metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C23.23D26, (C22×C52)⋊2C2, (C2×C4).65D26, (C2×C26).37D4, C26.42(C2×D4), (C22×C4)⋊3D13, D26⋊C4⋊2C2, C26.D4⋊3C2, C23.D13⋊6C2, C26.18(C4○D4), (C2×C52).78C22, (C2×C26).47C23, C13⋊4(C22.D4), C22.9(C13⋊D4), C2.18(D52⋊5C2), (C22×C26).39C22, (C22×D13).9C22, C22.55(C22×D13), (C2×Dic13).15C22, C2.6(C2×C13⋊D4), (C2×C13⋊D4).6C2, SmallGroup(416,150)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C23.23D26
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=bd25 >
Subgroups: 488 in 78 conjugacy classes, 33 normal (15 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C2×C4, C2×C4, D4, C23, C23, C13, C22⋊C4, C4⋊C4, C22×C4, C2×D4, D13, C26, C26, C26, C22.D4, Dic13, C52, D26, C2×C26, C2×C26, C2×C26, C2×Dic13, C2×Dic13, C13⋊D4, C2×C52, C2×C52, C22×D13, C22×C26, C26.D4, D26⋊C4, C23.D13, C2×C13⋊D4, C22×C52, C23.23D26
Quotients: C1, C2, C22, D4, C23, C2×D4, C4○D4, D13, C22.D4, D26, C13⋊D4, C22×D13, D52⋊5C2, C2×C13⋊D4, C23.23D26
►On 208 points
Generators in S208
(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)
(1 197)(2 198)(3 199)(4 200)(5 201)(6 202)(7 203)(8 204)(9 205)(10 206)(11 207)(12 208)(13 157)(14 158)(15 159)(16 160)(17 161)(18 162)(19 163)(20 164)(21 165)(22 166)(23 167)(24 168)(25 169)(26 170)(27 171)(28 172)(29 173)(30 174)(31 175)(32 176)(33 177)(34 178)(35 179)(36 180)(37 181)(38 182)(39 183)(40 184)(41 185)(42 186)(43 187)(44 188)(45 189)(46 190)(47 191)(48 192)(49 193)(50 194)(51 195)(52 196)(53 155)(54 156)(55 105)(56 106)(57 107)(58 108)(59 109)(60 110)(61 111)(62 112)(63 113)(64 114)(65 115)(66 116)(67 117)(68 118)(69 119)(70 120)(71 121)(72 122)(73 123)(74 124)(75 125)(76 126)(77 127)(78 128)(79 129)(80 130)(81 131)(82 132)(83 133)(84 134)(85 135)(86 136)(87 137)(88 138)(89 139)(90 140)(91 141)(92 142)(93 143)(94 144)(95 145)(96 146)(97 147)(98 148)(99 149)(100 150)(101 151)(102 152)(103 153)(104 154)
(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)
(1 143 171 67)(2 66 172 142)(3 141 173 65)(4 64 174 140)(5 139 175 63)(6 62 176 138)(7 137 177 61)(8 60 178 136)(9 135 179 59)(10 58 180 134)(11 133 181 57)(12 56 182 132)(13 131 183 55)(14 54 184 130)(15 129 185 53)(16 104 186 128)(17 127 187 103)(18 102 188 126)(19 125 189 101)(20 100 190 124)(21 123 191 99)(22 98 192 122)(23 121 193 97)(24 96 194 120)(25 119 195 95)(26 94 196 118)(27 117 197 93)(28 92 198 116)(29 115 199 91)(30 90 200 114)(31 113 201 89)(32 88 202 112)(33 111 203 87)(34 86 204 110)(35 109 205 85)(36 84 206 108)(37 107 207 83)(38 82 208 106)(39 105 157 81)(40 80 158 156)(41 155 159 79)(42 78 160 154)(43 153 161 77)(44 76 162 152)(45 151 163 75)(46 74 164 150)(47 149 165 73)(48 72 166 148)(49 147 167 71)(50 70 168 146)(51 145 169 69)(52 68 170 144)
G:=sub<Sym(208)| (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), (1,197)(2,198)(3,199)(4,200)(5,201)(6,202)(7,203)(8,204)(9,205)(10,206)(11,207)(12,208)(13,157)(14,158)(15,159)(16,160)(17,161)(18,162)(19,163)(20,164)(21,165)(22,166)(23,167)(24,168)(25,169)(26,170)(27,171)(28,172)(29,173)(30,174)(31,175)(32,176)(33,177)(34,178)(35,179)(36,180)(37,181)(38,182)(39,183)(40,184)(41,185)(42,186)(43,187)(44,188)(45,189)(46,190)(47,191)(48,192)(49,193)(50,194)(51,195)(52,196)(53,155)(54,156)(55,105)(56,106)(57,107)(58,108)(59,109)(60,110)(61,111)(62,112)(63,113)(64,114)(65,115)(66,116)(67,117)(68,118)(69,119)(70,120)(71,121)(72,122)(73,123)(74,124)(75,125)(76,126)(77,127)(78,128)(79,129)(80,130)(81,131)(82,132)(83,133)(84,134)(85,135)(86,136)(87,137)(88,138)(89,139)(90,140)(91,141)(92,142)(93,143)(94,144)(95,145)(96,146)(97,147)(98,148)(99,149)(100,150)(101,151)(102,152)(103,153)(104,154), (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), (1,143,171,67)(2,66,172,142)(3,141,173,65)(4,64,174,140)(5,139,175,63)(6,62,176,138)(7,137,177,61)(8,60,178,136)(9,135,179,59)(10,58,180,134)(11,133,181,57)(12,56,182,132)(13,131,183,55)(14,54,184,130)(15,129,185,53)(16,104,186,128)(17,127,187,103)(18,102,188,126)(19,125,189,101)(20,100,190,124)(21,123,191,99)(22,98,192,122)(23,121,193,97)(24,96,194,120)(25,119,195,95)(26,94,196,118)(27,117,197,93)(28,92,198,116)(29,115,199,91)(30,90,200,114)(31,113,201,89)(32,88,202,112)(33,111,203,87)(34,86,204,110)(35,109,205,85)(36,84,206,108)(37,107,207,83)(38,82,208,106)(39,105,157,81)(40,80,158,156)(41,155,159,79)(42,78,160,154)(43,153,161,77)(44,76,162,152)(45,151,163,75)(46,74,164,150)(47,149,165,73)(48,72,166,148)(49,147,167,71)(50,70,168,146)(51,145,169,69)(52,68,170,144)>;
G:=Group( (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), (1,197)(2,198)(3,199)(4,200)(5,201)(6,202)(7,203)(8,204)(9,205)(10,206)(11,207)(12,208)(13,157)(14,158)(15,159)(16,160)(17,161)(18,162)(19,163)(20,164)(21,165)(22,166)(23,167)(24,168)(25,169)(26,170)(27,171)(28,172)(29,173)(30,174)(31,175)(32,176)(33,177)(34,178)(35,179)(36,180)(37,181)(38,182)(39,183)(40,184)(41,185)(42,186)(43,187)(44,188)(45,189)(46,190)(47,191)(48,192)(49,193)(50,194)(51,195)(52,196)(53,155)(54,156)(55,105)(56,106)(57,107)(58,108)(59,109)(60,110)(61,111)(62,112)(63,113)(64,114)(65,115)(66,116)(67,117)(68,118)(69,119)(70,120)(71,121)(72,122)(73,123)(74,124)(75,125)(76,126)(77,127)(78,128)(79,129)(80,130)(81,131)(82,132)(83,133)(84,134)(85,135)(86,136)(87,137)(88,138)(89,139)(90,140)(91,141)(92,142)(93,143)(94,144)(95,145)(96,146)(97,147)(98,148)(99,149)(100,150)(101,151)(102,152)(103,153)(104,154), (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), (1,143,171,67)(2,66,172,142)(3,141,173,65)(4,64,174,140)(5,139,175,63)(6,62,176,138)(7,137,177,61)(8,60,178,136)(9,135,179,59)(10,58,180,134)(11,133,181,57)(12,56,182,132)(13,131,183,55)(14,54,184,130)(15,129,185,53)(16,104,186,128)(17,127,187,103)(18,102,188,126)(19,125,189,101)(20,100,190,124)(21,123,191,99)(22,98,192,122)(23,121,193,97)(24,96,194,120)(25,119,195,95)(26,94,196,118)(27,117,197,93)(28,92,198,116)(29,115,199,91)(30,90,200,114)(31,113,201,89)(32,88,202,112)(33,111,203,87)(34,86,204,110)(35,109,205,85)(36,84,206,108)(37,107,207,83)(38,82,208,106)(39,105,157,81)(40,80,158,156)(41,155,159,79)(42,78,160,154)(43,153,161,77)(44,76,162,152)(45,151,163,75)(46,74,164,150)(47,149,165,73)(48,72,166,148)(49,147,167,71)(50,70,168,146)(51,145,169,69)(52,68,170,144) );
G=PermutationGroup([[(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)], [(1,197),(2,198),(3,199),(4,200),(5,201),(6,202),(7,203),(8,204),(9,205),(10,206),(11,207),(12,208),(13,157),(14,158),(15,159),(16,160),(17,161),(18,162),(19,163),(20,164),(21,165),(22,166),(23,167),(24,168),(25,169),(26,170),(27,171),(28,172),(29,173),(30,174),(31,175),(32,176),(33,177),(34,178),(35,179),(36,180),(37,181),(38,182),(39,183),(40,184),(41,185),(42,186),(43,187),(44,188),(45,189),(46,190),(47,191),(48,192),(49,193),(50,194),(51,195),(52,196),(53,155),(54,156),(55,105),(56,106),(57,107),(58,108),(59,109),(60,110),(61,111),(62,112),(63,113),(64,114),(65,115),(66,116),(67,117),(68,118),(69,119),(70,120),(71,121),(72,122),(73,123),(74,124),(75,125),(76,126),(77,127),(78,128),(79,129),(80,130),(81,131),(82,132),(83,133),(84,134),(85,135),(86,136),(87,137),(88,138),(89,139),(90,140),(91,141),(92,142),(93,143),(94,144),(95,145),(96,146),(97,147),(98,148),(99,149),(100,150),(101,151),(102,152),(103,153),(104,154)], [(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)], [(1,143,171,67),(2,66,172,142),(3,141,173,65),(4,64,174,140),(5,139,175,63),(6,62,176,138),(7,137,177,61),(8,60,178,136),(9,135,179,59),(10,58,180,134),(11,133,181,57),(12,56,182,132),(13,131,183,55),(14,54,184,130),(15,129,185,53),(16,104,186,128),(17,127,187,103),(18,102,188,126),(19,125,189,101),(20,100,190,124),(21,123,191,99),(22,98,192,122),(23,121,193,97),(24,96,194,120),(25,119,195,95),(26,94,196,118),(27,117,197,93),(28,92,198,116),(29,115,199,91),(30,90,200,114),(31,113,201,89),(32,88,202,112),(33,111,203,87),(34,86,204,110),(35,109,205,85),(36,84,206,108),(37,107,207,83),(38,82,208,106),(39,105,157,81),(40,80,158,156),(41,155,159,79),(42,78,160,154),(43,153,161,77),(44,76,162,152),(45,151,163,75),(46,74,164,150),(47,149,165,73),(48,72,166,148),(49,147,167,71),(50,70,168,146),(51,145,169,69),(52,68,170,144)]])
110 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 13A | ··· | 13F | 26A | ··· | 26AP | 52A | ··· | 52AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 13 | ··· | 13 | 26 | ··· | 26 | 52 | ··· | 52 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 52 | 2 | 2 | 2 | 2 | 52 | 52 | 52 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
110 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | C4○D4 | D13 | D26 | D26 | C13⋊D4 | D52⋊5C2 |
| kernel | C23.23D26 | C26.D4 | D26⋊C4 | C23.D13 | C2×C13⋊D4 | C22×C52 | C2×C26 | C26 | C22×C4 | C2×C4 | C23 | C22 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 2 | 4 | 6 | 12 | 6 | 24 | 48 |
Matrix representation of C23.23D26 ►in GL4(𝔽53) generated by
| 1 | 0 | 0 | 0 |
| 29 | 52 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 52 |
| 52 | 0 | 0 | 0 |
| 0 | 52 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 52 | 0 | 0 | 0 |
| 0 | 52 | 0 | 0 |
| 0 | 0 | 52 | 0 |
| 0 | 0 | 0 | 52 |
| 45 | 0 | 0 | 0 |
| 15 | 33 | 0 | 0 |
| 0 | 0 | 48 | 0 |
| 0 | 0 | 0 | 32 |
| 50 | 13 | 0 | 0 |
| 32 | 3 | 0 | 0 |
| 0 | 0 | 0 | 32 |
| 0 | 0 | 48 | 0 |
G:=sub<GL(4,GF(53))| [1,29,0,0,0,52,0,0,0,0,1,0,0,0,0,52],[52,0,0,0,0,52,0,0,0,0,1,0,0,0,0,1],[52,0,0,0,0,52,0,0,0,0,52,0,0,0,0,52],[45,15,0,0,0,33,0,0,0,0,48,0,0,0,0,32],[50,32,0,0,13,3,0,0,0,0,0,48,0,0,32,0] >;
C23.23D26 in GAP, Magma, Sage, TeX
C_2^3._{23}D_{26} % in TeX
G:=Group("C2^3.23D26"); // GroupNames label
G:=SmallGroup(416,150);
// by ID
G=gap.SmallGroup(416,150);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-13,217,218,86,13829]);
// 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=b*d^25>;
// generators/relations