direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×D4⋊2D13, D4⋊5D26, C26.6C24, C52.20C23, D26.2C23, C23.19D26, Dic26⋊7C22, Dic13.3C23, (C2×D4)⋊8D13, (D4×C26)⋊6C2, C26⋊2(C4○D4), (C2×C4).60D26, (C4×D13)⋊4C22, (D4×C13)⋊6C22, C13⋊D4⋊2C22, (C2×C26).1C23, C2.7(C23×D13), (C2×Dic26)⋊12C2, (C2×C52).45C22, C4.20(C22×D13), (C22×Dic13)⋊8C2, (C2×Dic13)⋊9C22, C22.1(C22×D13), (C22×C26).23C22, (C22×D13).32C22, (C2×C4×D13)⋊4C2, C13⋊2(C2×C4○D4), (C2×C13⋊D4)⋊10C2, SmallGroup(416,217)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×D4⋊2D13
G = < a,b,c,d,e | a2=b4=c2=d13=e2=1, ab=ba, ac=ca, ad=da, ae=ea, cbc=b-1, bd=db, be=eb, cd=dc, ece=b2c, ede=d-1 >
Subgroups: 896 in 164 conjugacy classes, 89 normal (15 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C2×C4, C2×C4, D4, D4, Q8, C23, C23, C13, C22×C4, C2×D4, C2×D4, C2×Q8, C4○D4, D13, C26, C26, C26, C2×C4○D4, Dic13, C52, D26, D26, C2×C26, C2×C26, C2×C26, Dic26, C4×D13, C2×Dic13, C2×Dic13, C13⋊D4, C2×C52, D4×C13, C22×D13, C22×C26, C2×Dic26, C2×C4×D13, D4⋊2D13, C22×Dic13, C2×C13⋊D4, D4×C26, C2×D4⋊2D13
Quotients: C1, C2, C22, C23, C4○D4, C24, D13, C2×C4○D4, D26, C22×D13, D4⋊2D13, C23×D13, C2×D4⋊2D13
►On 208 points
Generators in S208
(1 27)(2 28)(3 29)(4 30)(5 31)(6 32)(7 33)(8 34)(9 35)(10 36)(11 37)(12 38)(13 39)(14 40)(15 41)(16 42)(17 43)(18 44)(19 45)(20 46)(21 47)(22 48)(23 49)(24 50)(25 51)(26 52)(53 79)(54 80)(55 81)(56 82)(57 83)(58 84)(59 85)(60 86)(61 87)(62 88)(63 89)(64 90)(65 91)(66 92)(67 93)(68 94)(69 95)(70 96)(71 97)(72 98)(73 99)(74 100)(75 101)(76 102)(77 103)(78 104)(105 138)(106 139)(107 140)(108 141)(109 142)(110 143)(111 131)(112 132)(113 133)(114 134)(115 135)(116 136)(117 137)(118 145)(119 146)(120 147)(121 148)(122 149)(123 150)(124 151)(125 152)(126 153)(127 154)(128 155)(129 156)(130 144)(157 190)(158 191)(159 192)(160 193)(161 194)(162 195)(163 183)(164 184)(165 185)(166 186)(167 187)(168 188)(169 189)(170 207)(171 208)(172 196)(173 197)(174 198)(175 199)(176 200)(177 201)(178 202)(179 203)(180 204)(181 205)(182 206)
(1 66 14 53)(2 67 15 54)(3 68 16 55)(4 69 17 56)(5 70 18 57)(6 71 19 58)(7 72 20 59)(8 73 21 60)(9 74 22 61)(10 75 23 62)(11 76 24 63)(12 77 25 64)(13 78 26 65)(27 92 40 79)(28 93 41 80)(29 94 42 81)(30 95 43 82)(31 96 44 83)(32 97 45 84)(33 98 46 85)(34 99 47 86)(35 100 48 87)(36 101 49 88)(37 102 50 89)(38 103 51 90)(39 104 52 91)(105 180 122 159)(106 181 123 160)(107 182 124 161)(108 170 125 162)(109 171 126 163)(110 172 127 164)(111 173 128 165)(112 174 129 166)(113 175 130 167)(114 176 118 168)(115 177 119 169)(116 178 120 157)(117 179 121 158)(131 197 155 185)(132 198 156 186)(133 199 144 187)(134 200 145 188)(135 201 146 189)(136 202 147 190)(137 203 148 191)(138 204 149 192)(139 205 150 193)(140 206 151 194)(141 207 152 195)(142 208 153 183)(143 196 154 184)
(1 79)(2 80)(3 81)(4 82)(5 83)(6 84)(7 85)(8 86)(9 87)(10 88)(11 89)(12 90)(13 91)(14 92)(15 93)(16 94)(17 95)(18 96)(19 97)(20 98)(21 99)(22 100)(23 101)(24 102)(25 103)(26 104)(27 53)(28 54)(29 55)(30 56)(31 57)(32 58)(33 59)(34 60)(35 61)(36 62)(37 63)(38 64)(39 65)(40 66)(41 67)(42 68)(43 69)(44 70)(45 71)(46 72)(47 73)(48 74)(49 75)(50 76)(51 77)(52 78)(105 204)(106 205)(107 206)(108 207)(109 208)(110 196)(111 197)(112 198)(113 199)(114 200)(115 201)(116 202)(117 203)(118 188)(119 189)(120 190)(121 191)(122 192)(123 193)(124 194)(125 195)(126 183)(127 184)(128 185)(129 186)(130 187)(131 173)(132 174)(133 175)(134 176)(135 177)(136 178)(137 179)(138 180)(139 181)(140 182)(141 170)(142 171)(143 172)(144 167)(145 168)(146 169)(147 157)(148 158)(149 159)(150 160)(151 161)(152 162)(153 163)(154 164)(155 165)(156 166)
(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)
(1 105)(2 117)(3 116)(4 115)(5 114)(6 113)(7 112)(8 111)(9 110)(10 109)(11 108)(12 107)(13 106)(14 122)(15 121)(16 120)(17 119)(18 118)(19 130)(20 129)(21 128)(22 127)(23 126)(24 125)(25 124)(26 123)(27 138)(28 137)(29 136)(30 135)(31 134)(32 133)(33 132)(34 131)(35 143)(36 142)(37 141)(38 140)(39 139)(40 149)(41 148)(42 147)(43 146)(44 145)(45 144)(46 156)(47 155)(48 154)(49 153)(50 152)(51 151)(52 150)(53 159)(54 158)(55 157)(56 169)(57 168)(58 167)(59 166)(60 165)(61 164)(62 163)(63 162)(64 161)(65 160)(66 180)(67 179)(68 178)(69 177)(70 176)(71 175)(72 174)(73 173)(74 172)(75 171)(76 170)(77 182)(78 181)(79 192)(80 191)(81 190)(82 189)(83 188)(84 187)(85 186)(86 185)(87 184)(88 183)(89 195)(90 194)(91 193)(92 204)(93 203)(94 202)(95 201)(96 200)(97 199)(98 198)(99 197)(100 196)(101 208)(102 207)(103 206)(104 205)
G:=sub<Sym(208)| (1,27)(2,28)(3,29)(4,30)(5,31)(6,32)(7,33)(8,34)(9,35)(10,36)(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52)(53,79)(54,80)(55,81)(56,82)(57,83)(58,84)(59,85)(60,86)(61,87)(62,88)(63,89)(64,90)(65,91)(66,92)(67,93)(68,94)(69,95)(70,96)(71,97)(72,98)(73,99)(74,100)(75,101)(76,102)(77,103)(78,104)(105,138)(106,139)(107,140)(108,141)(109,142)(110,143)(111,131)(112,132)(113,133)(114,134)(115,135)(116,136)(117,137)(118,145)(119,146)(120,147)(121,148)(122,149)(123,150)(124,151)(125,152)(126,153)(127,154)(128,155)(129,156)(130,144)(157,190)(158,191)(159,192)(160,193)(161,194)(162,195)(163,183)(164,184)(165,185)(166,186)(167,187)(168,188)(169,189)(170,207)(171,208)(172,196)(173,197)(174,198)(175,199)(176,200)(177,201)(178,202)(179,203)(180,204)(181,205)(182,206), (1,66,14,53)(2,67,15,54)(3,68,16,55)(4,69,17,56)(5,70,18,57)(6,71,19,58)(7,72,20,59)(8,73,21,60)(9,74,22,61)(10,75,23,62)(11,76,24,63)(12,77,25,64)(13,78,26,65)(27,92,40,79)(28,93,41,80)(29,94,42,81)(30,95,43,82)(31,96,44,83)(32,97,45,84)(33,98,46,85)(34,99,47,86)(35,100,48,87)(36,101,49,88)(37,102,50,89)(38,103,51,90)(39,104,52,91)(105,180,122,159)(106,181,123,160)(107,182,124,161)(108,170,125,162)(109,171,126,163)(110,172,127,164)(111,173,128,165)(112,174,129,166)(113,175,130,167)(114,176,118,168)(115,177,119,169)(116,178,120,157)(117,179,121,158)(131,197,155,185)(132,198,156,186)(133,199,144,187)(134,200,145,188)(135,201,146,189)(136,202,147,190)(137,203,148,191)(138,204,149,192)(139,205,150,193)(140,206,151,194)(141,207,152,195)(142,208,153,183)(143,196,154,184), (1,79)(2,80)(3,81)(4,82)(5,83)(6,84)(7,85)(8,86)(9,87)(10,88)(11,89)(12,90)(13,91)(14,92)(15,93)(16,94)(17,95)(18,96)(19,97)(20,98)(21,99)(22,100)(23,101)(24,102)(25,103)(26,104)(27,53)(28,54)(29,55)(30,56)(31,57)(32,58)(33,59)(34,60)(35,61)(36,62)(37,63)(38,64)(39,65)(40,66)(41,67)(42,68)(43,69)(44,70)(45,71)(46,72)(47,73)(48,74)(49,75)(50,76)(51,77)(52,78)(105,204)(106,205)(107,206)(108,207)(109,208)(110,196)(111,197)(112,198)(113,199)(114,200)(115,201)(116,202)(117,203)(118,188)(119,189)(120,190)(121,191)(122,192)(123,193)(124,194)(125,195)(126,183)(127,184)(128,185)(129,186)(130,187)(131,173)(132,174)(133,175)(134,176)(135,177)(136,178)(137,179)(138,180)(139,181)(140,182)(141,170)(142,171)(143,172)(144,167)(145,168)(146,169)(147,157)(148,158)(149,159)(150,160)(151,161)(152,162)(153,163)(154,164)(155,165)(156,166), (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), (1,105)(2,117)(3,116)(4,115)(5,114)(6,113)(7,112)(8,111)(9,110)(10,109)(11,108)(12,107)(13,106)(14,122)(15,121)(16,120)(17,119)(18,118)(19,130)(20,129)(21,128)(22,127)(23,126)(24,125)(25,124)(26,123)(27,138)(28,137)(29,136)(30,135)(31,134)(32,133)(33,132)(34,131)(35,143)(36,142)(37,141)(38,140)(39,139)(40,149)(41,148)(42,147)(43,146)(44,145)(45,144)(46,156)(47,155)(48,154)(49,153)(50,152)(51,151)(52,150)(53,159)(54,158)(55,157)(56,169)(57,168)(58,167)(59,166)(60,165)(61,164)(62,163)(63,162)(64,161)(65,160)(66,180)(67,179)(68,178)(69,177)(70,176)(71,175)(72,174)(73,173)(74,172)(75,171)(76,170)(77,182)(78,181)(79,192)(80,191)(81,190)(82,189)(83,188)(84,187)(85,186)(86,185)(87,184)(88,183)(89,195)(90,194)(91,193)(92,204)(93,203)(94,202)(95,201)(96,200)(97,199)(98,198)(99,197)(100,196)(101,208)(102,207)(103,206)(104,205)>;
G:=Group( (1,27)(2,28)(3,29)(4,30)(5,31)(6,32)(7,33)(8,34)(9,35)(10,36)(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52)(53,79)(54,80)(55,81)(56,82)(57,83)(58,84)(59,85)(60,86)(61,87)(62,88)(63,89)(64,90)(65,91)(66,92)(67,93)(68,94)(69,95)(70,96)(71,97)(72,98)(73,99)(74,100)(75,101)(76,102)(77,103)(78,104)(105,138)(106,139)(107,140)(108,141)(109,142)(110,143)(111,131)(112,132)(113,133)(114,134)(115,135)(116,136)(117,137)(118,145)(119,146)(120,147)(121,148)(122,149)(123,150)(124,151)(125,152)(126,153)(127,154)(128,155)(129,156)(130,144)(157,190)(158,191)(159,192)(160,193)(161,194)(162,195)(163,183)(164,184)(165,185)(166,186)(167,187)(168,188)(169,189)(170,207)(171,208)(172,196)(173,197)(174,198)(175,199)(176,200)(177,201)(178,202)(179,203)(180,204)(181,205)(182,206), (1,66,14,53)(2,67,15,54)(3,68,16,55)(4,69,17,56)(5,70,18,57)(6,71,19,58)(7,72,20,59)(8,73,21,60)(9,74,22,61)(10,75,23,62)(11,76,24,63)(12,77,25,64)(13,78,26,65)(27,92,40,79)(28,93,41,80)(29,94,42,81)(30,95,43,82)(31,96,44,83)(32,97,45,84)(33,98,46,85)(34,99,47,86)(35,100,48,87)(36,101,49,88)(37,102,50,89)(38,103,51,90)(39,104,52,91)(105,180,122,159)(106,181,123,160)(107,182,124,161)(108,170,125,162)(109,171,126,163)(110,172,127,164)(111,173,128,165)(112,174,129,166)(113,175,130,167)(114,176,118,168)(115,177,119,169)(116,178,120,157)(117,179,121,158)(131,197,155,185)(132,198,156,186)(133,199,144,187)(134,200,145,188)(135,201,146,189)(136,202,147,190)(137,203,148,191)(138,204,149,192)(139,205,150,193)(140,206,151,194)(141,207,152,195)(142,208,153,183)(143,196,154,184), (1,79)(2,80)(3,81)(4,82)(5,83)(6,84)(7,85)(8,86)(9,87)(10,88)(11,89)(12,90)(13,91)(14,92)(15,93)(16,94)(17,95)(18,96)(19,97)(20,98)(21,99)(22,100)(23,101)(24,102)(25,103)(26,104)(27,53)(28,54)(29,55)(30,56)(31,57)(32,58)(33,59)(34,60)(35,61)(36,62)(37,63)(38,64)(39,65)(40,66)(41,67)(42,68)(43,69)(44,70)(45,71)(46,72)(47,73)(48,74)(49,75)(50,76)(51,77)(52,78)(105,204)(106,205)(107,206)(108,207)(109,208)(110,196)(111,197)(112,198)(113,199)(114,200)(115,201)(116,202)(117,203)(118,188)(119,189)(120,190)(121,191)(122,192)(123,193)(124,194)(125,195)(126,183)(127,184)(128,185)(129,186)(130,187)(131,173)(132,174)(133,175)(134,176)(135,177)(136,178)(137,179)(138,180)(139,181)(140,182)(141,170)(142,171)(143,172)(144,167)(145,168)(146,169)(147,157)(148,158)(149,159)(150,160)(151,161)(152,162)(153,163)(154,164)(155,165)(156,166), (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), (1,105)(2,117)(3,116)(4,115)(5,114)(6,113)(7,112)(8,111)(9,110)(10,109)(11,108)(12,107)(13,106)(14,122)(15,121)(16,120)(17,119)(18,118)(19,130)(20,129)(21,128)(22,127)(23,126)(24,125)(25,124)(26,123)(27,138)(28,137)(29,136)(30,135)(31,134)(32,133)(33,132)(34,131)(35,143)(36,142)(37,141)(38,140)(39,139)(40,149)(41,148)(42,147)(43,146)(44,145)(45,144)(46,156)(47,155)(48,154)(49,153)(50,152)(51,151)(52,150)(53,159)(54,158)(55,157)(56,169)(57,168)(58,167)(59,166)(60,165)(61,164)(62,163)(63,162)(64,161)(65,160)(66,180)(67,179)(68,178)(69,177)(70,176)(71,175)(72,174)(73,173)(74,172)(75,171)(76,170)(77,182)(78,181)(79,192)(80,191)(81,190)(82,189)(83,188)(84,187)(85,186)(86,185)(87,184)(88,183)(89,195)(90,194)(91,193)(92,204)(93,203)(94,202)(95,201)(96,200)(97,199)(98,198)(99,197)(100,196)(101,208)(102,207)(103,206)(104,205) );
G=PermutationGroup([[(1,27),(2,28),(3,29),(4,30),(5,31),(6,32),(7,33),(8,34),(9,35),(10,36),(11,37),(12,38),(13,39),(14,40),(15,41),(16,42),(17,43),(18,44),(19,45),(20,46),(21,47),(22,48),(23,49),(24,50),(25,51),(26,52),(53,79),(54,80),(55,81),(56,82),(57,83),(58,84),(59,85),(60,86),(61,87),(62,88),(63,89),(64,90),(65,91),(66,92),(67,93),(68,94),(69,95),(70,96),(71,97),(72,98),(73,99),(74,100),(75,101),(76,102),(77,103),(78,104),(105,138),(106,139),(107,140),(108,141),(109,142),(110,143),(111,131),(112,132),(113,133),(114,134),(115,135),(116,136),(117,137),(118,145),(119,146),(120,147),(121,148),(122,149),(123,150),(124,151),(125,152),(126,153),(127,154),(128,155),(129,156),(130,144),(157,190),(158,191),(159,192),(160,193),(161,194),(162,195),(163,183),(164,184),(165,185),(166,186),(167,187),(168,188),(169,189),(170,207),(171,208),(172,196),(173,197),(174,198),(175,199),(176,200),(177,201),(178,202),(179,203),(180,204),(181,205),(182,206)], [(1,66,14,53),(2,67,15,54),(3,68,16,55),(4,69,17,56),(5,70,18,57),(6,71,19,58),(7,72,20,59),(8,73,21,60),(9,74,22,61),(10,75,23,62),(11,76,24,63),(12,77,25,64),(13,78,26,65),(27,92,40,79),(28,93,41,80),(29,94,42,81),(30,95,43,82),(31,96,44,83),(32,97,45,84),(33,98,46,85),(34,99,47,86),(35,100,48,87),(36,101,49,88),(37,102,50,89),(38,103,51,90),(39,104,52,91),(105,180,122,159),(106,181,123,160),(107,182,124,161),(108,170,125,162),(109,171,126,163),(110,172,127,164),(111,173,128,165),(112,174,129,166),(113,175,130,167),(114,176,118,168),(115,177,119,169),(116,178,120,157),(117,179,121,158),(131,197,155,185),(132,198,156,186),(133,199,144,187),(134,200,145,188),(135,201,146,189),(136,202,147,190),(137,203,148,191),(138,204,149,192),(139,205,150,193),(140,206,151,194),(141,207,152,195),(142,208,153,183),(143,196,154,184)], [(1,79),(2,80),(3,81),(4,82),(5,83),(6,84),(7,85),(8,86),(9,87),(10,88),(11,89),(12,90),(13,91),(14,92),(15,93),(16,94),(17,95),(18,96),(19,97),(20,98),(21,99),(22,100),(23,101),(24,102),(25,103),(26,104),(27,53),(28,54),(29,55),(30,56),(31,57),(32,58),(33,59),(34,60),(35,61),(36,62),(37,63),(38,64),(39,65),(40,66),(41,67),(42,68),(43,69),(44,70),(45,71),(46,72),(47,73),(48,74),(49,75),(50,76),(51,77),(52,78),(105,204),(106,205),(107,206),(108,207),(109,208),(110,196),(111,197),(112,198),(113,199),(114,200),(115,201),(116,202),(117,203),(118,188),(119,189),(120,190),(121,191),(122,192),(123,193),(124,194),(125,195),(126,183),(127,184),(128,185),(129,186),(130,187),(131,173),(132,174),(133,175),(134,176),(135,177),(136,178),(137,179),(138,180),(139,181),(140,182),(141,170),(142,171),(143,172),(144,167),(145,168),(146,169),(147,157),(148,158),(149,159),(150,160),(151,161),(152,162),(153,163),(154,164),(155,165),(156,166)], [(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)], [(1,105),(2,117),(3,116),(4,115),(5,114),(6,113),(7,112),(8,111),(9,110),(10,109),(11,108),(12,107),(13,106),(14,122),(15,121),(16,120),(17,119),(18,118),(19,130),(20,129),(21,128),(22,127),(23,126),(24,125),(25,124),(26,123),(27,138),(28,137),(29,136),(30,135),(31,134),(32,133),(33,132),(34,131),(35,143),(36,142),(37,141),(38,140),(39,139),(40,149),(41,148),(42,147),(43,146),(44,145),(45,144),(46,156),(47,155),(48,154),(49,153),(50,152),(51,151),(52,150),(53,159),(54,158),(55,157),(56,169),(57,168),(58,167),(59,166),(60,165),(61,164),(62,163),(63,162),(64,161),(65,160),(66,180),(67,179),(68,178),(69,177),(70,176),(71,175),(72,174),(73,173),(74,172),(75,171),(76,170),(77,182),(78,181),(79,192),(80,191),(81,190),(82,189),(83,188),(84,187),(85,186),(86,185),(87,184),(88,183),(89,195),(90,194),(91,193),(92,204),(93,203),(94,202),(95,201),(96,200),(97,199),(98,198),(99,197),(100,196),(101,208),(102,207),(103,206),(104,205)]])
80 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 13A | ··· | 13F | 26A | ··· | 26R | 26S | ··· | 26AP | 52A | ··· | 52L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 13 | ··· | 13 | 26 | ··· | 26 | 26 | ··· | 26 | 52 | ··· | 52 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 26 | 26 | 2 | 2 | 13 | 13 | 13 | 13 | 26 | 26 | 26 | 26 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
80 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C4○D4 | D13 | D26 | D26 | D26 | D4⋊2D13 |
| kernel | C2×D4⋊2D13 | C2×Dic26 | C2×C4×D13 | D4⋊2D13 | C22×Dic13 | C2×C13⋊D4 | D4×C26 | C26 | C2×D4 | C2×C4 | D4 | C23 | C2 |
| # reps | 1 | 1 | 1 | 8 | 2 | 2 | 1 | 4 | 6 | 6 | 24 | 12 | 12 |
Matrix representation of C2×D4⋊2D13 ►in GL4(𝔽53) generated by
| 52 | 0 | 0 | 0 |
| 0 | 52 | 0 | 0 |
| 0 | 0 | 52 | 0 |
| 0 | 0 | 0 | 52 |
| 52 | 0 | 0 | 0 |
| 0 | 52 | 0 | 0 |
| 0 | 0 | 1 | 21 |
| 0 | 0 | 10 | 52 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 52 | 32 |
| 0 | 0 | 0 | 1 |
| 0 | 52 | 0 | 0 |
| 1 | 38 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 41 | 6 | 0 | 0 |
| 38 | 12 | 0 | 0 |
| 0 | 0 | 30 | 47 |
| 0 | 0 | 35 | 23 |
G:=sub<GL(4,GF(53))| [52,0,0,0,0,52,0,0,0,0,52,0,0,0,0,52],[52,0,0,0,0,52,0,0,0,0,1,10,0,0,21,52],[1,0,0,0,0,1,0,0,0,0,52,0,0,0,32,1],[0,1,0,0,52,38,0,0,0,0,1,0,0,0,0,1],[41,38,0,0,6,12,0,0,0,0,30,35,0,0,47,23] >;
C2×D4⋊2D13 in GAP, Magma, Sage, TeX
C_2\times D_4\rtimes_2D_{13} % in TeX
G:=Group("C2xD4:2D13"); // GroupNames label
G:=SmallGroup(416,217);
// by ID
G=gap.SmallGroup(416,217);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-13,86,579,159,13829]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^4=c^2=d^13=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=b^-1,b*d=d*b,b*e=e*b,c*d=d*c,e*c*e=b^2*c,e*d*e=d^-1>;
// generators/relations