(92,188)(93,189)(94,190)(95,191)(96,192)(97,193)(98,194)(99,195)(100,196)(101,169)(102,170)(103,171)(104,172)(105,173)(106,174)(107,175)(108,176)(109,177)(110,178)(111,179)(112,180)(113,157)(114,158)(115,159)(116,160)(117,161)(118,162)(119,163)(120,164)(121,165)(122,166)(123,167)(124,168)(125,141)(126,142)(127,143)(128,144)(129,145)(130,146)(131,147)(132,148)(133,149)(134,150)(135,151)(136,152)(137,153)(138,154)(139,155)(140,156), (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), (1,185)(2,184)(3,183)(4,182)(5,181)(6,180)(7,179)(8,178)(9,177)(10,176)(11,175)(12,174)(13,173)(14,172)(15,171)(16,170)(17,169)(18,196)(19,195)(20,194)(21,193)(22,192)(23,191)(24,190)(25,189)(26,188)(27,187)(28,186)(29,158)(30,157)(31,156)(32,155)(33,154)(34,153)(35,152)(36,151)(37,150)(38,149)(39,148)(40,147)(41,146)(42,145)(43,144)(44,143)(45,142)(46,141)(47,168)(48,167)(49,166)(50,165)(51,164)(52,163)(53,162)(54,161)(55,160)(56,159)(57,126)(58,125)(59,124)(60,123)(61,122)(62,121)(63,120)(64,119)(65,118)(66,117)(67,116)(68,115)(69,114)(70,113)(71,140)(72,139)(73,138)(74,137)(75,136)(76,135)(77,134)(78,133)(79,132)(80,131)(81,130)(82,129)(83,128)(84,127)(85,220)(86,219)(87,218)(88,217)(89,216)(90,215)(91,214)(92,213)(93,212)(94,211)(95,210)(96,209)(97,208)(98,207)(99,206)(100,205)(101,204)(102,203)(103,202)(104,201)(105,200)(106,199)(107,198)(108,197)(109,224)(110,223)(111,222)(112,221), (1,141,179,80)(2,156,180,67)(3,143,181,82)(4,158,182,69)(5,145,183,84)(6,160,184,71)(7,147,185,58)(8,162,186,73)(9,149,187,60)(10,164,188,75)(11,151,189,62)(12,166,190,77)(13,153,191,64)(14,168,192,79)(15,155,193,66)(16,142,194,81)(17,157,195,68)(18,144,196,83)(19,159,169,70)(20,146,170,57)(21,161,171,72)(22,148,172,59)(23,163,173,74)(24,150,174,61)(25,165,175,76)(26,152,176,63)(27,167,177,78)(28,154,178,65)(29,219,114,86)(30,206,115,101)(31,221,116,88)(32,208,117,103)(33,223,118,90)(34,210,119,105)(35,197,120,92)(36,212,121,107)(37,199,122,94)(38,214,123,109)(39,201,124,96)(40,216,125,111)(41,203,126,98)(42,218,127,85)(43,205,128,100)(44,220,129,87)(45,207,130,102)(46,222,131,89)(47,209,132,104)(48,224,133,91)(49,211,134,106)(50,198,135,93)(51,213,136,108)(52,200,137,95)(53,215,138,110)(54,202,139,97)(55,217,140,112)(56,204,113,99)>;
G:=Group( (1,216)(2,217)(3,218)(4,219)(5,220)(6,221)(7,222)(8,223)(9,224)(10,197)(11,198)(12,199)(13,200)(14,201)(15,202)(16,203)(17,204)(18,205)(19,206)(20,207)(21,208)(22,209)(23,210)(24,211)(25,212)(26,213)(27,214)(28,215)(29,69)(30,70)(31,71)(32,72)(33,73)(34,74)(35,75)(36,76)(37,77)(38,78)(39,79)(40,80)(41,81)(42,82)(43,83)(44,84)(45,57)(46,58)(47,59)(48,60)(49,61)(50,62)(51,63)(52,64)(53,65)(54,66)(55,67)(56,68)(85,181)(86,182)(87,183)(88,184)(89,185)(90,186)(91,187)(92,188)(93,189)(94,190)(95,191)(96,192)(97,193)(98,194)(99,195)(100,196)(101,169)(102,170)(103,171)(104,172)(105,173)(106,174)(107,175)(108,176)(109,177)(110,178)(111,179)(112,180)(113,157)(114,158)(115,159)(116,160)(117,161)(118,162)(119,163)(120,164)(121,165)(122,166)(123,167)(124,168)(125,141)(126,142)(127,143)(128,144)(129,145)(130,146)(131,147)(132,148)(133,149)(134,150)(135,151)(136,152)(137,153)(138,154)(139,155)(140,156), (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), (1,185)(2,184)(3,183)(4,182)(5,181)(6,180)(7,179)(8,178)(9,177)(10,176)(11,175)(12,174)(13,173)(14,172)(15,171)(16,170)(17,169)(18,196)(19,195)(20,194)(21,193)(22,192)(23,191)(24,190)(25,189)(26,188)(27,187)(28,186)(29,158)(30,157)(31,156)(32,155)(33,154)(34,153)(35,152)(36,151)(37,150)(38,149)(39,148)(40,147)(41,146)(42,145)(43,144)(44,143)(45,142)(46,141)(47,168)(48,167)(49,166)(50,165)(51,164)(52,163)(53,162)(54,161)(55,160)(56,159)(57,126)(58,125)(59,124)(60,123)(61,122)(62,121)(63,120)(64,119)(65,118)(66,117)(67,116)(68,115)(69,114)(70,113)(71,140)(72,139)(73,138)(74,137)(75,136)(76,135)(77,134)(78,133)(79,132)(80,131)(81,130)(82,129)(83,128)(84,127)(85,220)(86,219)(87,218)(88,217)(89,216)(90,215)(91,214)(92,213)(93,212)(94,211)(95,210)(96,209)(97,208)(98,207)(99,206)(100,205)(101,204)(102,203)(103,202)(104,201)(105,200)(106,199)(107,198)(108,197)(109,224)(110,223)(111,222)(112,221), (1,141,179,80)(2,156,180,67)(3,143,181,82)(4,158,182,69)(5,145,183,84)(6,160,184,71)(7,147,185,58)(8,162,186,73)(9,149,187,60)(10,164,188,75)(11,151,189,62)(12,166,190,77)(13,153,191,64)(14,168,192,79)(15,155,193,66)(16,142,194,81)(17,157,195,68)(18,144,196,83)(19,159,169,70)(20,146,170,57)(21,161,171,72)(22,148,172,59)(23,163,173,74)(24,150,174,61)(25,165,175,76)(26,152,176,63)(27,167,177,78)(28,154,178,65)(29,219,114,86)(30,206,115,101)(31,221,116,88)(32,208,117,103)(33,223,118,90)(34,210,119,105)(35,197,120,92)(36,212,121,107)(37,199,122,94)(38,214,123,109)(39,201,124,96)(40,216,125,111)(41,203,126,98)(42,218,127,85)(43,205,128,100)(44,220,129,87)(45,207,130,102)(46,222,131,89)(47,209,132,104)(48,224,133,91)(49,211,134,106)(50,198,135,93)(51,213,136,108)(52,200,137,95)(53,215,138,110)(54,202,139,97)(55,217,140,112)(56,204,113,99) );
G=PermutationGroup([[(1,216),(2,217),(3,218),(4,219),(5,220),(6,221),(7,222),(8,223),(9,224),(10,197),(11,198),(12,199),(13,200),(14,201),(15,202),(16,203),(17,204),(18,205),(19,206),(20,207),(21,208),(22,209),(23,210),(24,211),(25,212),(26,213),(27,214),(28,215),(29,69),(30,70),(31,71),(32,72),(33,73),(34,74),(35,75),(36,76),(37,77),(38,78),(39,79),(40,80),(41,81),(42,82),(43,83),(44,84),(45,57),(46,58),(47,59),(48,60),(49,61),(50,62),(51,63),(52,64),(53,65),(54,66),(55,67),(56,68),(85,181),(86,182),(87,183),(88,184),(89,185),(90,186),(91,187),(92,188),(93,189),(94,190),(95,191),(96,192),(97,193),(98,194),(99,195),(100,196),(101,169),(102,170),(103,171),(104,172),(105,173),(106,174),(107,175),(108,176),(109,177),(110,178),(111,179),(112,180),(113,157),(114,158),(115,159),(116,160),(117,161),(118,162),(119,163),(120,164),(121,165),(122,166),(123,167),(124,168),(125,141),(126,142),(127,143),(128,144),(129,145),(130,146),(131,147),(132,148),(133,149),(134,150),(135,151),(136,152),(137,153),(138,154),(139,155),(140,156)], [(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)], [(1,185),(2,184),(3,183),(4,182),(5,181),(6,180),(7,179),(8,178),(9,177),(10,176),(11,175),(12,174),(13,173),(14,172),(15,171),(16,170),(17,169),(18,196),(19,195),(20,194),(21,193),(22,192),(23,191),(24,190),(25,189),(26,188),(27,187),(28,186),(29,158),(30,157),(31,156),(32,155),(33,154),(34,153),(35,152),(36,151),(37,150),(38,149),(39,148),(40,147),(41,146),(42,145),(43,144),(44,143),(45,142),(46,141),(47,168),(48,167),(49,166),(50,165),(51,164),(52,163),(53,162),(54,161),(55,160),(56,159),(57,126),(58,125),(59,124),(60,123),(61,122),(62,121),(63,120),(64,119),(65,118),(66,117),(67,116),(68,115),(69,114),(70,113),(71,140),(72,139),(73,138),(74,137),(75,136),(76,135),(77,134),(78,133),(79,132),(80,131),(81,130),(82,129),(83,128),(84,127),(85,220),(86,219),(87,218),(88,217),(89,216),(90,215),(91,214),(92,213),(93,212),(94,211),(95,210),(96,209),(97,208),(98,207),(99,206),(100,205),(101,204),(102,203),(103,202),(104,201),(105,200),(106,199),(107,198),(108,197),(109,224),(110,223),(111,222),(112,221)], [(1,141,179,80),(2,156,180,67),(3,143,181,82),(4,158,182,69),(5,145,183,84),(6,160,184,71),(7,147,185,58),(8,162,186,73),(9,149,187,60),(10,164,188,75),(11,151,189,62),(12,166,190,77),(13,153,191,64),(14,168,192,79),(15,155,193,66),(16,142,194,81),(17,157,195,68),(18,144,196,83),(19,159,169,70),(20,146,170,57),(21,161,171,72),(22,148,172,59),(23,163,173,74),(24,150,174,61),(25,165,175,76),(26,152,176,63),(27,167,177,78),(28,154,178,65),(29,219,114,86),(30,206,115,101),(31,221,116,88),(32,208,117,103),(33,223,118,90),(34,210,119,105),(35,197,120,92),(36,212,121,107),(37,199,122,94),(38,214,123,109),(39,201,124,96),(40,216,125,111),(41,203,126,98),(42,218,127,85),(43,205,128,100),(44,220,129,87),(45,207,130,102),(46,222,131,89),(47,209,132,104),(48,224,133,91),(49,211,134,106),(50,198,135,93),(51,213,136,108),(52,200,137,95),(53,215,138,110),(54,202,139,97),(55,217,140,112),(56,204,113,99)]])
88 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4P | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 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 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | D7 | C4○D4 | D14 | C4×D7 | D28 | C7⋊D4 | D4×D7 | Q8⋊2D7 |
| kernel | (C2×D28)⋊10C4 | C2×C4×Dic7 | C2×D14⋊C4 | C14×C4⋊C4 | C22×D28 | C2×D28 | C2×Dic7 | C2×C28 | C2×C4⋊C4 | C2×C14 | C22×C4 | C2×C4 | C2×C4 | C2×C4 | C22 | C22 |
| # reps | 1 | 1 | 4 | 1 | 1 | 8 | 4 | 4 | 3 | 4 | 9 | 12 | 12 | 12 | 6 | 6 |
Matrix representation of (C2×D28)⋊10C4 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 11 | 11 | 0 | 0 | 0 | 0 |
| 7 | 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 11 | 0 | 0 |
| 0 | 0 | 7 | 15 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 19 |
| 0 | 0 | 0 | 0 | 15 | 27 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 26 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 3 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 12 | 28 |
| 22 | 24 | 0 | 0 | 0 | 0 |
| 10 | 7 | 0 | 0 | 0 | 0 |
| 0 | 0 | 26 | 2 | 0 | 0 |
| 0 | 0 | 25 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 28 | 17 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[11,7,0,0,0,0,11,15,0,0,0,0,0,0,11,7,0,0,0,0,11,15,0,0,0,0,0,0,2,15,0,0,0,0,19,27],[28,26,0,0,0,0,0,1,0,0,0,0,0,0,1,3,0,0,0,0,0,28,0,0,0,0,0,0,1,12,0,0,0,0,0,28],[22,10,0,0,0,0,24,7,0,0,0,0,0,0,26,25,0,0,0,0,2,3,0,0,0,0,0,0,12,28,0,0,0,0,0,17] >;
(C2×D28)⋊10C4 in GAP, Magma, Sage, TeX
(C_2\times D_{28})\rtimes_{10}C_4 % in TeX
G:=Group("(C2xD28):10C4"); // GroupNames label
G:=SmallGroup(448,522);
// by ID
G=gap.SmallGroup(448,522);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,232,422,387,58,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^28=c^2=d^4=1,a*b=b*a,d*c*d^-1=a*c=c*a,a*d=d*a,c*b*c=b^-1,d*b*d^-1=b^15>;
// generators/relations