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G = C23.21D26order 416 = 25·13

2nd non-split extension by C23 of D26 acting via D26/C26=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C23.21D26, (C2×C52)⋊11C4, C52.58(C2×C4), C523C417C2, (C2×C4)⋊4Dic13, (C2×C4).102D26, (C22×C4).7D13, C135(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(D525C2), 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

C1C26 — C23.21D26
C1C13C26C2×C26C2×Dic13C4×Dic13 — C23.21D26
C13C26 — C23.21D26
C1C2×C4C22×C4

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 [×2], C2 [×2], C4 [×4], C4 [×4], C22, C22 [×2], C22 [×2], C2×C4 [×2], C2×C4 [×4], C2×C4 [×4], C23, C13, C42 [×2], C22⋊C4 [×2], C4⋊C4 [×2], C22×C4, C26, C26 [×2], C26 [×2], C42⋊C2, Dic13 [×4], C52 [×4], C2×C26, C2×C26 [×2], C2×C26 [×2], C2×Dic13 [×4], C2×C52 [×2], C2×C52 [×4], C22×C26, C4×Dic13 [×2], C523C4 [×2], C23.D13 [×2], C22×C52, C23.21D26
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], C23, C22×C4, C4○D4 [×2], D13, C42⋊C2, Dic13 [×4], D26 [×3], C2×Dic13 [×6], C22×D13, D525C2 [×2], C22×Dic13, C23.21D26

Smallest permutation representation of C23.21D26
On 208 points
Generators in S208
(1 200)(2 201)(3 202)(4 203)(5 204)(6 205)(7 206)(8 207)(9 208)(10 157)(11 158)(12 159)(13 160)(14 161)(15 162)(16 163)(17 164)(18 165)(19 166)(20 167)(21 168)(22 169)(23 170)(24 171)(25 172)(26 173)(27 174)(28 175)(29 176)(30 177)(31 178)(32 179)(33 180)(34 181)(35 182)(36 183)(37 184)(38 185)(39 186)(40 187)(41 188)(42 189)(43 190)(44 191)(45 192)(46 193)(47 194)(48 195)(49 196)(50 197)(51 198)(52 199)(53 123)(54 124)(55 125)(56 126)(57 127)(58 128)(59 129)(60 130)(61 131)(62 132)(63 133)(64 134)(65 135)(66 136)(67 137)(68 138)(69 139)(70 140)(71 141)(72 142)(73 143)(74 144)(75 145)(76 146)(77 147)(78 148)(79 149)(80 150)(81 151)(82 152)(83 153)(84 154)(85 155)(86 156)(87 105)(88 106)(89 107)(90 108)(91 109)(92 110)(93 111)(94 112)(95 113)(96 114)(97 115)(98 116)(99 117)(100 118)(101 119)(102 120)(103 121)(104 122)
(1 200)(2 201)(3 202)(4 203)(5 204)(6 205)(7 206)(8 207)(9 208)(10 157)(11 158)(12 159)(13 160)(14 161)(15 162)(16 163)(17 164)(18 165)(19 166)(20 167)(21 168)(22 169)(23 170)(24 171)(25 172)(26 173)(27 174)(28 175)(29 176)(30 177)(31 178)(32 179)(33 180)(34 181)(35 182)(36 183)(37 184)(38 185)(39 186)(40 187)(41 188)(42 189)(43 190)(44 191)(45 192)(46 193)(47 194)(48 195)(49 196)(50 197)(51 198)(52 199)(53 149)(54 150)(55 151)(56 152)(57 153)(58 154)(59 155)(60 156)(61 105)(62 106)(63 107)(64 108)(65 109)(66 110)(67 111)(68 112)(69 113)(70 114)(71 115)(72 116)(73 117)(74 118)(75 119)(76 120)(77 121)(78 122)(79 123)(80 124)(81 125)(82 126)(83 127)(84 128)(85 129)(86 130)(87 131)(88 132)(89 133)(90 134)(91 135)(92 136)(93 137)(94 138)(95 139)(96 140)(97 141)(98 142)(99 143)(100 144)(101 145)(102 146)(103 147)(104 148)
(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)
(1 106 174 88)(2 131 175 61)(3 156 176 86)(4 129 177 59)(5 154 178 84)(6 127 179 57)(7 152 180 82)(8 125 181 55)(9 150 182 80)(10 123 183 53)(11 148 184 78)(12 121 185 103)(13 146 186 76)(14 119 187 101)(15 144 188 74)(16 117 189 99)(17 142 190 72)(18 115 191 97)(19 140 192 70)(20 113 193 95)(21 138 194 68)(22 111 195 93)(23 136 196 66)(24 109 197 91)(25 134 198 64)(26 107 199 89)(27 132 200 62)(28 105 201 87)(29 130 202 60)(30 155 203 85)(31 128 204 58)(32 153 205 83)(33 126 206 56)(34 151 207 81)(35 124 208 54)(36 149 157 79)(37 122 158 104)(38 147 159 77)(39 120 160 102)(40 145 161 75)(41 118 162 100)(42 143 163 73)(43 116 164 98)(44 141 165 71)(45 114 166 96)(46 139 167 69)(47 112 168 94)(48 137 169 67)(49 110 170 92)(50 135 171 65)(51 108 172 90)(52 133 173 63)

G:=sub<Sym(208)| (1,200)(2,201)(3,202)(4,203)(5,204)(6,205)(7,206)(8,207)(9,208)(10,157)(11,158)(12,159)(13,160)(14,161)(15,162)(16,163)(17,164)(18,165)(19,166)(20,167)(21,168)(22,169)(23,170)(24,171)(25,172)(26,173)(27,174)(28,175)(29,176)(30,177)(31,178)(32,179)(33,180)(34,181)(35,182)(36,183)(37,184)(38,185)(39,186)(40,187)(41,188)(42,189)(43,190)(44,191)(45,192)(46,193)(47,194)(48,195)(49,196)(50,197)(51,198)(52,199)(53,123)(54,124)(55,125)(56,126)(57,127)(58,128)(59,129)(60,130)(61,131)(62,132)(63,133)(64,134)(65,135)(66,136)(67,137)(68,138)(69,139)(70,140)(71,141)(72,142)(73,143)(74,144)(75,145)(76,146)(77,147)(78,148)(79,149)(80,150)(81,151)(82,152)(83,153)(84,154)(85,155)(86,156)(87,105)(88,106)(89,107)(90,108)(91,109)(92,110)(93,111)(94,112)(95,113)(96,114)(97,115)(98,116)(99,117)(100,118)(101,119)(102,120)(103,121)(104,122), (1,200)(2,201)(3,202)(4,203)(5,204)(6,205)(7,206)(8,207)(9,208)(10,157)(11,158)(12,159)(13,160)(14,161)(15,162)(16,163)(17,164)(18,165)(19,166)(20,167)(21,168)(22,169)(23,170)(24,171)(25,172)(26,173)(27,174)(28,175)(29,176)(30,177)(31,178)(32,179)(33,180)(34,181)(35,182)(36,183)(37,184)(38,185)(39,186)(40,187)(41,188)(42,189)(43,190)(44,191)(45,192)(46,193)(47,194)(48,195)(49,196)(50,197)(51,198)(52,199)(53,149)(54,150)(55,151)(56,152)(57,153)(58,154)(59,155)(60,156)(61,105)(62,106)(63,107)(64,108)(65,109)(66,110)(67,111)(68,112)(69,113)(70,114)(71,115)(72,116)(73,117)(74,118)(75,119)(76,120)(77,121)(78,122)(79,123)(80,124)(81,125)(82,126)(83,127)(84,128)(85,129)(86,130)(87,131)(88,132)(89,133)(90,134)(91,135)(92,136)(93,137)(94,138)(95,139)(96,140)(97,141)(98,142)(99,143)(100,144)(101,145)(102,146)(103,147)(104,148), (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), (1,106,174,88)(2,131,175,61)(3,156,176,86)(4,129,177,59)(5,154,178,84)(6,127,179,57)(7,152,180,82)(8,125,181,55)(9,150,182,80)(10,123,183,53)(11,148,184,78)(12,121,185,103)(13,146,186,76)(14,119,187,101)(15,144,188,74)(16,117,189,99)(17,142,190,72)(18,115,191,97)(19,140,192,70)(20,113,193,95)(21,138,194,68)(22,111,195,93)(23,136,196,66)(24,109,197,91)(25,134,198,64)(26,107,199,89)(27,132,200,62)(28,105,201,87)(29,130,202,60)(30,155,203,85)(31,128,204,58)(32,153,205,83)(33,126,206,56)(34,151,207,81)(35,124,208,54)(36,149,157,79)(37,122,158,104)(38,147,159,77)(39,120,160,102)(40,145,161,75)(41,118,162,100)(42,143,163,73)(43,116,164,98)(44,141,165,71)(45,114,166,96)(46,139,167,69)(47,112,168,94)(48,137,169,67)(49,110,170,92)(50,135,171,65)(51,108,172,90)(52,133,173,63)>;

G:=Group( (1,200)(2,201)(3,202)(4,203)(5,204)(6,205)(7,206)(8,207)(9,208)(10,157)(11,158)(12,159)(13,160)(14,161)(15,162)(16,163)(17,164)(18,165)(19,166)(20,167)(21,168)(22,169)(23,170)(24,171)(25,172)(26,173)(27,174)(28,175)(29,176)(30,177)(31,178)(32,179)(33,180)(34,181)(35,182)(36,183)(37,184)(38,185)(39,186)(40,187)(41,188)(42,189)(43,190)(44,191)(45,192)(46,193)(47,194)(48,195)(49,196)(50,197)(51,198)(52,199)(53,123)(54,124)(55,125)(56,126)(57,127)(58,128)(59,129)(60,130)(61,131)(62,132)(63,133)(64,134)(65,135)(66,136)(67,137)(68,138)(69,139)(70,140)(71,141)(72,142)(73,143)(74,144)(75,145)(76,146)(77,147)(78,148)(79,149)(80,150)(81,151)(82,152)(83,153)(84,154)(85,155)(86,156)(87,105)(88,106)(89,107)(90,108)(91,109)(92,110)(93,111)(94,112)(95,113)(96,114)(97,115)(98,116)(99,117)(100,118)(101,119)(102,120)(103,121)(104,122), (1,200)(2,201)(3,202)(4,203)(5,204)(6,205)(7,206)(8,207)(9,208)(10,157)(11,158)(12,159)(13,160)(14,161)(15,162)(16,163)(17,164)(18,165)(19,166)(20,167)(21,168)(22,169)(23,170)(24,171)(25,172)(26,173)(27,174)(28,175)(29,176)(30,177)(31,178)(32,179)(33,180)(34,181)(35,182)(36,183)(37,184)(38,185)(39,186)(40,187)(41,188)(42,189)(43,190)(44,191)(45,192)(46,193)(47,194)(48,195)(49,196)(50,197)(51,198)(52,199)(53,149)(54,150)(55,151)(56,152)(57,153)(58,154)(59,155)(60,156)(61,105)(62,106)(63,107)(64,108)(65,109)(66,110)(67,111)(68,112)(69,113)(70,114)(71,115)(72,116)(73,117)(74,118)(75,119)(76,120)(77,121)(78,122)(79,123)(80,124)(81,125)(82,126)(83,127)(84,128)(85,129)(86,130)(87,131)(88,132)(89,133)(90,134)(91,135)(92,136)(93,137)(94,138)(95,139)(96,140)(97,141)(98,142)(99,143)(100,144)(101,145)(102,146)(103,147)(104,148), (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), (1,106,174,88)(2,131,175,61)(3,156,176,86)(4,129,177,59)(5,154,178,84)(6,127,179,57)(7,152,180,82)(8,125,181,55)(9,150,182,80)(10,123,183,53)(11,148,184,78)(12,121,185,103)(13,146,186,76)(14,119,187,101)(15,144,188,74)(16,117,189,99)(17,142,190,72)(18,115,191,97)(19,140,192,70)(20,113,193,95)(21,138,194,68)(22,111,195,93)(23,136,196,66)(24,109,197,91)(25,134,198,64)(26,107,199,89)(27,132,200,62)(28,105,201,87)(29,130,202,60)(30,155,203,85)(31,128,204,58)(32,153,205,83)(33,126,206,56)(34,151,207,81)(35,124,208,54)(36,149,157,79)(37,122,158,104)(38,147,159,77)(39,120,160,102)(40,145,161,75)(41,118,162,100)(42,143,163,73)(43,116,164,98)(44,141,165,71)(45,114,166,96)(46,139,167,69)(47,112,168,94)(48,137,169,67)(49,110,170,92)(50,135,171,65)(51,108,172,90)(52,133,173,63) );

G=PermutationGroup([(1,200),(2,201),(3,202),(4,203),(5,204),(6,205),(7,206),(8,207),(9,208),(10,157),(11,158),(12,159),(13,160),(14,161),(15,162),(16,163),(17,164),(18,165),(19,166),(20,167),(21,168),(22,169),(23,170),(24,171),(25,172),(26,173),(27,174),(28,175),(29,176),(30,177),(31,178),(32,179),(33,180),(34,181),(35,182),(36,183),(37,184),(38,185),(39,186),(40,187),(41,188),(42,189),(43,190),(44,191),(45,192),(46,193),(47,194),(48,195),(49,196),(50,197),(51,198),(52,199),(53,123),(54,124),(55,125),(56,126),(57,127),(58,128),(59,129),(60,130),(61,131),(62,132),(63,133),(64,134),(65,135),(66,136),(67,137),(68,138),(69,139),(70,140),(71,141),(72,142),(73,143),(74,144),(75,145),(76,146),(77,147),(78,148),(79,149),(80,150),(81,151),(82,152),(83,153),(84,154),(85,155),(86,156),(87,105),(88,106),(89,107),(90,108),(91,109),(92,110),(93,111),(94,112),(95,113),(96,114),(97,115),(98,116),(99,117),(100,118),(101,119),(102,120),(103,121),(104,122)], [(1,200),(2,201),(3,202),(4,203),(5,204),(6,205),(7,206),(8,207),(9,208),(10,157),(11,158),(12,159),(13,160),(14,161),(15,162),(16,163),(17,164),(18,165),(19,166),(20,167),(21,168),(22,169),(23,170),(24,171),(25,172),(26,173),(27,174),(28,175),(29,176),(30,177),(31,178),(32,179),(33,180),(34,181),(35,182),(36,183),(37,184),(38,185),(39,186),(40,187),(41,188),(42,189),(43,190),(44,191),(45,192),(46,193),(47,194),(48,195),(49,196),(50,197),(51,198),(52,199),(53,149),(54,150),(55,151),(56,152),(57,153),(58,154),(59,155),(60,156),(61,105),(62,106),(63,107),(64,108),(65,109),(66,110),(67,111),(68,112),(69,113),(70,114),(71,115),(72,116),(73,117),(74,118),(75,119),(76,120),(77,121),(78,122),(79,123),(80,124),(81,125),(82,126),(83,127),(84,128),(85,129),(86,130),(87,131),(88,132),(89,133),(90,134),(91,135),(92,136),(93,137),(94,138),(95,139),(96,140),(97,141),(98,142),(99,143),(100,144),(101,145),(102,146),(103,147),(104,148)], [(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)], [(1,106,174,88),(2,131,175,61),(3,156,176,86),(4,129,177,59),(5,154,178,84),(6,127,179,57),(7,152,180,82),(8,125,181,55),(9,150,182,80),(10,123,183,53),(11,148,184,78),(12,121,185,103),(13,146,186,76),(14,119,187,101),(15,144,188,74),(16,117,189,99),(17,142,190,72),(18,115,191,97),(19,140,192,70),(20,113,193,95),(21,138,194,68),(22,111,195,93),(23,136,196,66),(24,109,197,91),(25,134,198,64),(26,107,199,89),(27,132,200,62),(28,105,201,87),(29,130,202,60),(30,155,203,85),(31,128,204,58),(32,153,205,83),(33,126,206,56),(34,151,207,81),(35,124,208,54),(36,149,157,79),(37,122,158,104),(38,147,159,77),(39,120,160,102),(40,145,161,75),(41,118,162,100),(42,143,163,73),(43,116,164,98),(44,141,165,71),(45,114,166,96),(46,139,167,69),(47,112,168,94),(48,137,169,67),(49,110,170,92),(50,135,171,65),(51,108,172,90),(52,133,173,63)])

116 conjugacy classes

class 1 2A2B2C2D2E4A4B4C4D4E4F4G···4N13A···13F26A···26AP52A···52AV
order1222224444444···413···1326···2652···52
size11112211112226···262···22···22···2

116 irreducible representations

dim111111222222
type++++++-++
imageC1C2C2C2C2C4C4○D4D13Dic13D26D26D525C2
kernelC23.21D26C4×Dic13C523C4C23.D13C22×C52C2×C52C26C22×C4C2×C4C2×C4C23C2
# reps122218462412648

Matrix representation of C23.21D26 in GL3(𝔽53) generated by

100
017
0052
,
5200
010
001
,
100
0520
0052
,
5200
03917
0019
,
2300
0338
03620
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

׿
×
𝔽