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## G = C2×D4⋊D13order 416 = 25·13

### Direct product of C2 and D4⋊D13

Series: Derived Chief Lower central Upper central

 Derived series C1 — C52 — C2×D4⋊D13
 Chief series C1 — C13 — C26 — C52 — D52 — C2×D52 — C2×D4⋊D13
 Lower central C13 — C26 — C52 — C2×D4⋊D13
 Upper central C1 — C22 — C2×C4 — C2×D4

Generators and relations for C2×D4⋊D13
G = < a,b,c,d,e | a2=b4=c2=d13=e2=1, ab=ba, ac=ca, ad=da, ae=ea, cbc=ebe=b-1, bd=db, cd=dc, ece=bc, ede=d-1 >

Subgroups: 560 in 76 conjugacy classes, 33 normal (17 characteristic)
C1, C2, C2 [×2], C2 [×4], C4 [×2], C22, C22 [×8], C8 [×2], C2×C4, D4 [×2], D4 [×4], C23 [×2], C13, C2×C8, D8 [×4], C2×D4, C2×D4, D13 [×2], C26, C26 [×2], C26 [×2], C2×D8, C52 [×2], D26 [×4], C2×C26, C2×C26 [×4], C132C8 [×2], D52 [×2], D52, C2×C52, D4×C13 [×2], D4×C13, C22×D13, C22×C26, C2×C132C8, D4⋊D13 [×4], C2×D52, D4×C26, C2×D4⋊D13
Quotients: C1, C2 [×7], C22 [×7], D4 [×2], C23, D8 [×2], C2×D4, D13, C2×D8, D26 [×3], C13⋊D4 [×2], C22×D13, D4⋊D13 [×2], C2×C13⋊D4, C2×D4⋊D13

Smallest permutation representation of C2×D4⋊D13
On 208 points
Generators in S208
(1 105)(2 106)(3 107)(4 108)(5 109)(6 110)(7 111)(8 112)(9 113)(10 114)(11 115)(12 116)(13 117)(14 118)(15 119)(16 120)(17 121)(18 122)(19 123)(20 124)(21 125)(22 126)(23 127)(24 128)(25 129)(26 130)(27 131)(28 132)(29 133)(30 134)(31 135)(32 136)(33 137)(34 138)(35 139)(36 140)(37 141)(38 142)(39 143)(40 144)(41 145)(42 146)(43 147)(44 148)(45 149)(46 150)(47 151)(48 152)(49 153)(50 154)(51 155)(52 156)(53 157)(54 158)(55 159)(56 160)(57 161)(58 162)(59 163)(60 164)(61 165)(62 166)(63 167)(64 168)(65 169)(66 170)(67 171)(68 172)(69 173)(70 174)(71 175)(72 176)(73 177)(74 178)(75 179)(76 180)(77 181)(78 182)(79 183)(80 184)(81 185)(82 186)(83 187)(84 188)(85 189)(86 190)(87 191)(88 192)(89 193)(90 194)(91 195)(92 196)(93 197)(94 198)(95 199)(96 200)(97 201)(98 202)(99 203)(100 204)(101 205)(102 206)(103 207)(104 208)
(1 40 14 27)(2 41 15 28)(3 42 16 29)(4 43 17 30)(5 44 18 31)(6 45 19 32)(7 46 20 33)(8 47 21 34)(9 48 22 35)(10 49 23 36)(11 50 24 37)(12 51 25 38)(13 52 26 39)(53 79 66 92)(54 80 67 93)(55 81 68 94)(56 82 69 95)(57 83 70 96)(58 84 71 97)(59 85 72 98)(60 86 73 99)(61 87 74 100)(62 88 75 101)(63 89 76 102)(64 90 77 103)(65 91 78 104)(105 144 118 131)(106 145 119 132)(107 146 120 133)(108 147 121 134)(109 148 122 135)(110 149 123 136)(111 150 124 137)(112 151 125 138)(113 152 126 139)(114 153 127 140)(115 154 128 141)(116 155 129 142)(117 156 130 143)(157 183 170 196)(158 184 171 197)(159 185 172 198)(160 186 173 199)(161 187 174 200)(162 188 175 201)(163 189 176 202)(164 190 177 203)(165 191 178 204)(166 192 179 205)(167 193 180 206)(168 194 181 207)(169 195 182 208)
(1 196)(2 197)(3 198)(4 199)(5 200)(6 201)(7 202)(8 203)(9 204)(10 205)(11 206)(12 207)(13 208)(14 183)(15 184)(16 185)(17 186)(18 187)(19 188)(20 189)(21 190)(22 191)(23 192)(24 193)(25 194)(26 195)(27 157)(28 158)(29 159)(30 160)(31 161)(32 162)(33 163)(34 164)(35 165)(36 166)(37 167)(38 168)(39 169)(40 170)(41 171)(42 172)(43 173)(44 174)(45 175)(46 176)(47 177)(48 178)(49 179)(50 180)(51 181)(52 182)(53 131)(54 132)(55 133)(56 134)(57 135)(58 136)(59 137)(60 138)(61 139)(62 140)(63 141)(64 142)(65 143)(66 144)(67 145)(68 146)(69 147)(70 148)(71 149)(72 150)(73 151)(74 152)(75 153)(76 154)(77 155)(78 156)(79 118)(80 119)(81 120)(82 121)(83 122)(84 123)(85 124)(86 125)(87 126)(88 127)(89 128)(90 129)(91 130)(92 105)(93 106)(94 107)(95 108)(96 109)(97 110)(98 111)(99 112)(100 113)(101 114)(102 115)(103 116)(104 117)
(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)
(1 117)(2 116)(3 115)(4 114)(5 113)(6 112)(7 111)(8 110)(9 109)(10 108)(11 107)(12 106)(13 105)(14 130)(15 129)(16 128)(17 127)(18 126)(19 125)(20 124)(21 123)(22 122)(23 121)(24 120)(25 119)(26 118)(27 156)(28 155)(29 154)(30 153)(31 152)(32 151)(33 150)(34 149)(35 148)(36 147)(37 146)(38 145)(39 144)(40 143)(41 142)(42 141)(43 140)(44 139)(45 138)(46 137)(47 136)(48 135)(49 134)(50 133)(51 132)(52 131)(53 195)(54 194)(55 193)(56 192)(57 191)(58 190)(59 189)(60 188)(61 187)(62 186)(63 185)(64 184)(65 183)(66 208)(67 207)(68 206)(69 205)(70 204)(71 203)(72 202)(73 201)(74 200)(75 199)(76 198)(77 197)(78 196)(79 169)(80 168)(81 167)(82 166)(83 165)(84 164)(85 163)(86 162)(87 161)(88 160)(89 159)(90 158)(91 157)(92 182)(93 181)(94 180)(95 179)(96 178)(97 177)(98 176)(99 175)(100 174)(101 173)(102 172)(103 171)(104 170)

G:=sub<Sym(208)| (1,105)(2,106)(3,107)(4,108)(5,109)(6,110)(7,111)(8,112)(9,113)(10,114)(11,115)(12,116)(13,117)(14,118)(15,119)(16,120)(17,121)(18,122)(19,123)(20,124)(21,125)(22,126)(23,127)(24,128)(25,129)(26,130)(27,131)(28,132)(29,133)(30,134)(31,135)(32,136)(33,137)(34,138)(35,139)(36,140)(37,141)(38,142)(39,143)(40,144)(41,145)(42,146)(43,147)(44,148)(45,149)(46,150)(47,151)(48,152)(49,153)(50,154)(51,155)(52,156)(53,157)(54,158)(55,159)(56,160)(57,161)(58,162)(59,163)(60,164)(61,165)(62,166)(63,167)(64,168)(65,169)(66,170)(67,171)(68,172)(69,173)(70,174)(71,175)(72,176)(73,177)(74,178)(75,179)(76,180)(77,181)(78,182)(79,183)(80,184)(81,185)(82,186)(83,187)(84,188)(85,189)(86,190)(87,191)(88,192)(89,193)(90,194)(91,195)(92,196)(93,197)(94,198)(95,199)(96,200)(97,201)(98,202)(99,203)(100,204)(101,205)(102,206)(103,207)(104,208), (1,40,14,27)(2,41,15,28)(3,42,16,29)(4,43,17,30)(5,44,18,31)(6,45,19,32)(7,46,20,33)(8,47,21,34)(9,48,22,35)(10,49,23,36)(11,50,24,37)(12,51,25,38)(13,52,26,39)(53,79,66,92)(54,80,67,93)(55,81,68,94)(56,82,69,95)(57,83,70,96)(58,84,71,97)(59,85,72,98)(60,86,73,99)(61,87,74,100)(62,88,75,101)(63,89,76,102)(64,90,77,103)(65,91,78,104)(105,144,118,131)(106,145,119,132)(107,146,120,133)(108,147,121,134)(109,148,122,135)(110,149,123,136)(111,150,124,137)(112,151,125,138)(113,152,126,139)(114,153,127,140)(115,154,128,141)(116,155,129,142)(117,156,130,143)(157,183,170,196)(158,184,171,197)(159,185,172,198)(160,186,173,199)(161,187,174,200)(162,188,175,201)(163,189,176,202)(164,190,177,203)(165,191,178,204)(166,192,179,205)(167,193,180,206)(168,194,181,207)(169,195,182,208), (1,196)(2,197)(3,198)(4,199)(5,200)(6,201)(7,202)(8,203)(9,204)(10,205)(11,206)(12,207)(13,208)(14,183)(15,184)(16,185)(17,186)(18,187)(19,188)(20,189)(21,190)(22,191)(23,192)(24,193)(25,194)(26,195)(27,157)(28,158)(29,159)(30,160)(31,161)(32,162)(33,163)(34,164)(35,165)(36,166)(37,167)(38,168)(39,169)(40,170)(41,171)(42,172)(43,173)(44,174)(45,175)(46,176)(47,177)(48,178)(49,179)(50,180)(51,181)(52,182)(53,131)(54,132)(55,133)(56,134)(57,135)(58,136)(59,137)(60,138)(61,139)(62,140)(63,141)(64,142)(65,143)(66,144)(67,145)(68,146)(69,147)(70,148)(71,149)(72,150)(73,151)(74,152)(75,153)(76,154)(77,155)(78,156)(79,118)(80,119)(81,120)(82,121)(83,122)(84,123)(85,124)(86,125)(87,126)(88,127)(89,128)(90,129)(91,130)(92,105)(93,106)(94,107)(95,108)(96,109)(97,110)(98,111)(99,112)(100,113)(101,114)(102,115)(103,116)(104,117), (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), (1,117)(2,116)(3,115)(4,114)(5,113)(6,112)(7,111)(8,110)(9,109)(10,108)(11,107)(12,106)(13,105)(14,130)(15,129)(16,128)(17,127)(18,126)(19,125)(20,124)(21,123)(22,122)(23,121)(24,120)(25,119)(26,118)(27,156)(28,155)(29,154)(30,153)(31,152)(32,151)(33,150)(34,149)(35,148)(36,147)(37,146)(38,145)(39,144)(40,143)(41,142)(42,141)(43,140)(44,139)(45,138)(46,137)(47,136)(48,135)(49,134)(50,133)(51,132)(52,131)(53,195)(54,194)(55,193)(56,192)(57,191)(58,190)(59,189)(60,188)(61,187)(62,186)(63,185)(64,184)(65,183)(66,208)(67,207)(68,206)(69,205)(70,204)(71,203)(72,202)(73,201)(74,200)(75,199)(76,198)(77,197)(78,196)(79,169)(80,168)(81,167)(82,166)(83,165)(84,164)(85,163)(86,162)(87,161)(88,160)(89,159)(90,158)(91,157)(92,182)(93,181)(94,180)(95,179)(96,178)(97,177)(98,176)(99,175)(100,174)(101,173)(102,172)(103,171)(104,170)>;

G:=Group( (1,105)(2,106)(3,107)(4,108)(5,109)(6,110)(7,111)(8,112)(9,113)(10,114)(11,115)(12,116)(13,117)(14,118)(15,119)(16,120)(17,121)(18,122)(19,123)(20,124)(21,125)(22,126)(23,127)(24,128)(25,129)(26,130)(27,131)(28,132)(29,133)(30,134)(31,135)(32,136)(33,137)(34,138)(35,139)(36,140)(37,141)(38,142)(39,143)(40,144)(41,145)(42,146)(43,147)(44,148)(45,149)(46,150)(47,151)(48,152)(49,153)(50,154)(51,155)(52,156)(53,157)(54,158)(55,159)(56,160)(57,161)(58,162)(59,163)(60,164)(61,165)(62,166)(63,167)(64,168)(65,169)(66,170)(67,171)(68,172)(69,173)(70,174)(71,175)(72,176)(73,177)(74,178)(75,179)(76,180)(77,181)(78,182)(79,183)(80,184)(81,185)(82,186)(83,187)(84,188)(85,189)(86,190)(87,191)(88,192)(89,193)(90,194)(91,195)(92,196)(93,197)(94,198)(95,199)(96,200)(97,201)(98,202)(99,203)(100,204)(101,205)(102,206)(103,207)(104,208), (1,40,14,27)(2,41,15,28)(3,42,16,29)(4,43,17,30)(5,44,18,31)(6,45,19,32)(7,46,20,33)(8,47,21,34)(9,48,22,35)(10,49,23,36)(11,50,24,37)(12,51,25,38)(13,52,26,39)(53,79,66,92)(54,80,67,93)(55,81,68,94)(56,82,69,95)(57,83,70,96)(58,84,71,97)(59,85,72,98)(60,86,73,99)(61,87,74,100)(62,88,75,101)(63,89,76,102)(64,90,77,103)(65,91,78,104)(105,144,118,131)(106,145,119,132)(107,146,120,133)(108,147,121,134)(109,148,122,135)(110,149,123,136)(111,150,124,137)(112,151,125,138)(113,152,126,139)(114,153,127,140)(115,154,128,141)(116,155,129,142)(117,156,130,143)(157,183,170,196)(158,184,171,197)(159,185,172,198)(160,186,173,199)(161,187,174,200)(162,188,175,201)(163,189,176,202)(164,190,177,203)(165,191,178,204)(166,192,179,205)(167,193,180,206)(168,194,181,207)(169,195,182,208), (1,196)(2,197)(3,198)(4,199)(5,200)(6,201)(7,202)(8,203)(9,204)(10,205)(11,206)(12,207)(13,208)(14,183)(15,184)(16,185)(17,186)(18,187)(19,188)(20,189)(21,190)(22,191)(23,192)(24,193)(25,194)(26,195)(27,157)(28,158)(29,159)(30,160)(31,161)(32,162)(33,163)(34,164)(35,165)(36,166)(37,167)(38,168)(39,169)(40,170)(41,171)(42,172)(43,173)(44,174)(45,175)(46,176)(47,177)(48,178)(49,179)(50,180)(51,181)(52,182)(53,131)(54,132)(55,133)(56,134)(57,135)(58,136)(59,137)(60,138)(61,139)(62,140)(63,141)(64,142)(65,143)(66,144)(67,145)(68,146)(69,147)(70,148)(71,149)(72,150)(73,151)(74,152)(75,153)(76,154)(77,155)(78,156)(79,118)(80,119)(81,120)(82,121)(83,122)(84,123)(85,124)(86,125)(87,126)(88,127)(89,128)(90,129)(91,130)(92,105)(93,106)(94,107)(95,108)(96,109)(97,110)(98,111)(99,112)(100,113)(101,114)(102,115)(103,116)(104,117), (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), (1,117)(2,116)(3,115)(4,114)(5,113)(6,112)(7,111)(8,110)(9,109)(10,108)(11,107)(12,106)(13,105)(14,130)(15,129)(16,128)(17,127)(18,126)(19,125)(20,124)(21,123)(22,122)(23,121)(24,120)(25,119)(26,118)(27,156)(28,155)(29,154)(30,153)(31,152)(32,151)(33,150)(34,149)(35,148)(36,147)(37,146)(38,145)(39,144)(40,143)(41,142)(42,141)(43,140)(44,139)(45,138)(46,137)(47,136)(48,135)(49,134)(50,133)(51,132)(52,131)(53,195)(54,194)(55,193)(56,192)(57,191)(58,190)(59,189)(60,188)(61,187)(62,186)(63,185)(64,184)(65,183)(66,208)(67,207)(68,206)(69,205)(70,204)(71,203)(72,202)(73,201)(74,200)(75,199)(76,198)(77,197)(78,196)(79,169)(80,168)(81,167)(82,166)(83,165)(84,164)(85,163)(86,162)(87,161)(88,160)(89,159)(90,158)(91,157)(92,182)(93,181)(94,180)(95,179)(96,178)(97,177)(98,176)(99,175)(100,174)(101,173)(102,172)(103,171)(104,170) );

G=PermutationGroup([(1,105),(2,106),(3,107),(4,108),(5,109),(6,110),(7,111),(8,112),(9,113),(10,114),(11,115),(12,116),(13,117),(14,118),(15,119),(16,120),(17,121),(18,122),(19,123),(20,124),(21,125),(22,126),(23,127),(24,128),(25,129),(26,130),(27,131),(28,132),(29,133),(30,134),(31,135),(32,136),(33,137),(34,138),(35,139),(36,140),(37,141),(38,142),(39,143),(40,144),(41,145),(42,146),(43,147),(44,148),(45,149),(46,150),(47,151),(48,152),(49,153),(50,154),(51,155),(52,156),(53,157),(54,158),(55,159),(56,160),(57,161),(58,162),(59,163),(60,164),(61,165),(62,166),(63,167),(64,168),(65,169),(66,170),(67,171),(68,172),(69,173),(70,174),(71,175),(72,176),(73,177),(74,178),(75,179),(76,180),(77,181),(78,182),(79,183),(80,184),(81,185),(82,186),(83,187),(84,188),(85,189),(86,190),(87,191),(88,192),(89,193),(90,194),(91,195),(92,196),(93,197),(94,198),(95,199),(96,200),(97,201),(98,202),(99,203),(100,204),(101,205),(102,206),(103,207),(104,208)], [(1,40,14,27),(2,41,15,28),(3,42,16,29),(4,43,17,30),(5,44,18,31),(6,45,19,32),(7,46,20,33),(8,47,21,34),(9,48,22,35),(10,49,23,36),(11,50,24,37),(12,51,25,38),(13,52,26,39),(53,79,66,92),(54,80,67,93),(55,81,68,94),(56,82,69,95),(57,83,70,96),(58,84,71,97),(59,85,72,98),(60,86,73,99),(61,87,74,100),(62,88,75,101),(63,89,76,102),(64,90,77,103),(65,91,78,104),(105,144,118,131),(106,145,119,132),(107,146,120,133),(108,147,121,134),(109,148,122,135),(110,149,123,136),(111,150,124,137),(112,151,125,138),(113,152,126,139),(114,153,127,140),(115,154,128,141),(116,155,129,142),(117,156,130,143),(157,183,170,196),(158,184,171,197),(159,185,172,198),(160,186,173,199),(161,187,174,200),(162,188,175,201),(163,189,176,202),(164,190,177,203),(165,191,178,204),(166,192,179,205),(167,193,180,206),(168,194,181,207),(169,195,182,208)], [(1,196),(2,197),(3,198),(4,199),(5,200),(6,201),(7,202),(8,203),(9,204),(10,205),(11,206),(12,207),(13,208),(14,183),(15,184),(16,185),(17,186),(18,187),(19,188),(20,189),(21,190),(22,191),(23,192),(24,193),(25,194),(26,195),(27,157),(28,158),(29,159),(30,160),(31,161),(32,162),(33,163),(34,164),(35,165),(36,166),(37,167),(38,168),(39,169),(40,170),(41,171),(42,172),(43,173),(44,174),(45,175),(46,176),(47,177),(48,178),(49,179),(50,180),(51,181),(52,182),(53,131),(54,132),(55,133),(56,134),(57,135),(58,136),(59,137),(60,138),(61,139),(62,140),(63,141),(64,142),(65,143),(66,144),(67,145),(68,146),(69,147),(70,148),(71,149),(72,150),(73,151),(74,152),(75,153),(76,154),(77,155),(78,156),(79,118),(80,119),(81,120),(82,121),(83,122),(84,123),(85,124),(86,125),(87,126),(88,127),(89,128),(90,129),(91,130),(92,105),(93,106),(94,107),(95,108),(96,109),(97,110),(98,111),(99,112),(100,113),(101,114),(102,115),(103,116),(104,117)], [(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)], [(1,117),(2,116),(3,115),(4,114),(5,113),(6,112),(7,111),(8,110),(9,109),(10,108),(11,107),(12,106),(13,105),(14,130),(15,129),(16,128),(17,127),(18,126),(19,125),(20,124),(21,123),(22,122),(23,121),(24,120),(25,119),(26,118),(27,156),(28,155),(29,154),(30,153),(31,152),(32,151),(33,150),(34,149),(35,148),(36,147),(37,146),(38,145),(39,144),(40,143),(41,142),(42,141),(43,140),(44,139),(45,138),(46,137),(47,136),(48,135),(49,134),(50,133),(51,132),(52,131),(53,195),(54,194),(55,193),(56,192),(57,191),(58,190),(59,189),(60,188),(61,187),(62,186),(63,185),(64,184),(65,183),(66,208),(67,207),(68,206),(69,205),(70,204),(71,203),(72,202),(73,201),(74,200),(75,199),(76,198),(77,197),(78,196),(79,169),(80,168),(81,167),(82,166),(83,165),(84,164),(85,163),(86,162),(87,161),(88,160),(89,159),(90,158),(91,157),(92,182),(93,181),(94,180),(95,179),(96,178),(97,177),(98,176),(99,175),(100,174),(101,173),(102,172),(103,171),(104,170)])

74 conjugacy classes

 class 1 2A 2B 2C 2D 2E 2F 2G 4A 4B 8A 8B 8C 8D 13A ··· 13F 26A ··· 26R 26S ··· 26AP 52A ··· 52L order 1 2 2 2 2 2 2 2 4 4 8 8 8 8 13 ··· 13 26 ··· 26 26 ··· 26 52 ··· 52 size 1 1 1 1 4 4 52 52 2 2 26 26 26 26 2 ··· 2 2 ··· 2 4 ··· 4 4 ··· 4

74 irreducible representations

 dim 1 1 1 1 1 2 2 2 2 2 2 2 2 4 type + + + + + + + + + + + + image C1 C2 C2 C2 C2 D4 D4 D8 D13 D26 D26 C13⋊D4 C13⋊D4 D4⋊D13 kernel C2×D4⋊D13 C2×C13⋊2C8 D4⋊D13 C2×D52 D4×C26 C52 C2×C26 C26 C2×D4 C2×C4 D4 C4 C22 C2 # reps 1 1 4 1 1 1 1 4 6 6 12 12 12 12

Matrix representation of C2×D4⋊D13 in GL4(𝔽313) generated by

 312 0 0 0 0 312 0 0 0 0 312 0 0 0 0 312
,
 1 0 0 0 0 1 0 0 0 0 0 1 0 0 312 0
,
 312 0 0 0 0 312 0 0 0 0 60 253 0 0 253 253
,
 0 312 0 0 1 24 0 0 0 0 1 0 0 0 0 1
,
 24 1 0 0 51 289 0 0 0 0 312 0 0 0 0 1
G:=sub<GL(4,GF(313))| [312,0,0,0,0,312,0,0,0,0,312,0,0,0,0,312],[1,0,0,0,0,1,0,0,0,0,0,312,0,0,1,0],[312,0,0,0,0,312,0,0,0,0,60,253,0,0,253,253],[0,1,0,0,312,24,0,0,0,0,1,0,0,0,0,1],[24,51,0,0,1,289,0,0,0,0,312,0,0,0,0,1] >;

C2×D4⋊D13 in GAP, Magma, Sage, TeX

C_2\times D_4\rtimes D_{13}
% in TeX

G:=Group("C2xD4:D13");
// GroupNames label

G:=SmallGroup(416,152);
// by ID

G=gap.SmallGroup(416,152);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-2,-13,218,579,159,69,13829]);
// 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=e*b*e=b^-1,b*d=d*b,c*d=d*c,e*c*e=b*c,e*d*e=d^-1>;
// generators/relations

׿
×
𝔽