metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C23.21D26, (C2×C52)⋊11C4, C52.58(C2×C4), C52⋊3C4⋊17C2, (C2×C4)⋊4Dic13, (C2×C4).102D26, (C22×C4).7D13, C13⋊5(C42⋊C2), (C4×Dic13)⋊15C2, C26.16(C4○D4), C26.37(C22×C4), (C22×C52).10C2, (C2×C26).44C23, (C2×C52).93C22, C4.15(C2×Dic13), C23.D13.5C2, C2.4(D52⋊5C2), C2.5(C22×Dic13), C22.5(C2×Dic13), (C22×C26).36C22, C22.22(C22×D13), (C2×Dic13).38C22, (C2×C26).55(C2×C4), SmallGroup(416,147)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C23.21D26
G = < a,b,c,d,e | a2=b2=c2=1, d26=c, e2=cb=bc, ab=ba, eae-1=ac=ca, ad=da, bd=db, be=eb, cd=dc, ce=ec, ede-1=d25 >
Subgroups: 320 in 76 conjugacy classes, 49 normal (15 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C2×C4, C2×C4, C2×C4, C23, C13, C42, C22⋊C4, C4⋊C4, C22×C4, C26, C26, C26, C42⋊C2, Dic13, C52, C2×C26, C2×C26, C2×C26, C2×Dic13, C2×C52, C2×C52, C22×C26, C4×Dic13, C52⋊3C4, C23.D13, C22×C52, C23.21D26
Quotients: C1, C2, C4, C22, C2×C4, C23, C22×C4, C4○D4, D13, C42⋊C2, Dic13, D26, C2×Dic13, C22×D13, D52⋊5C2, C22×Dic13, C23.21D26
►On 208 points
Generators in S208
(1 199)(2 200)(3 201)(4 202)(5 203)(6 204)(7 205)(8 206)(9 207)(10 208)(11 157)(12 158)(13 159)(14 160)(15 161)(16 162)(17 163)(18 164)(19 165)(20 166)(21 167)(22 168)(23 169)(24 170)(25 171)(26 172)(27 173)(28 174)(29 175)(30 176)(31 177)(32 178)(33 179)(34 180)(35 181)(36 182)(37 183)(38 184)(39 185)(40 186)(41 187)(42 188)(43 189)(44 190)(45 191)(46 192)(47 193)(48 194)(49 195)(50 196)(51 197)(52 198)(53 124)(54 125)(55 126)(56 127)(57 128)(58 129)(59 130)(60 131)(61 132)(62 133)(63 134)(64 135)(65 136)(66 137)(67 138)(68 139)(69 140)(70 141)(71 142)(72 143)(73 144)(74 145)(75 146)(76 147)(77 148)(78 149)(79 150)(80 151)(81 152)(82 153)(83 154)(84 155)(85 156)(86 105)(87 106)(88 107)(89 108)(90 109)(91 110)(92 111)(93 112)(94 113)(95 114)(96 115)(97 116)(98 117)(99 118)(100 119)(101 120)(102 121)(103 122)(104 123)
(1 199)(2 200)(3 201)(4 202)(5 203)(6 204)(7 205)(8 206)(9 207)(10 208)(11 157)(12 158)(13 159)(14 160)(15 161)(16 162)(17 163)(18 164)(19 165)(20 166)(21 167)(22 168)(23 169)(24 170)(25 171)(26 172)(27 173)(28 174)(29 175)(30 176)(31 177)(32 178)(33 179)(34 180)(35 181)(36 182)(37 183)(38 184)(39 185)(40 186)(41 187)(42 188)(43 189)(44 190)(45 191)(46 192)(47 193)(48 194)(49 195)(50 196)(51 197)(52 198)(53 150)(54 151)(55 152)(56 153)(57 154)(58 155)(59 156)(60 105)(61 106)(62 107)(63 108)(64 109)(65 110)(66 111)(67 112)(68 113)(69 114)(70 115)(71 116)(72 117)(73 118)(74 119)(75 120)(76 121)(77 122)(78 123)(79 124)(80 125)(81 126)(82 127)(83 128)(84 129)(85 130)(86 131)(87 132)(88 133)(89 134)(90 135)(91 136)(92 137)(93 138)(94 139)(95 140)(96 141)(97 142)(98 143)(99 144)(100 145)(101 146)(102 147)(103 148)(104 149)
(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 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 54 173 125)(2 79 174 150)(3 104 175 123)(4 77 176 148)(5 102 177 121)(6 75 178 146)(7 100 179 119)(8 73 180 144)(9 98 181 117)(10 71 182 142)(11 96 183 115)(12 69 184 140)(13 94 185 113)(14 67 186 138)(15 92 187 111)(16 65 188 136)(17 90 189 109)(18 63 190 134)(19 88 191 107)(20 61 192 132)(21 86 193 105)(22 59 194 130)(23 84 195 155)(24 57 196 128)(25 82 197 153)(26 55 198 126)(27 80 199 151)(28 53 200 124)(29 78 201 149)(30 103 202 122)(31 76 203 147)(32 101 204 120)(33 74 205 145)(34 99 206 118)(35 72 207 143)(36 97 208 116)(37 70 157 141)(38 95 158 114)(39 68 159 139)(40 93 160 112)(41 66 161 137)(42 91 162 110)(43 64 163 135)(44 89 164 108)(45 62 165 133)(46 87 166 106)(47 60 167 131)(48 85 168 156)(49 58 169 129)(50 83 170 154)(51 56 171 127)(52 81 172 152)
G:=sub<Sym(208)| (1,199)(2,200)(3,201)(4,202)(5,203)(6,204)(7,205)(8,206)(9,207)(10,208)(11,157)(12,158)(13,159)(14,160)(15,161)(16,162)(17,163)(18,164)(19,165)(20,166)(21,167)(22,168)(23,169)(24,170)(25,171)(26,172)(27,173)(28,174)(29,175)(30,176)(31,177)(32,178)(33,179)(34,180)(35,181)(36,182)(37,183)(38,184)(39,185)(40,186)(41,187)(42,188)(43,189)(44,190)(45,191)(46,192)(47,193)(48,194)(49,195)(50,196)(51,197)(52,198)(53,124)(54,125)(55,126)(56,127)(57,128)(58,129)(59,130)(60,131)(61,132)(62,133)(63,134)(64,135)(65,136)(66,137)(67,138)(68,139)(69,140)(70,141)(71,142)(72,143)(73,144)(74,145)(75,146)(76,147)(77,148)(78,149)(79,150)(80,151)(81,152)(82,153)(83,154)(84,155)(85,156)(86,105)(87,106)(88,107)(89,108)(90,109)(91,110)(92,111)(93,112)(94,113)(95,114)(96,115)(97,116)(98,117)(99,118)(100,119)(101,120)(102,121)(103,122)(104,123), (1,199)(2,200)(3,201)(4,202)(5,203)(6,204)(7,205)(8,206)(9,207)(10,208)(11,157)(12,158)(13,159)(14,160)(15,161)(16,162)(17,163)(18,164)(19,165)(20,166)(21,167)(22,168)(23,169)(24,170)(25,171)(26,172)(27,173)(28,174)(29,175)(30,176)(31,177)(32,178)(33,179)(34,180)(35,181)(36,182)(37,183)(38,184)(39,185)(40,186)(41,187)(42,188)(43,189)(44,190)(45,191)(46,192)(47,193)(48,194)(49,195)(50,196)(51,197)(52,198)(53,150)(54,151)(55,152)(56,153)(57,154)(58,155)(59,156)(60,105)(61,106)(62,107)(63,108)(64,109)(65,110)(66,111)(67,112)(68,113)(69,114)(70,115)(71,116)(72,117)(73,118)(74,119)(75,120)(76,121)(77,122)(78,123)(79,124)(80,125)(81,126)(82,127)(83,128)(84,129)(85,130)(86,131)(87,132)(88,133)(89,134)(90,135)(91,136)(92,137)(93,138)(94,139)(95,140)(96,141)(97,142)(98,143)(99,144)(100,145)(101,146)(102,147)(103,148)(104,149), (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), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52)(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), (1,54,173,125)(2,79,174,150)(3,104,175,123)(4,77,176,148)(5,102,177,121)(6,75,178,146)(7,100,179,119)(8,73,180,144)(9,98,181,117)(10,71,182,142)(11,96,183,115)(12,69,184,140)(13,94,185,113)(14,67,186,138)(15,92,187,111)(16,65,188,136)(17,90,189,109)(18,63,190,134)(19,88,191,107)(20,61,192,132)(21,86,193,105)(22,59,194,130)(23,84,195,155)(24,57,196,128)(25,82,197,153)(26,55,198,126)(27,80,199,151)(28,53,200,124)(29,78,201,149)(30,103,202,122)(31,76,203,147)(32,101,204,120)(33,74,205,145)(34,99,206,118)(35,72,207,143)(36,97,208,116)(37,70,157,141)(38,95,158,114)(39,68,159,139)(40,93,160,112)(41,66,161,137)(42,91,162,110)(43,64,163,135)(44,89,164,108)(45,62,165,133)(46,87,166,106)(47,60,167,131)(48,85,168,156)(49,58,169,129)(50,83,170,154)(51,56,171,127)(52,81,172,152)>;
G:=Group( (1,199)(2,200)(3,201)(4,202)(5,203)(6,204)(7,205)(8,206)(9,207)(10,208)(11,157)(12,158)(13,159)(14,160)(15,161)(16,162)(17,163)(18,164)(19,165)(20,166)(21,167)(22,168)(23,169)(24,170)(25,171)(26,172)(27,173)(28,174)(29,175)(30,176)(31,177)(32,178)(33,179)(34,180)(35,181)(36,182)(37,183)(38,184)(39,185)(40,186)(41,187)(42,188)(43,189)(44,190)(45,191)(46,192)(47,193)(48,194)(49,195)(50,196)(51,197)(52,198)(53,124)(54,125)(55,126)(56,127)(57,128)(58,129)(59,130)(60,131)(61,132)(62,133)(63,134)(64,135)(65,136)(66,137)(67,138)(68,139)(69,140)(70,141)(71,142)(72,143)(73,144)(74,145)(75,146)(76,147)(77,148)(78,149)(79,150)(80,151)(81,152)(82,153)(83,154)(84,155)(85,156)(86,105)(87,106)(88,107)(89,108)(90,109)(91,110)(92,111)(93,112)(94,113)(95,114)(96,115)(97,116)(98,117)(99,118)(100,119)(101,120)(102,121)(103,122)(104,123), (1,199)(2,200)(3,201)(4,202)(5,203)(6,204)(7,205)(8,206)(9,207)(10,208)(11,157)(12,158)(13,159)(14,160)(15,161)(16,162)(17,163)(18,164)(19,165)(20,166)(21,167)(22,168)(23,169)(24,170)(25,171)(26,172)(27,173)(28,174)(29,175)(30,176)(31,177)(32,178)(33,179)(34,180)(35,181)(36,182)(37,183)(38,184)(39,185)(40,186)(41,187)(42,188)(43,189)(44,190)(45,191)(46,192)(47,193)(48,194)(49,195)(50,196)(51,197)(52,198)(53,150)(54,151)(55,152)(56,153)(57,154)(58,155)(59,156)(60,105)(61,106)(62,107)(63,108)(64,109)(65,110)(66,111)(67,112)(68,113)(69,114)(70,115)(71,116)(72,117)(73,118)(74,119)(75,120)(76,121)(77,122)(78,123)(79,124)(80,125)(81,126)(82,127)(83,128)(84,129)(85,130)(86,131)(87,132)(88,133)(89,134)(90,135)(91,136)(92,137)(93,138)(94,139)(95,140)(96,141)(97,142)(98,143)(99,144)(100,145)(101,146)(102,147)(103,148)(104,149), (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), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52)(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), (1,54,173,125)(2,79,174,150)(3,104,175,123)(4,77,176,148)(5,102,177,121)(6,75,178,146)(7,100,179,119)(8,73,180,144)(9,98,181,117)(10,71,182,142)(11,96,183,115)(12,69,184,140)(13,94,185,113)(14,67,186,138)(15,92,187,111)(16,65,188,136)(17,90,189,109)(18,63,190,134)(19,88,191,107)(20,61,192,132)(21,86,193,105)(22,59,194,130)(23,84,195,155)(24,57,196,128)(25,82,197,153)(26,55,198,126)(27,80,199,151)(28,53,200,124)(29,78,201,149)(30,103,202,122)(31,76,203,147)(32,101,204,120)(33,74,205,145)(34,99,206,118)(35,72,207,143)(36,97,208,116)(37,70,157,141)(38,95,158,114)(39,68,159,139)(40,93,160,112)(41,66,161,137)(42,91,162,110)(43,64,163,135)(44,89,164,108)(45,62,165,133)(46,87,166,106)(47,60,167,131)(48,85,168,156)(49,58,169,129)(50,83,170,154)(51,56,171,127)(52,81,172,152) );
G=PermutationGroup([[(1,199),(2,200),(3,201),(4,202),(5,203),(6,204),(7,205),(8,206),(9,207),(10,208),(11,157),(12,158),(13,159),(14,160),(15,161),(16,162),(17,163),(18,164),(19,165),(20,166),(21,167),(22,168),(23,169),(24,170),(25,171),(26,172),(27,173),(28,174),(29,175),(30,176),(31,177),(32,178),(33,179),(34,180),(35,181),(36,182),(37,183),(38,184),(39,185),(40,186),(41,187),(42,188),(43,189),(44,190),(45,191),(46,192),(47,193),(48,194),(49,195),(50,196),(51,197),(52,198),(53,124),(54,125),(55,126),(56,127),(57,128),(58,129),(59,130),(60,131),(61,132),(62,133),(63,134),(64,135),(65,136),(66,137),(67,138),(68,139),(69,140),(70,141),(71,142),(72,143),(73,144),(74,145),(75,146),(76,147),(77,148),(78,149),(79,150),(80,151),(81,152),(82,153),(83,154),(84,155),(85,156),(86,105),(87,106),(88,107),(89,108),(90,109),(91,110),(92,111),(93,112),(94,113),(95,114),(96,115),(97,116),(98,117),(99,118),(100,119),(101,120),(102,121),(103,122),(104,123)], [(1,199),(2,200),(3,201),(4,202),(5,203),(6,204),(7,205),(8,206),(9,207),(10,208),(11,157),(12,158),(13,159),(14,160),(15,161),(16,162),(17,163),(18,164),(19,165),(20,166),(21,167),(22,168),(23,169),(24,170),(25,171),(26,172),(27,173),(28,174),(29,175),(30,176),(31,177),(32,178),(33,179),(34,180),(35,181),(36,182),(37,183),(38,184),(39,185),(40,186),(41,187),(42,188),(43,189),(44,190),(45,191),(46,192),(47,193),(48,194),(49,195),(50,196),(51,197),(52,198),(53,150),(54,151),(55,152),(56,153),(57,154),(58,155),(59,156),(60,105),(61,106),(62,107),(63,108),(64,109),(65,110),(66,111),(67,112),(68,113),(69,114),(70,115),(71,116),(72,117),(73,118),(74,119),(75,120),(76,121),(77,122),(78,123),(79,124),(80,125),(81,126),(82,127),(83,128),(84,129),(85,130),(86,131),(87,132),(88,133),(89,134),(90,135),(91,136),(92,137),(93,138),(94,139),(95,140),(96,141),(97,142),(98,143),(99,144),(100,145),(101,146),(102,147),(103,148),(104,149)], [(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)], [(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52),(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)], [(1,54,173,125),(2,79,174,150),(3,104,175,123),(4,77,176,148),(5,102,177,121),(6,75,178,146),(7,100,179,119),(8,73,180,144),(9,98,181,117),(10,71,182,142),(11,96,183,115),(12,69,184,140),(13,94,185,113),(14,67,186,138),(15,92,187,111),(16,65,188,136),(17,90,189,109),(18,63,190,134),(19,88,191,107),(20,61,192,132),(21,86,193,105),(22,59,194,130),(23,84,195,155),(24,57,196,128),(25,82,197,153),(26,55,198,126),(27,80,199,151),(28,53,200,124),(29,78,201,149),(30,103,202,122),(31,76,203,147),(32,101,204,120),(33,74,205,145),(34,99,206,118),(35,72,207,143),(36,97,208,116),(37,70,157,141),(38,95,158,114),(39,68,159,139),(40,93,160,112),(41,66,161,137),(42,91,162,110),(43,64,163,135),(44,89,164,108),(45,62,165,133),(46,87,166,106),(47,60,167,131),(48,85,168,156),(49,58,169,129),(50,83,170,154),(51,56,171,127),(52,81,172,152)]])
116 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | ··· | 4N | 13A | ··· | 13F | 26A | ··· | 26AP | 52A | ··· | 52AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 13 | ··· | 13 | 26 | ··· | 26 | 52 | ··· | 52 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | 2 | 26 | ··· | 26 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
116 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | - | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C4 | C4○D4 | D13 | Dic13 | D26 | D26 | D52⋊5C2 |
| kernel | C23.21D26 | C4×Dic13 | C52⋊3C4 | C23.D13 | C22×C52 | C2×C52 | C26 | C22×C4 | C2×C4 | C2×C4 | C23 | C2 |
| # reps | 1 | 2 | 2 | 2 | 1 | 8 | 4 | 6 | 24 | 12 | 6 | 48 |
Matrix representation of C23.21D26 ►in GL3(𝔽53) generated by
| 1 | 0 | 0 |
| 0 | 1 | 7 |
| 0 | 0 | 52 |
| 52 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 1 |
| 1 | 0 | 0 |
| 0 | 52 | 0 |
| 0 | 0 | 52 |
| 52 | 0 | 0 |
| 0 | 39 | 17 |
| 0 | 0 | 19 |
| 23 | 0 | 0 |
| 0 | 33 | 8 |
| 0 | 36 | 20 |
G:=sub<GL(3,GF(53))| [1,0,0,0,1,0,0,7,52],[52,0,0,0,1,0,0,0,1],[1,0,0,0,52,0,0,0,52],[52,0,0,0,39,0,0,17,19],[23,0,0,0,33,36,0,8,20] >;
C23.21D26 in GAP, Magma, Sage, TeX
C_2^3._{21}D_{26} % in TeX
G:=Group("C2^3.21D26"); // GroupNames label
G:=SmallGroup(416,147);
// by ID
G=gap.SmallGroup(416,147);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-13,48,103,362,13829]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^2=1,d^26=c,e^2=c*b=b*c,a*b=b*a,e*a*e^-1=a*c=c*a,a*d=d*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