Copied to
clipboard

G = C23.6D26order 416 = 25·13

6th non-split extension by C23 of D26 acting via D26/C13=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C23.6D26, Dic13.5D4, (C2×C4).8D26, C22⋊C45D13, C26.21(C2×D4), C2.10(D4×D13), D26⋊C46C2, (C2×Dic26)⋊3C2, C132(C4.4D4), C23.D135C2, (C4×Dic13)⋊12C2, C26.10(C4○D4), (C2×C52).54C22, (C2×C26).26C23, C2.9(D42D13), C2.12(D525C2), (C22×C26).15C22, (C22×D13).4C22, C22.44(C22×D13), (C2×Dic13).30C22, (C13×C22⋊C4)⋊7C2, (C2×C13⋊D4).4C2, SmallGroup(416,106)

Series: Derived Chief Lower central Upper central

C1C2×C26 — C23.6D26
C1C13C26C2×C26C22×D13D26⋊C4 — C23.6D26
C13C2×C26 — C23.6D26
C1C22C22⋊C4

Generators and relations for C23.6D26
 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=cd25 >

Subgroups: 536 in 76 conjugacy classes, 31 normal (29 characteristic)
C1, C2 [×3], C2 [×2], C4 [×6], C22, C22 [×6], C2×C4 [×2], C2×C4 [×3], D4 [×2], Q8 [×2], C23, C23, C13, C42, C22⋊C4, C22⋊C4 [×3], C2×D4, C2×Q8, D13, C26 [×3], C26, C4.4D4, Dic13 [×2], Dic13 [×2], C52 [×2], D26 [×3], C2×C26, C2×C26 [×3], Dic26 [×2], C2×Dic13 [×3], C13⋊D4 [×2], C2×C52 [×2], C22×D13, C22×C26, C4×Dic13, D26⋊C4 [×2], C23.D13, C13×C22⋊C4, C2×Dic26, C2×C13⋊D4, C23.6D26
Quotients: C1, C2 [×7], C22 [×7], D4 [×2], C23, C2×D4, C4○D4 [×2], D13, C4.4D4, D26 [×3], C22×D13, D525C2, D4×D13, D42D13, C23.6D26

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

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

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

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

74 conjugacy classes

class 1 2A2B2C2D2E4A4B4C4D4E4F4G4H13A···13F26A···26R26S···26AD52A···52X
order1222224444444413···1326···2626···2652···52
size111145222426262626522···22···24···44···4

74 irreducible representations

dim111111122222244
type++++++++++++-
imageC1C2C2C2C2C2C2D4C4○D4D13D26D26D525C2D4×D13D42D13
kernelC23.6D26C4×Dic13D26⋊C4C23.D13C13×C22⋊C4C2×Dic26C2×C13⋊D4Dic13C26C22⋊C4C2×C4C23C2C2C2
# reps11211112461262466

Matrix representation of C23.6D26 in GL4(𝔽53) generated by

144700
63900
0010
002352
,
52000
05200
00520
00052
,
1000
0100
00520
00052
,
432200
312200
004742
00136
,
224300
223100
00611
004547
G:=sub<GL(4,GF(53))| [14,6,0,0,47,39,0,0,0,0,1,23,0,0,0,52],[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],[43,31,0,0,22,22,0,0,0,0,47,13,0,0,42,6],[22,22,0,0,43,31,0,0,0,0,6,45,0,0,11,47] >;

C23.6D26 in GAP, Magma, Sage, TeX

C_2^3._6D_{26}
% in TeX

G:=Group("C2^3.6D26");
// GroupNames label

G:=SmallGroup(416,106);
// by ID

G=gap.SmallGroup(416,106);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-2,-13,217,55,506,188,13829]);
// 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=c*d^25>;
// generators/relations

׿
×
𝔽