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G = C2×D42D13order 416 = 25·13

Direct product of C2 and D42D13

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C2×D42D13, D45D26, C26.6C24, C52.20C23, D26.2C23, C23.19D26, Dic267C22, Dic13.3C23, (C2×D4)⋊8D13, (D4×C26)⋊6C2, C262(C4○D4), (C2×C4).60D26, (C4×D13)⋊4C22, (D4×C13)⋊6C22, C13⋊D42C22, (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, C132(C2×C4○D4), (C2×C13⋊D4)⋊10C2, SmallGroup(416,217)

Series: Derived Chief Lower central Upper central

C1C26 — C2×D42D13
C1C13C26D26C22×D13C2×C4×D13 — C2×D42D13
C13C26 — C2×D42D13
C1C22C2×D4

Generators and relations for C2×D42D13
 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 [×2], C2 [×6], C4 [×2], C4 [×6], C22, C22 [×4], C22 [×8], C2×C4, C2×C4 [×15], D4 [×4], D4 [×8], Q8 [×4], C23 [×2], C23, C13, C22×C4 [×3], C2×D4, C2×D4 [×2], C2×Q8, C4○D4 [×8], D13 [×2], C26, C26 [×2], C26 [×4], C2×C4○D4, Dic13 [×6], C52 [×2], D26 [×2], D26 [×2], C2×C26, C2×C26 [×4], C2×C26 [×4], Dic26 [×4], C4×D13 [×4], C2×Dic13, C2×Dic13 [×10], C13⋊D4 [×8], C2×C52, D4×C13 [×4], C22×D13, C22×C26 [×2], C2×Dic26, C2×C4×D13, D42D13 [×8], C22×Dic13 [×2], C2×C13⋊D4 [×2], D4×C26, C2×D42D13
Quotients: C1, C2 [×15], C22 [×35], C23 [×15], C4○D4 [×2], C24, D13, C2×C4○D4, D26 [×7], C22×D13 [×7], D42D13 [×2], C23×D13, C2×D42D13

Smallest permutation representation of C2×D42D13
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)(105 131)(106 132)(107 133)(108 134)(109 135)(110 136)(111 137)(112 138)(113 139)(114 140)(115 141)(116 142)(117 143)(118 144)(119 145)(120 146)(121 147)(122 148)(123 149)(124 150)(125 151)(126 152)(127 153)(128 154)(129 155)(130 156)(157 183)(158 184)(159 185)(160 186)(161 187)(162 188)(163 189)(164 190)(165 191)(166 192)(167 193)(168 194)(169 195)(170 196)(171 197)(172 198)(173 199)(174 200)(175 201)(176 202)(177 203)(178 204)(179 205)(180 206)(181 207)(182 208)
(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)(105 170 118 157)(106 171 119 158)(107 172 120 159)(108 173 121 160)(109 174 122 161)(110 175 123 162)(111 176 124 163)(112 177 125 164)(113 178 126 165)(114 179 127 166)(115 180 128 167)(116 181 129 168)(117 182 130 169)(131 196 144 183)(132 197 145 184)(133 198 146 185)(134 199 147 186)(135 200 148 187)(136 201 149 188)(137 202 150 189)(138 203 151 190)(139 204 152 191)(140 205 153 192)(141 206 154 193)(142 207 155 194)(143 208 156 195)
(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)(105 196)(106 197)(107 198)(108 199)(109 200)(110 201)(111 202)(112 203)(113 204)(114 205)(115 206)(116 207)(117 208)(118 183)(119 184)(120 185)(121 186)(122 187)(123 188)(124 189)(125 190)(126 191)(127 192)(128 193)(129 194)(130 195)(131 170)(132 171)(133 172)(134 173)(135 174)(136 175)(137 176)(138 177)(139 178)(140 179)(141 180)(142 181)(143 182)(144 157)(145 158)(146 159)(147 160)(148 161)(149 162)(150 163)(151 164)(152 165)(153 166)(154 167)(155 168)(156 169)
(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)
(1 115)(2 114)(3 113)(4 112)(5 111)(6 110)(7 109)(8 108)(9 107)(10 106)(11 105)(12 117)(13 116)(14 128)(15 127)(16 126)(17 125)(18 124)(19 123)(20 122)(21 121)(22 120)(23 119)(24 118)(25 130)(26 129)(27 141)(28 140)(29 139)(30 138)(31 137)(32 136)(33 135)(34 134)(35 133)(36 132)(37 131)(38 143)(39 142)(40 154)(41 153)(42 152)(43 151)(44 150)(45 149)(46 148)(47 147)(48 146)(49 145)(50 144)(51 156)(52 155)(53 167)(54 166)(55 165)(56 164)(57 163)(58 162)(59 161)(60 160)(61 159)(62 158)(63 157)(64 169)(65 168)(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)(79 193)(80 192)(81 191)(82 190)(83 189)(84 188)(85 187)(86 186)(87 185)(88 184)(89 183)(90 195)(91 194)(92 206)(93 205)(94 204)(95 203)(96 202)(97 201)(98 200)(99 199)(100 198)(101 197)(102 196)(103 208)(104 207)

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)(105,131)(106,132)(107,133)(108,134)(109,135)(110,136)(111,137)(112,138)(113,139)(114,140)(115,141)(116,142)(117,143)(118,144)(119,145)(120,146)(121,147)(122,148)(123,149)(124,150)(125,151)(126,152)(127,153)(128,154)(129,155)(130,156)(157,183)(158,184)(159,185)(160,186)(161,187)(162,188)(163,189)(164,190)(165,191)(166,192)(167,193)(168,194)(169,195)(170,196)(171,197)(172,198)(173,199)(174,200)(175,201)(176,202)(177,203)(178,204)(179,205)(180,206)(181,207)(182,208), (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)(105,170,118,157)(106,171,119,158)(107,172,120,159)(108,173,121,160)(109,174,122,161)(110,175,123,162)(111,176,124,163)(112,177,125,164)(113,178,126,165)(114,179,127,166)(115,180,128,167)(116,181,129,168)(117,182,130,169)(131,196,144,183)(132,197,145,184)(133,198,146,185)(134,199,147,186)(135,200,148,187)(136,201,149,188)(137,202,150,189)(138,203,151,190)(139,204,152,191)(140,205,153,192)(141,206,154,193)(142,207,155,194)(143,208,156,195), (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)(105,196)(106,197)(107,198)(108,199)(109,200)(110,201)(111,202)(112,203)(113,204)(114,205)(115,206)(116,207)(117,208)(118,183)(119,184)(120,185)(121,186)(122,187)(123,188)(124,189)(125,190)(126,191)(127,192)(128,193)(129,194)(130,195)(131,170)(132,171)(133,172)(134,173)(135,174)(136,175)(137,176)(138,177)(139,178)(140,179)(141,180)(142,181)(143,182)(144,157)(145,158)(146,159)(147,160)(148,161)(149,162)(150,163)(151,164)(152,165)(153,166)(154,167)(155,168)(156,169), (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), (1,115)(2,114)(3,113)(4,112)(5,111)(6,110)(7,109)(8,108)(9,107)(10,106)(11,105)(12,117)(13,116)(14,128)(15,127)(16,126)(17,125)(18,124)(19,123)(20,122)(21,121)(22,120)(23,119)(24,118)(25,130)(26,129)(27,141)(28,140)(29,139)(30,138)(31,137)(32,136)(33,135)(34,134)(35,133)(36,132)(37,131)(38,143)(39,142)(40,154)(41,153)(42,152)(43,151)(44,150)(45,149)(46,148)(47,147)(48,146)(49,145)(50,144)(51,156)(52,155)(53,167)(54,166)(55,165)(56,164)(57,163)(58,162)(59,161)(60,160)(61,159)(62,158)(63,157)(64,169)(65,168)(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)(79,193)(80,192)(81,191)(82,190)(83,189)(84,188)(85,187)(86,186)(87,185)(88,184)(89,183)(90,195)(91,194)(92,206)(93,205)(94,204)(95,203)(96,202)(97,201)(98,200)(99,199)(100,198)(101,197)(102,196)(103,208)(104,207)>;

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)(105,131)(106,132)(107,133)(108,134)(109,135)(110,136)(111,137)(112,138)(113,139)(114,140)(115,141)(116,142)(117,143)(118,144)(119,145)(120,146)(121,147)(122,148)(123,149)(124,150)(125,151)(126,152)(127,153)(128,154)(129,155)(130,156)(157,183)(158,184)(159,185)(160,186)(161,187)(162,188)(163,189)(164,190)(165,191)(166,192)(167,193)(168,194)(169,195)(170,196)(171,197)(172,198)(173,199)(174,200)(175,201)(176,202)(177,203)(178,204)(179,205)(180,206)(181,207)(182,208), (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)(105,170,118,157)(106,171,119,158)(107,172,120,159)(108,173,121,160)(109,174,122,161)(110,175,123,162)(111,176,124,163)(112,177,125,164)(113,178,126,165)(114,179,127,166)(115,180,128,167)(116,181,129,168)(117,182,130,169)(131,196,144,183)(132,197,145,184)(133,198,146,185)(134,199,147,186)(135,200,148,187)(136,201,149,188)(137,202,150,189)(138,203,151,190)(139,204,152,191)(140,205,153,192)(141,206,154,193)(142,207,155,194)(143,208,156,195), (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)(105,196)(106,197)(107,198)(108,199)(109,200)(110,201)(111,202)(112,203)(113,204)(114,205)(115,206)(116,207)(117,208)(118,183)(119,184)(120,185)(121,186)(122,187)(123,188)(124,189)(125,190)(126,191)(127,192)(128,193)(129,194)(130,195)(131,170)(132,171)(133,172)(134,173)(135,174)(136,175)(137,176)(138,177)(139,178)(140,179)(141,180)(142,181)(143,182)(144,157)(145,158)(146,159)(147,160)(148,161)(149,162)(150,163)(151,164)(152,165)(153,166)(154,167)(155,168)(156,169), (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), (1,115)(2,114)(3,113)(4,112)(5,111)(6,110)(7,109)(8,108)(9,107)(10,106)(11,105)(12,117)(13,116)(14,128)(15,127)(16,126)(17,125)(18,124)(19,123)(20,122)(21,121)(22,120)(23,119)(24,118)(25,130)(26,129)(27,141)(28,140)(29,139)(30,138)(31,137)(32,136)(33,135)(34,134)(35,133)(36,132)(37,131)(38,143)(39,142)(40,154)(41,153)(42,152)(43,151)(44,150)(45,149)(46,148)(47,147)(48,146)(49,145)(50,144)(51,156)(52,155)(53,167)(54,166)(55,165)(56,164)(57,163)(58,162)(59,161)(60,160)(61,159)(62,158)(63,157)(64,169)(65,168)(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)(79,193)(80,192)(81,191)(82,190)(83,189)(84,188)(85,187)(86,186)(87,185)(88,184)(89,183)(90,195)(91,194)(92,206)(93,205)(94,204)(95,203)(96,202)(97,201)(98,200)(99,199)(100,198)(101,197)(102,196)(103,208)(104,207) );

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),(105,131),(106,132),(107,133),(108,134),(109,135),(110,136),(111,137),(112,138),(113,139),(114,140),(115,141),(116,142),(117,143),(118,144),(119,145),(120,146),(121,147),(122,148),(123,149),(124,150),(125,151),(126,152),(127,153),(128,154),(129,155),(130,156),(157,183),(158,184),(159,185),(160,186),(161,187),(162,188),(163,189),(164,190),(165,191),(166,192),(167,193),(168,194),(169,195),(170,196),(171,197),(172,198),(173,199),(174,200),(175,201),(176,202),(177,203),(178,204),(179,205),(180,206),(181,207),(182,208)], [(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),(105,170,118,157),(106,171,119,158),(107,172,120,159),(108,173,121,160),(109,174,122,161),(110,175,123,162),(111,176,124,163),(112,177,125,164),(113,178,126,165),(114,179,127,166),(115,180,128,167),(116,181,129,168),(117,182,130,169),(131,196,144,183),(132,197,145,184),(133,198,146,185),(134,199,147,186),(135,200,148,187),(136,201,149,188),(137,202,150,189),(138,203,151,190),(139,204,152,191),(140,205,153,192),(141,206,154,193),(142,207,155,194),(143,208,156,195)], [(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),(105,196),(106,197),(107,198),(108,199),(109,200),(110,201),(111,202),(112,203),(113,204),(114,205),(115,206),(116,207),(117,208),(118,183),(119,184),(120,185),(121,186),(122,187),(123,188),(124,189),(125,190),(126,191),(127,192),(128,193),(129,194),(130,195),(131,170),(132,171),(133,172),(134,173),(135,174),(136,175),(137,176),(138,177),(139,178),(140,179),(141,180),(142,181),(143,182),(144,157),(145,158),(146,159),(147,160),(148,161),(149,162),(150,163),(151,164),(152,165),(153,166),(154,167),(155,168),(156,169)], [(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)], [(1,115),(2,114),(3,113),(4,112),(5,111),(6,110),(7,109),(8,108),(9,107),(10,106),(11,105),(12,117),(13,116),(14,128),(15,127),(16,126),(17,125),(18,124),(19,123),(20,122),(21,121),(22,120),(23,119),(24,118),(25,130),(26,129),(27,141),(28,140),(29,139),(30,138),(31,137),(32,136),(33,135),(34,134),(35,133),(36,132),(37,131),(38,143),(39,142),(40,154),(41,153),(42,152),(43,151),(44,150),(45,149),(46,148),(47,147),(48,146),(49,145),(50,144),(51,156),(52,155),(53,167),(54,166),(55,165),(56,164),(57,163),(58,162),(59,161),(60,160),(61,159),(62,158),(63,157),(64,169),(65,168),(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),(79,193),(80,192),(81,191),(82,190),(83,189),(84,188),(85,187),(86,186),(87,185),(88,184),(89,183),(90,195),(91,194),(92,206),(93,205),(94,204),(95,203),(96,202),(97,201),(98,200),(99,199),(100,198),(101,197),(102,196),(103,208),(104,207)])

80 conjugacy classes

class 1 2A2B2C2D2E2F2G2H2I4A4B4C4D4E4F4G4H4I4J13A···13F26A···26R26S···26AP52A···52L
order1222222222444444444413···1326···2626···2652···52
size1111222226262213131313262626262···22···24···44···4

80 irreducible representations

dim1111111222224
type+++++++++++-
imageC1C2C2C2C2C2C2C4○D4D13D26D26D26D42D13
kernelC2×D42D13C2×Dic26C2×C4×D13D42D13C22×Dic13C2×C13⋊D4D4×C26C26C2×D4C2×C4D4C23C2
# reps1118221466241212

Matrix representation of C2×D42D13 in GL4(𝔽53) generated by

52000
05200
00520
00052
,
52000
05200
00121
001052
,
1000
0100
005232
0001
,
05200
13800
0010
0001
,
41600
381200
003047
003523
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×D42D13 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

׿
×
𝔽