metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C23.3D26, C52⋊3C4⋊3C2, (C2×C4).27D26, C26.7(C4○D4), C26.D4⋊8C2, (C2×C52).2C22, C22⋊C4.2D13, C13⋊2(C42⋊2C2), (C4×Dic13)⋊10C2, (C2×C26).20C23, C23.D13.3C2, C2.7(D4⋊2D13), C2.9(D52⋊5C2), (C22×C26).9C22, C22.40(C22×D13), (C2×Dic13).29C22, (C13×C22⋊C4).2C2, SmallGroup(416,100)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C23.D26
G = < a,b,c,d,e | a2=b2=c2=1, d26=b, e2=cb=bc, eae-1=ab=ba, dad-1=ac=ca, bd=db, be=eb, cd=dc, ce=ec, ede-1=d25 >
Subgroups: 312 in 60 conjugacy classes, 29 normal (all characteristic)
C1, C2, C2, C4, C22, C22, C2×C4, C2×C4, C23, C13, C42, C22⋊C4, C22⋊C4, C4⋊C4, C26, C26, C42⋊2C2, Dic13, C52, C2×C26, C2×C26, C2×Dic13, C2×C52, C22×C26, C4×Dic13, C26.D4, C52⋊3C4, C23.D13, C13×C22⋊C4, C23.D26
Quotients: C1, C2, C22, C23, C4○D4, D13, C42⋊2C2, D26, C22×D13, D52⋊5C2, D4⋊2D13, C23.D26
►On 208 points
Generators in S208
(2 136)(4 138)(6 140)(8 142)(10 144)(12 146)(14 148)(16 150)(18 152)(20 154)(22 156)(24 106)(26 108)(28 110)(30 112)(32 114)(34 116)(36 118)(38 120)(40 122)(42 124)(44 126)(46 128)(48 130)(50 132)(52 134)(53 158)(54 80)(55 160)(56 82)(57 162)(58 84)(59 164)(60 86)(61 166)(62 88)(63 168)(64 90)(65 170)(66 92)(67 172)(68 94)(69 174)(70 96)(71 176)(72 98)(73 178)(74 100)(75 180)(76 102)(77 182)(78 104)(79 184)(81 186)(83 188)(85 190)(87 192)(89 194)(91 196)(93 198)(95 200)(97 202)(99 204)(101 206)(103 208)(157 183)(159 185)(161 187)(163 189)(165 191)(167 193)(169 195)(171 197)(173 199)(175 201)(177 203)(179 205)(181 207)
(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)
(1 135)(2 136)(3 137)(4 138)(5 139)(6 140)(7 141)(8 142)(9 143)(10 144)(11 145)(12 146)(13 147)(14 148)(15 149)(16 150)(17 151)(18 152)(19 153)(20 154)(21 155)(22 156)(23 105)(24 106)(25 107)(26 108)(27 109)(28 110)(29 111)(30 112)(31 113)(32 114)(33 115)(34 116)(35 117)(36 118)(37 119)(38 120)(39 121)(40 122)(41 123)(42 124)(43 125)(44 126)(45 127)(46 128)(47 129)(48 130)(49 131)(50 132)(51 133)(52 134)(53 184)(54 185)(55 186)(56 187)(57 188)(58 189)(59 190)(60 191)(61 192)(62 193)(63 194)(64 195)(65 196)(66 197)(67 198)(68 199)(69 200)(70 201)(71 202)(72 203)(73 204)(74 205)(75 206)(76 207)(77 208)(78 157)(79 158)(80 159)(81 160)(82 161)(83 162)(84 163)(85 164)(86 165)(87 166)(88 167)(89 168)(90 169)(91 170)(92 171)(93 172)(94 173)(95 174)(96 175)(97 176)(98 177)(99 178)(100 179)(101 180)(102 181)(103 182)(104 183)
(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)
(1 203 109 98)(2 176 110 71)(3 201 111 96)(4 174 112 69)(5 199 113 94)(6 172 114 67)(7 197 115 92)(8 170 116 65)(9 195 117 90)(10 168 118 63)(11 193 119 88)(12 166 120 61)(13 191 121 86)(14 164 122 59)(15 189 123 84)(16 162 124 57)(17 187 125 82)(18 160 126 55)(19 185 127 80)(20 158 128 53)(21 183 129 78)(22 208 130 103)(23 181 131 76)(24 206 132 101)(25 179 133 74)(26 204 134 99)(27 177 135 72)(28 202 136 97)(29 175 137 70)(30 200 138 95)(31 173 139 68)(32 198 140 93)(33 171 141 66)(34 196 142 91)(35 169 143 64)(36 194 144 89)(37 167 145 62)(38 192 146 87)(39 165 147 60)(40 190 148 85)(41 163 149 58)(42 188 150 83)(43 161 151 56)(44 186 152 81)(45 159 153 54)(46 184 154 79)(47 157 155 104)(48 182 156 77)(49 207 105 102)(50 180 106 75)(51 205 107 100)(52 178 108 73)
G:=sub<Sym(208)| (2,136)(4,138)(6,140)(8,142)(10,144)(12,146)(14,148)(16,150)(18,152)(20,154)(22,156)(24,106)(26,108)(28,110)(30,112)(32,114)(34,116)(36,118)(38,120)(40,122)(42,124)(44,126)(46,128)(48,130)(50,132)(52,134)(53,158)(54,80)(55,160)(56,82)(57,162)(58,84)(59,164)(60,86)(61,166)(62,88)(63,168)(64,90)(65,170)(66,92)(67,172)(68,94)(69,174)(70,96)(71,176)(72,98)(73,178)(74,100)(75,180)(76,102)(77,182)(78,104)(79,184)(81,186)(83,188)(85,190)(87,192)(89,194)(91,196)(93,198)(95,200)(97,202)(99,204)(101,206)(103,208)(157,183)(159,185)(161,187)(163,189)(165,191)(167,193)(169,195)(171,197)(173,199)(175,201)(177,203)(179,205)(181,207), (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), (1,135)(2,136)(3,137)(4,138)(5,139)(6,140)(7,141)(8,142)(9,143)(10,144)(11,145)(12,146)(13,147)(14,148)(15,149)(16,150)(17,151)(18,152)(19,153)(20,154)(21,155)(22,156)(23,105)(24,106)(25,107)(26,108)(27,109)(28,110)(29,111)(30,112)(31,113)(32,114)(33,115)(34,116)(35,117)(36,118)(37,119)(38,120)(39,121)(40,122)(41,123)(42,124)(43,125)(44,126)(45,127)(46,128)(47,129)(48,130)(49,131)(50,132)(51,133)(52,134)(53,184)(54,185)(55,186)(56,187)(57,188)(58,189)(59,190)(60,191)(61,192)(62,193)(63,194)(64,195)(65,196)(66,197)(67,198)(68,199)(69,200)(70,201)(71,202)(72,203)(73,204)(74,205)(75,206)(76,207)(77,208)(78,157)(79,158)(80,159)(81,160)(82,161)(83,162)(84,163)(85,164)(86,165)(87,166)(88,167)(89,168)(90,169)(91,170)(92,171)(93,172)(94,173)(95,174)(96,175)(97,176)(98,177)(99,178)(100,179)(101,180)(102,181)(103,182)(104,183), (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), (1,203,109,98)(2,176,110,71)(3,201,111,96)(4,174,112,69)(5,199,113,94)(6,172,114,67)(7,197,115,92)(8,170,116,65)(9,195,117,90)(10,168,118,63)(11,193,119,88)(12,166,120,61)(13,191,121,86)(14,164,122,59)(15,189,123,84)(16,162,124,57)(17,187,125,82)(18,160,126,55)(19,185,127,80)(20,158,128,53)(21,183,129,78)(22,208,130,103)(23,181,131,76)(24,206,132,101)(25,179,133,74)(26,204,134,99)(27,177,135,72)(28,202,136,97)(29,175,137,70)(30,200,138,95)(31,173,139,68)(32,198,140,93)(33,171,141,66)(34,196,142,91)(35,169,143,64)(36,194,144,89)(37,167,145,62)(38,192,146,87)(39,165,147,60)(40,190,148,85)(41,163,149,58)(42,188,150,83)(43,161,151,56)(44,186,152,81)(45,159,153,54)(46,184,154,79)(47,157,155,104)(48,182,156,77)(49,207,105,102)(50,180,106,75)(51,205,107,100)(52,178,108,73)>;
G:=Group( (2,136)(4,138)(6,140)(8,142)(10,144)(12,146)(14,148)(16,150)(18,152)(20,154)(22,156)(24,106)(26,108)(28,110)(30,112)(32,114)(34,116)(36,118)(38,120)(40,122)(42,124)(44,126)(46,128)(48,130)(50,132)(52,134)(53,158)(54,80)(55,160)(56,82)(57,162)(58,84)(59,164)(60,86)(61,166)(62,88)(63,168)(64,90)(65,170)(66,92)(67,172)(68,94)(69,174)(70,96)(71,176)(72,98)(73,178)(74,100)(75,180)(76,102)(77,182)(78,104)(79,184)(81,186)(83,188)(85,190)(87,192)(89,194)(91,196)(93,198)(95,200)(97,202)(99,204)(101,206)(103,208)(157,183)(159,185)(161,187)(163,189)(165,191)(167,193)(169,195)(171,197)(173,199)(175,201)(177,203)(179,205)(181,207), (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), (1,135)(2,136)(3,137)(4,138)(5,139)(6,140)(7,141)(8,142)(9,143)(10,144)(11,145)(12,146)(13,147)(14,148)(15,149)(16,150)(17,151)(18,152)(19,153)(20,154)(21,155)(22,156)(23,105)(24,106)(25,107)(26,108)(27,109)(28,110)(29,111)(30,112)(31,113)(32,114)(33,115)(34,116)(35,117)(36,118)(37,119)(38,120)(39,121)(40,122)(41,123)(42,124)(43,125)(44,126)(45,127)(46,128)(47,129)(48,130)(49,131)(50,132)(51,133)(52,134)(53,184)(54,185)(55,186)(56,187)(57,188)(58,189)(59,190)(60,191)(61,192)(62,193)(63,194)(64,195)(65,196)(66,197)(67,198)(68,199)(69,200)(70,201)(71,202)(72,203)(73,204)(74,205)(75,206)(76,207)(77,208)(78,157)(79,158)(80,159)(81,160)(82,161)(83,162)(84,163)(85,164)(86,165)(87,166)(88,167)(89,168)(90,169)(91,170)(92,171)(93,172)(94,173)(95,174)(96,175)(97,176)(98,177)(99,178)(100,179)(101,180)(102,181)(103,182)(104,183), (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), (1,203,109,98)(2,176,110,71)(3,201,111,96)(4,174,112,69)(5,199,113,94)(6,172,114,67)(7,197,115,92)(8,170,116,65)(9,195,117,90)(10,168,118,63)(11,193,119,88)(12,166,120,61)(13,191,121,86)(14,164,122,59)(15,189,123,84)(16,162,124,57)(17,187,125,82)(18,160,126,55)(19,185,127,80)(20,158,128,53)(21,183,129,78)(22,208,130,103)(23,181,131,76)(24,206,132,101)(25,179,133,74)(26,204,134,99)(27,177,135,72)(28,202,136,97)(29,175,137,70)(30,200,138,95)(31,173,139,68)(32,198,140,93)(33,171,141,66)(34,196,142,91)(35,169,143,64)(36,194,144,89)(37,167,145,62)(38,192,146,87)(39,165,147,60)(40,190,148,85)(41,163,149,58)(42,188,150,83)(43,161,151,56)(44,186,152,81)(45,159,153,54)(46,184,154,79)(47,157,155,104)(48,182,156,77)(49,207,105,102)(50,180,106,75)(51,205,107,100)(52,178,108,73) );
G=PermutationGroup([[(2,136),(4,138),(6,140),(8,142),(10,144),(12,146),(14,148),(16,150),(18,152),(20,154),(22,156),(24,106),(26,108),(28,110),(30,112),(32,114),(34,116),(36,118),(38,120),(40,122),(42,124),(44,126),(46,128),(48,130),(50,132),(52,134),(53,158),(54,80),(55,160),(56,82),(57,162),(58,84),(59,164),(60,86),(61,166),(62,88),(63,168),(64,90),(65,170),(66,92),(67,172),(68,94),(69,174),(70,96),(71,176),(72,98),(73,178),(74,100),(75,180),(76,102),(77,182),(78,104),(79,184),(81,186),(83,188),(85,190),(87,192),(89,194),(91,196),(93,198),(95,200),(97,202),(99,204),(101,206),(103,208),(157,183),(159,185),(161,187),(163,189),(165,191),(167,193),(169,195),(171,197),(173,199),(175,201),(177,203),(179,205),(181,207)], [(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)], [(1,135),(2,136),(3,137),(4,138),(5,139),(6,140),(7,141),(8,142),(9,143),(10,144),(11,145),(12,146),(13,147),(14,148),(15,149),(16,150),(17,151),(18,152),(19,153),(20,154),(21,155),(22,156),(23,105),(24,106),(25,107),(26,108),(27,109),(28,110),(29,111),(30,112),(31,113),(32,114),(33,115),(34,116),(35,117),(36,118),(37,119),(38,120),(39,121),(40,122),(41,123),(42,124),(43,125),(44,126),(45,127),(46,128),(47,129),(48,130),(49,131),(50,132),(51,133),(52,134),(53,184),(54,185),(55,186),(56,187),(57,188),(58,189),(59,190),(60,191),(61,192),(62,193),(63,194),(64,195),(65,196),(66,197),(67,198),(68,199),(69,200),(70,201),(71,202),(72,203),(73,204),(74,205),(75,206),(76,207),(77,208),(78,157),(79,158),(80,159),(81,160),(82,161),(83,162),(84,163),(85,164),(86,165),(87,166),(88,167),(89,168),(90,169),(91,170),(92,171),(93,172),(94,173),(95,174),(96,175),(97,176),(98,177),(99,178),(100,179),(101,180),(102,181),(103,182),(104,183)], [(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)], [(1,203,109,98),(2,176,110,71),(3,201,111,96),(4,174,112,69),(5,199,113,94),(6,172,114,67),(7,197,115,92),(8,170,116,65),(9,195,117,90),(10,168,118,63),(11,193,119,88),(12,166,120,61),(13,191,121,86),(14,164,122,59),(15,189,123,84),(16,162,124,57),(17,187,125,82),(18,160,126,55),(19,185,127,80),(20,158,128,53),(21,183,129,78),(22,208,130,103),(23,181,131,76),(24,206,132,101),(25,179,133,74),(26,204,134,99),(27,177,135,72),(28,202,136,97),(29,175,137,70),(30,200,138,95),(31,173,139,68),(32,198,140,93),(33,171,141,66),(34,196,142,91),(35,169,143,64),(36,194,144,89),(37,167,145,62),(38,192,146,87),(39,165,147,60),(40,190,148,85),(41,163,149,58),(42,188,150,83),(43,161,151,56),(44,186,152,81),(45,159,153,54),(46,184,154,79),(47,157,155,104),(48,182,156,77),(49,207,105,102),(50,180,106,75),(51,205,107,100),(52,178,108,73)]])
74 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 13A | ··· | 13F | 26A | ··· | 26R | 26S | ··· | 26AD | 52A | ··· | 52X |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 13 | ··· | 13 | 26 | ··· | 26 | 26 | ··· | 26 | 52 | ··· | 52 |
| size | 1 | 1 | 1 | 1 | 4 | 2 | 2 | 4 | 26 | 26 | 26 | 26 | 52 | 52 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
74 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4○D4 | D13 | D26 | D26 | D52⋊5C2 | D4⋊2D13 |
| kernel | C23.D26 | C4×Dic13 | C26.D4 | C52⋊3C4 | C23.D13 | C13×C22⋊C4 | C26 | C22⋊C4 | C2×C4 | C23 | C2 | C2 |
| # reps | 1 | 1 | 2 | 1 | 2 | 1 | 6 | 6 | 12 | 6 | 24 | 12 |
Matrix representation of C23.D26 ►in GL4(𝔽53) generated by
| 1 | 0 | 0 | 0 |
| 1 | 52 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 52 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 52 | 0 |
| 0 | 0 | 0 | 52 |
| 52 | 0 | 0 | 0 |
| 0 | 52 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 51 | 0 | 0 |
| 0 | 52 | 0 | 0 |
| 0 | 0 | 18 | 0 |
| 0 | 0 | 0 | 50 |
| 23 | 0 | 0 | 0 |
| 0 | 23 | 0 | 0 |
| 0 | 0 | 0 | 50 |
| 0 | 0 | 18 | 0 |
G:=sub<GL(4,GF(53))| [1,1,0,0,0,52,0,0,0,0,1,0,0,0,0,52],[1,0,0,0,0,1,0,0,0,0,52,0,0,0,0,52],[52,0,0,0,0,52,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,51,52,0,0,0,0,18,0,0,0,0,50],[23,0,0,0,0,23,0,0,0,0,0,18,0,0,50,0] >;
C23.D26 in GAP, Magma, Sage, TeX
C_2^3.D_{26} % in TeX
G:=Group("C2^3.D26"); // GroupNames label
G:=SmallGroup(416,100);
// by ID
G=gap.SmallGroup(416,100);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-13,96,55,506,188,13829]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^2=1,d^26=b,e^2=c*b=b*c,e*a*e^-1=a*b=b*a,d*a*d^-1=a*c=c*a,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^25>;
// generators/relations