metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C23.11D26, (C2×C4).26D26, (C2×Dic13)⋊4C4, (C4×Dic13)⋊9C2, C26.D4⋊7C2, C22⋊C4.3D13, C22.6(C4×D13), C13⋊3(C42⋊C2), C26.20(C4○D4), (C2×C26).18C23, C26.18(C22×C4), (C2×C52).50C22, C23.D13.1C2, C2.1(D4⋊2D13), Dic13.20(C2×C4), (C22×C26).7C22, (C22×Dic13).2C2, C22.12(C22×D13), (C2×Dic13).60C22, C2.7(C2×C4×D13), (C2×C26).24(C2×C4), (C13×C22⋊C4).3C2, SmallGroup(416,98)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C23.11D26
G = < a,b,c,d,e | a2=b2=c2=1, d26=b, e2=cb=bc, ab=ba, dad-1=eae-1=ac=ca, bd=db, be=eb, cd=dc, ce=ec, ede-1=d25 >
Subgroups: 368 in 76 conjugacy classes, 41 normal (15 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C2×C4, C2×C4, C23, C13, C42, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C26, C26, C26, C42⋊C2, Dic13, Dic13, C52, C2×C26, C2×C26, C2×C26, C2×Dic13, C2×Dic13, C2×C52, C22×C26, C4×Dic13, C26.D4, C23.D13, C13×C22⋊C4, C22×Dic13, C23.11D26
Quotients: C1, C2, C4, C22, C2×C4, C23, C22×C4, C4○D4, D13, C42⋊C2, D26, C4×D13, C22×D13, C2×C4×D13, D4⋊2D13, C23.11D26
►On 208 points
Generators in S208
(1 27)(2 56)(3 29)(4 58)(5 31)(6 60)(7 33)(8 62)(9 35)(10 64)(11 37)(12 66)(13 39)(14 68)(15 41)(16 70)(17 43)(18 72)(19 45)(20 74)(21 47)(22 76)(23 49)(24 78)(25 51)(26 80)(28 82)(30 84)(32 86)(34 88)(36 90)(38 92)(40 94)(42 96)(44 98)(46 100)(48 102)(50 104)(52 54)(53 79)(55 81)(57 83)(59 85)(61 87)(63 89)(65 91)(67 93)(69 95)(71 97)(73 99)(75 101)(77 103)(105 169)(106 132)(107 171)(108 134)(109 173)(110 136)(111 175)(112 138)(113 177)(114 140)(115 179)(116 142)(117 181)(118 144)(119 183)(120 146)(121 185)(122 148)(123 187)(124 150)(125 189)(126 152)(127 191)(128 154)(129 193)(130 156)(131 195)(133 197)(135 199)(137 201)(139 203)(141 205)(143 207)(145 157)(147 159)(149 161)(151 163)(153 165)(155 167)(158 184)(160 186)(162 188)(164 190)(166 192)(168 194)(170 196)(172 198)(174 200)(176 202)(178 204)(180 206)(182 208)
(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 81)(2 82)(3 83)(4 84)(5 85)(6 86)(7 87)(8 88)(9 89)(10 90)(11 91)(12 92)(13 93)(14 94)(15 95)(16 96)(17 97)(18 98)(19 99)(20 100)(21 101)(22 102)(23 103)(24 104)(25 53)(26 54)(27 55)(28 56)(29 57)(30 58)(31 59)(32 60)(33 61)(34 62)(35 63)(36 64)(37 65)(38 66)(39 67)(40 68)(41 69)(42 70)(43 71)(44 72)(45 73)(46 74)(47 75)(48 76)(49 77)(50 78)(51 79)(52 80)(105 195)(106 196)(107 197)(108 198)(109 199)(110 200)(111 201)(112 202)(113 203)(114 204)(115 205)(116 206)(117 207)(118 208)(119 157)(120 158)(121 159)(122 160)(123 161)(124 162)(125 163)(126 164)(127 165)(128 166)(129 167)(130 168)(131 169)(132 170)(133 171)(134 172)(135 173)(136 174)(137 175)(138 176)(139 177)(140 178)(141 179)(142 180)(143 181)(144 182)(145 183)(146 184)(147 185)(148 186)(149 187)(150 188)(151 189)(152 190)(153 191)(154 192)(155 193)(156 194)
(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)
(1 193 55 129)(2 166 56 154)(3 191 57 127)(4 164 58 152)(5 189 59 125)(6 162 60 150)(7 187 61 123)(8 160 62 148)(9 185 63 121)(10 158 64 146)(11 183 65 119)(12 208 66 144)(13 181 67 117)(14 206 68 142)(15 179 69 115)(16 204 70 140)(17 177 71 113)(18 202 72 138)(19 175 73 111)(20 200 74 136)(21 173 75 109)(22 198 76 134)(23 171 77 107)(24 196 78 132)(25 169 79 105)(26 194 80 130)(27 167 81 155)(28 192 82 128)(29 165 83 153)(30 190 84 126)(31 163 85 151)(32 188 86 124)(33 161 87 149)(34 186 88 122)(35 159 89 147)(36 184 90 120)(37 157 91 145)(38 182 92 118)(39 207 93 143)(40 180 94 116)(41 205 95 141)(42 178 96 114)(43 203 97 139)(44 176 98 112)(45 201 99 137)(46 174 100 110)(47 199 101 135)(48 172 102 108)(49 197 103 133)(50 170 104 106)(51 195 53 131)(52 168 54 156)
G:=sub<Sym(208)| (1,27)(2,56)(3,29)(4,58)(5,31)(6,60)(7,33)(8,62)(9,35)(10,64)(11,37)(12,66)(13,39)(14,68)(15,41)(16,70)(17,43)(18,72)(19,45)(20,74)(21,47)(22,76)(23,49)(24,78)(25,51)(26,80)(28,82)(30,84)(32,86)(34,88)(36,90)(38,92)(40,94)(42,96)(44,98)(46,100)(48,102)(50,104)(52,54)(53,79)(55,81)(57,83)(59,85)(61,87)(63,89)(65,91)(67,93)(69,95)(71,97)(73,99)(75,101)(77,103)(105,169)(106,132)(107,171)(108,134)(109,173)(110,136)(111,175)(112,138)(113,177)(114,140)(115,179)(116,142)(117,181)(118,144)(119,183)(120,146)(121,185)(122,148)(123,187)(124,150)(125,189)(126,152)(127,191)(128,154)(129,193)(130,156)(131,195)(133,197)(135,199)(137,201)(139,203)(141,205)(143,207)(145,157)(147,159)(149,161)(151,163)(153,165)(155,167)(158,184)(160,186)(162,188)(164,190)(166,192)(168,194)(170,196)(172,198)(174,200)(176,202)(178,204)(180,206)(182,208), (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), (1,81)(2,82)(3,83)(4,84)(5,85)(6,86)(7,87)(8,88)(9,89)(10,90)(11,91)(12,92)(13,93)(14,94)(15,95)(16,96)(17,97)(18,98)(19,99)(20,100)(21,101)(22,102)(23,103)(24,104)(25,53)(26,54)(27,55)(28,56)(29,57)(30,58)(31,59)(32,60)(33,61)(34,62)(35,63)(36,64)(37,65)(38,66)(39,67)(40,68)(41,69)(42,70)(43,71)(44,72)(45,73)(46,74)(47,75)(48,76)(49,77)(50,78)(51,79)(52,80)(105,195)(106,196)(107,197)(108,198)(109,199)(110,200)(111,201)(112,202)(113,203)(114,204)(115,205)(116,206)(117,207)(118,208)(119,157)(120,158)(121,159)(122,160)(123,161)(124,162)(125,163)(126,164)(127,165)(128,166)(129,167)(130,168)(131,169)(132,170)(133,171)(134,172)(135,173)(136,174)(137,175)(138,176)(139,177)(140,178)(141,179)(142,180)(143,181)(144,182)(145,183)(146,184)(147,185)(148,186)(149,187)(150,188)(151,189)(152,190)(153,191)(154,192)(155,193)(156,194), (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), (1,193,55,129)(2,166,56,154)(3,191,57,127)(4,164,58,152)(5,189,59,125)(6,162,60,150)(7,187,61,123)(8,160,62,148)(9,185,63,121)(10,158,64,146)(11,183,65,119)(12,208,66,144)(13,181,67,117)(14,206,68,142)(15,179,69,115)(16,204,70,140)(17,177,71,113)(18,202,72,138)(19,175,73,111)(20,200,74,136)(21,173,75,109)(22,198,76,134)(23,171,77,107)(24,196,78,132)(25,169,79,105)(26,194,80,130)(27,167,81,155)(28,192,82,128)(29,165,83,153)(30,190,84,126)(31,163,85,151)(32,188,86,124)(33,161,87,149)(34,186,88,122)(35,159,89,147)(36,184,90,120)(37,157,91,145)(38,182,92,118)(39,207,93,143)(40,180,94,116)(41,205,95,141)(42,178,96,114)(43,203,97,139)(44,176,98,112)(45,201,99,137)(46,174,100,110)(47,199,101,135)(48,172,102,108)(49,197,103,133)(50,170,104,106)(51,195,53,131)(52,168,54,156)>;
G:=Group( (1,27)(2,56)(3,29)(4,58)(5,31)(6,60)(7,33)(8,62)(9,35)(10,64)(11,37)(12,66)(13,39)(14,68)(15,41)(16,70)(17,43)(18,72)(19,45)(20,74)(21,47)(22,76)(23,49)(24,78)(25,51)(26,80)(28,82)(30,84)(32,86)(34,88)(36,90)(38,92)(40,94)(42,96)(44,98)(46,100)(48,102)(50,104)(52,54)(53,79)(55,81)(57,83)(59,85)(61,87)(63,89)(65,91)(67,93)(69,95)(71,97)(73,99)(75,101)(77,103)(105,169)(106,132)(107,171)(108,134)(109,173)(110,136)(111,175)(112,138)(113,177)(114,140)(115,179)(116,142)(117,181)(118,144)(119,183)(120,146)(121,185)(122,148)(123,187)(124,150)(125,189)(126,152)(127,191)(128,154)(129,193)(130,156)(131,195)(133,197)(135,199)(137,201)(139,203)(141,205)(143,207)(145,157)(147,159)(149,161)(151,163)(153,165)(155,167)(158,184)(160,186)(162,188)(164,190)(166,192)(168,194)(170,196)(172,198)(174,200)(176,202)(178,204)(180,206)(182,208), (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), (1,81)(2,82)(3,83)(4,84)(5,85)(6,86)(7,87)(8,88)(9,89)(10,90)(11,91)(12,92)(13,93)(14,94)(15,95)(16,96)(17,97)(18,98)(19,99)(20,100)(21,101)(22,102)(23,103)(24,104)(25,53)(26,54)(27,55)(28,56)(29,57)(30,58)(31,59)(32,60)(33,61)(34,62)(35,63)(36,64)(37,65)(38,66)(39,67)(40,68)(41,69)(42,70)(43,71)(44,72)(45,73)(46,74)(47,75)(48,76)(49,77)(50,78)(51,79)(52,80)(105,195)(106,196)(107,197)(108,198)(109,199)(110,200)(111,201)(112,202)(113,203)(114,204)(115,205)(116,206)(117,207)(118,208)(119,157)(120,158)(121,159)(122,160)(123,161)(124,162)(125,163)(126,164)(127,165)(128,166)(129,167)(130,168)(131,169)(132,170)(133,171)(134,172)(135,173)(136,174)(137,175)(138,176)(139,177)(140,178)(141,179)(142,180)(143,181)(144,182)(145,183)(146,184)(147,185)(148,186)(149,187)(150,188)(151,189)(152,190)(153,191)(154,192)(155,193)(156,194), (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), (1,193,55,129)(2,166,56,154)(3,191,57,127)(4,164,58,152)(5,189,59,125)(6,162,60,150)(7,187,61,123)(8,160,62,148)(9,185,63,121)(10,158,64,146)(11,183,65,119)(12,208,66,144)(13,181,67,117)(14,206,68,142)(15,179,69,115)(16,204,70,140)(17,177,71,113)(18,202,72,138)(19,175,73,111)(20,200,74,136)(21,173,75,109)(22,198,76,134)(23,171,77,107)(24,196,78,132)(25,169,79,105)(26,194,80,130)(27,167,81,155)(28,192,82,128)(29,165,83,153)(30,190,84,126)(31,163,85,151)(32,188,86,124)(33,161,87,149)(34,186,88,122)(35,159,89,147)(36,184,90,120)(37,157,91,145)(38,182,92,118)(39,207,93,143)(40,180,94,116)(41,205,95,141)(42,178,96,114)(43,203,97,139)(44,176,98,112)(45,201,99,137)(46,174,100,110)(47,199,101,135)(48,172,102,108)(49,197,103,133)(50,170,104,106)(51,195,53,131)(52,168,54,156) );
G=PermutationGroup([[(1,27),(2,56),(3,29),(4,58),(5,31),(6,60),(7,33),(8,62),(9,35),(10,64),(11,37),(12,66),(13,39),(14,68),(15,41),(16,70),(17,43),(18,72),(19,45),(20,74),(21,47),(22,76),(23,49),(24,78),(25,51),(26,80),(28,82),(30,84),(32,86),(34,88),(36,90),(38,92),(40,94),(42,96),(44,98),(46,100),(48,102),(50,104),(52,54),(53,79),(55,81),(57,83),(59,85),(61,87),(63,89),(65,91),(67,93),(69,95),(71,97),(73,99),(75,101),(77,103),(105,169),(106,132),(107,171),(108,134),(109,173),(110,136),(111,175),(112,138),(113,177),(114,140),(115,179),(116,142),(117,181),(118,144),(119,183),(120,146),(121,185),(122,148),(123,187),(124,150),(125,189),(126,152),(127,191),(128,154),(129,193),(130,156),(131,195),(133,197),(135,199),(137,201),(139,203),(141,205),(143,207),(145,157),(147,159),(149,161),(151,163),(153,165),(155,167),(158,184),(160,186),(162,188),(164,190),(166,192),(168,194),(170,196),(172,198),(174,200),(176,202),(178,204),(180,206),(182,208)], [(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)], [(1,81),(2,82),(3,83),(4,84),(5,85),(6,86),(7,87),(8,88),(9,89),(10,90),(11,91),(12,92),(13,93),(14,94),(15,95),(16,96),(17,97),(18,98),(19,99),(20,100),(21,101),(22,102),(23,103),(24,104),(25,53),(26,54),(27,55),(28,56),(29,57),(30,58),(31,59),(32,60),(33,61),(34,62),(35,63),(36,64),(37,65),(38,66),(39,67),(40,68),(41,69),(42,70),(43,71),(44,72),(45,73),(46,74),(47,75),(48,76),(49,77),(50,78),(51,79),(52,80),(105,195),(106,196),(107,197),(108,198),(109,199),(110,200),(111,201),(112,202),(113,203),(114,204),(115,205),(116,206),(117,207),(118,208),(119,157),(120,158),(121,159),(122,160),(123,161),(124,162),(125,163),(126,164),(127,165),(128,166),(129,167),(130,168),(131,169),(132,170),(133,171),(134,172),(135,173),(136,174),(137,175),(138,176),(139,177),(140,178),(141,179),(142,180),(143,181),(144,182),(145,183),(146,184),(147,185),(148,186),(149,187),(150,188),(151,189),(152,190),(153,191),(154,192),(155,193),(156,194)], [(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)], [(1,193,55,129),(2,166,56,154),(3,191,57,127),(4,164,58,152),(5,189,59,125),(6,162,60,150),(7,187,61,123),(8,160,62,148),(9,185,63,121),(10,158,64,146),(11,183,65,119),(12,208,66,144),(13,181,67,117),(14,206,68,142),(15,179,69,115),(16,204,70,140),(17,177,71,113),(18,202,72,138),(19,175,73,111),(20,200,74,136),(21,173,75,109),(22,198,76,134),(23,171,77,107),(24,196,78,132),(25,169,79,105),(26,194,80,130),(27,167,81,155),(28,192,82,128),(29,165,83,153),(30,190,84,126),(31,163,85,151),(32,188,86,124),(33,161,87,149),(34,186,88,122),(35,159,89,147),(36,184,90,120),(37,157,91,145),(38,182,92,118),(39,207,93,143),(40,180,94,116),(41,205,95,141),(42,178,96,114),(43,203,97,139),(44,176,98,112),(45,201,99,137),(46,174,100,110),(47,199,101,135),(48,172,102,108),(49,197,103,133),(50,170,104,106),(51,195,53,131),(52,168,54,156)]])
80 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4N | 13A | ··· | 13F | 26A | ··· | 26R | 26S | ··· | 26AD | 52A | ··· | 52X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 13 | ··· | 13 | 26 | ··· | 26 | 26 | ··· | 26 | 52 | ··· | 52 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 13 | 13 | 13 | 13 | 26 | ··· | 26 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
80 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | C4○D4 | D13 | D26 | D26 | C4×D13 | D4⋊2D13 |
| kernel | C23.11D26 | C4×Dic13 | C26.D4 | C23.D13 | C13×C22⋊C4 | C22×Dic13 | C2×Dic13 | C26 | C22⋊C4 | C2×C4 | C23 | C22 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 8 | 4 | 6 | 12 | 6 | 24 | 12 |
Matrix representation of C23.11D26 ►in GL4(𝔽53) generated by
| 52 | 0 | 0 | 0 |
| 0 | 52 | 0 | 0 |
| 0 | 0 | 52 | 0 |
| 0 | 0 | 23 | 1 |
| 52 | 0 | 0 | 0 |
| 0 | 52 | 0 | 0 |
| 0 | 0 | 52 | 0 |
| 0 | 0 | 0 | 52 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 52 | 0 |
| 0 | 0 | 0 | 52 |
| 40 | 17 | 0 | 0 |
| 3 | 41 | 0 | 0 |
| 0 | 0 | 30 | 51 |
| 0 | 0 | 0 | 23 |
| 20 | 30 | 0 | 0 |
| 52 | 33 | 0 | 0 |
| 0 | 0 | 52 | 46 |
| 0 | 0 | 0 | 1 |
G:=sub<GL(4,GF(53))| [52,0,0,0,0,52,0,0,0,0,52,23,0,0,0,1],[52,0,0,0,0,52,0,0,0,0,52,0,0,0,0,52],[1,0,0,0,0,1,0,0,0,0,52,0,0,0,0,52],[40,3,0,0,17,41,0,0,0,0,30,0,0,0,51,23],[20,52,0,0,30,33,0,0,0,0,52,0,0,0,46,1] >;
C23.11D26 in GAP, Magma, Sage, TeX
C_2^3._{11}D_{26} % in TeX
G:=Group("C2^3.11D26"); // GroupNames label
G:=SmallGroup(416,98);
// by ID
G=gap.SmallGroup(416,98);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-13,96,188,50,13829]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^2=1,d^26=b,e^2=c*b=b*c,a*b=b*a,d*a*d^-1=e*a*e^-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