direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Q8⋊D13, Q8⋊3D26, C26⋊3SD16, C52.18D4, C52.14C23, D52.9C22, (Q8×C26)⋊1C2, (C2×Q8)⋊1D13, C13⋊4(C2×SD16), (C2×D52).9C2, C26.53(C2×D4), (C2×C4).53D26, (C2×C26).41D4, C13⋊2C8⋊9C22, C4.8(C13⋊D4), (Q8×C13)⋊3C22, (C2×C52).36C22, C4.14(C22×D13), C22.23(C13⋊D4), (C2×C13⋊2C8)⋊6C2, C2.17(C2×C13⋊D4), SmallGroup(416,162)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×Q8⋊D13
G = < a,b,c,d,e | a2=b4=d13=e2=1, c2=b2, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=ebe=b-1, bd=db, cd=dc, ece=b-1c, ede=d-1 >
Subgroups: 528 in 68 conjugacy classes, 33 normal (17 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C8, C2×C4, C2×C4, D4, Q8, Q8, C23, C13, C2×C8, SD16, C2×D4, C2×Q8, D13, C26, C26, C2×SD16, C52, C52, D26, C2×C26, C13⋊2C8, D52, D52, C2×C52, C2×C52, Q8×C13, Q8×C13, C22×D13, C2×C13⋊2C8, Q8⋊D13, C2×D52, Q8×C26, C2×Q8⋊D13
Quotients: C1, C2, C22, D4, C23, SD16, C2×D4, D13, C2×SD16, D26, C13⋊D4, C22×D13, Q8⋊D13, C2×C13⋊D4, C2×Q8⋊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)
(1 170 14 157)(2 171 15 158)(3 172 16 159)(4 173 17 160)(5 174 18 161)(6 175 19 162)(7 176 20 163)(8 177 21 164)(9 178 22 165)(10 179 23 166)(11 180 24 167)(12 181 25 168)(13 182 26 169)(27 196 40 183)(28 197 41 184)(29 198 42 185)(30 199 43 186)(31 200 44 187)(32 201 45 188)(33 202 46 189)(34 203 47 190)(35 204 48 191)(36 205 49 192)(37 206 50 193)(38 207 51 194)(39 208 52 195)(53 105 66 118)(54 106 67 119)(55 107 68 120)(56 108 69 121)(57 109 70 122)(58 110 71 123)(59 111 72 124)(60 112 73 125)(61 113 74 126)(62 114 75 127)(63 115 76 128)(64 116 77 129)(65 117 78 130)(79 131 92 144)(80 132 93 145)(81 133 94 146)(82 134 95 147)(83 135 96 148)(84 136 97 149)(85 137 98 150)(86 138 99 151)(87 139 100 152)(88 140 101 153)(89 141 102 154)(90 142 103 155)(91 143 104 156)
(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)
(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), (1,170,14,157)(2,171,15,158)(3,172,16,159)(4,173,17,160)(5,174,18,161)(6,175,19,162)(7,176,20,163)(8,177,21,164)(9,178,22,165)(10,179,23,166)(11,180,24,167)(12,181,25,168)(13,182,26,169)(27,196,40,183)(28,197,41,184)(29,198,42,185)(30,199,43,186)(31,200,44,187)(32,201,45,188)(33,202,46,189)(34,203,47,190)(35,204,48,191)(36,205,49,192)(37,206,50,193)(38,207,51,194)(39,208,52,195)(53,105,66,118)(54,106,67,119)(55,107,68,120)(56,108,69,121)(57,109,70,122)(58,110,71,123)(59,111,72,124)(60,112,73,125)(61,113,74,126)(62,114,75,127)(63,115,76,128)(64,116,77,129)(65,117,78,130)(79,131,92,144)(80,132,93,145)(81,133,94,146)(82,134,95,147)(83,135,96,148)(84,136,97,149)(85,137,98,150)(86,138,99,151)(87,139,100,152)(88,140,101,153)(89,141,102,154)(90,142,103,155)(91,143,104,156), (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), (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), (1,170,14,157)(2,171,15,158)(3,172,16,159)(4,173,17,160)(5,174,18,161)(6,175,19,162)(7,176,20,163)(8,177,21,164)(9,178,22,165)(10,179,23,166)(11,180,24,167)(12,181,25,168)(13,182,26,169)(27,196,40,183)(28,197,41,184)(29,198,42,185)(30,199,43,186)(31,200,44,187)(32,201,45,188)(33,202,46,189)(34,203,47,190)(35,204,48,191)(36,205,49,192)(37,206,50,193)(38,207,51,194)(39,208,52,195)(53,105,66,118)(54,106,67,119)(55,107,68,120)(56,108,69,121)(57,109,70,122)(58,110,71,123)(59,111,72,124)(60,112,73,125)(61,113,74,126)(62,114,75,127)(63,115,76,128)(64,116,77,129)(65,117,78,130)(79,131,92,144)(80,132,93,145)(81,133,94,146)(82,134,95,147)(83,135,96,148)(84,136,97,149)(85,137,98,150)(86,138,99,151)(87,139,100,152)(88,140,101,153)(89,141,102,154)(90,142,103,155)(91,143,104,156), (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), (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)], [(1,170,14,157),(2,171,15,158),(3,172,16,159),(4,173,17,160),(5,174,18,161),(6,175,19,162),(7,176,20,163),(8,177,21,164),(9,178,22,165),(10,179,23,166),(11,180,24,167),(12,181,25,168),(13,182,26,169),(27,196,40,183),(28,197,41,184),(29,198,42,185),(30,199,43,186),(31,200,44,187),(32,201,45,188),(33,202,46,189),(34,203,47,190),(35,204,48,191),(36,205,49,192),(37,206,50,193),(38,207,51,194),(39,208,52,195),(53,105,66,118),(54,106,67,119),(55,107,68,120),(56,108,69,121),(57,109,70,122),(58,110,71,123),(59,111,72,124),(60,112,73,125),(61,113,74,126),(62,114,75,127),(63,115,76,128),(64,116,77,129),(65,117,78,130),(79,131,92,144),(80,132,93,145),(81,133,94,146),(82,134,95,147),(83,135,96,148),(84,136,97,149),(85,137,98,150),(86,138,99,151),(87,139,100,152),(88,140,101,153),(89,141,102,154),(90,142,103,155),(91,143,104,156)], [(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)], [(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 | 4A | 4B | 4C | 4D | 8A | 8B | 8C | 8D | 13A | ··· | 13F | 26A | ··· | 26R | 52A | ··· | 52AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 13 | ··· | 13 | 26 | ··· | 26 | 52 | ··· | 52 |
| size | 1 | 1 | 1 | 1 | 52 | 52 | 2 | 2 | 4 | 4 | 26 | 26 | 26 | 26 | 2 | ··· | 2 | 2 | ··· | 2 | 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 | SD16 | D13 | D26 | D26 | C13⋊D4 | C13⋊D4 | Q8⋊D13 |
| kernel | C2×Q8⋊D13 | C2×C13⋊2C8 | Q8⋊D13 | C2×D52 | Q8×C26 | C52 | C2×C26 | C26 | C2×Q8 | C2×C4 | Q8 | C4 | C22 | C2 |
| # reps | 1 | 1 | 4 | 1 | 1 | 1 | 1 | 4 | 6 | 6 | 12 | 12 | 12 | 12 |
Matrix representation of C2×Q8⋊D13 ►in GL4(𝔽313) generated by
| 312 | 0 | 0 | 0 |
| 0 | 312 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 312 | 238 |
| 0 | 0 | 192 | 1 |
| 312 | 0 | 0 | 0 |
| 0 | 312 | 0 | 0 |
| 0 | 0 | 0 | 133 |
| 0 | 0 | 40 | 0 |
| 198 | 312 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 115 | 1 | 0 | 0 |
| 235 | 198 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 121 | 312 |
G:=sub<GL(4,GF(313))| [312,0,0,0,0,312,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,312,192,0,0,238,1],[312,0,0,0,0,312,0,0,0,0,0,40,0,0,133,0],[198,1,0,0,312,0,0,0,0,0,1,0,0,0,0,1],[115,235,0,0,1,198,0,0,0,0,1,121,0,0,0,312] >;
C2×Q8⋊D13 in GAP, Magma, Sage, TeX
C_2\times Q_8\rtimes D_{13} % in TeX
G:=Group("C2xQ8:D13"); // GroupNames label
G:=SmallGroup(416,162);
// by ID
G=gap.SmallGroup(416,162);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-13,218,86,579,159,69,13829]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^4=d^13=e^2=1,c^2=b^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=e*b*e=b^-1,b*d=d*b,c*d=d*c,e*c*e=b^-1*c,e*d*e=d^-1>;
// generators/relations