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G = C23.23D26order 416 = 25·13

4th non-split extension by C23 of D26 acting via D26/C26=C2

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⋊C42C2, C26.D43C2, C23.D136C2, C26.18(C4○D4), (C2×C52).78C22, (C2×C26).47C23, C134(C22.D4), C22.9(C13⋊D4), C2.18(D525C2), (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

C1C2×C26 — C23.23D26
C1C13C26C2×C26C22×D13C2×C13⋊D4 — C23.23D26
C13C2×C26 — C23.23D26
C1C22C22×C4

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 [×2], C2 [×3], C4 [×5], C22, C22 [×2], C22 [×5], C2×C4 [×2], C2×C4 [×5], D4 [×2], C23, C23, C13, C22⋊C4 [×3], C4⋊C4 [×2], C22×C4, C2×D4, D13, C26, C26 [×2], C26 [×2], C22.D4, Dic13 [×3], C52 [×2], D26 [×3], C2×C26, C2×C26 [×2], C2×C26 [×2], C2×Dic13, C2×Dic13 [×2], C13⋊D4 [×2], C2×C52 [×2], C2×C52 [×2], C22×D13, C22×C26, C26.D4 [×2], D26⋊C4 [×2], C23.D13, C2×C13⋊D4, C22×C52, C23.23D26
Quotients: C1, C2 [×7], C22 [×7], D4 [×2], C23, C2×D4, C4○D4 [×2], D13, C22.D4, D26 [×3], C13⋊D4 [×2], C22×D13, D525C2 [×2], C2×C13⋊D4, C23.23D26

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

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

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

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

110 conjugacy classes

class 1 2A2B2C2D2E2F4A4B4C4D4E4F4G13A···13F26A···26AP52A···52AV
order1222222444444413···1326···2652···52
size1111225222225252522···22···22···2

110 irreducible representations

dim1111112222222
type++++++++++
imageC1C2C2C2C2C2D4C4○D4D13D26D26C13⋊D4D525C2
kernelC23.23D26C26.D4D26⋊C4C23.D13C2×C13⋊D4C22×C52C2×C26C26C22×C4C2×C4C23C22C2
# reps1221112461262448

Matrix representation of C23.23D26 in GL4(𝔽53) generated by

1000
295200
0010
00052
,
52000
05200
0010
0001
,
52000
05200
00520
00052
,
45000
153300
00480
00032
,
501300
32300
00032
00480
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

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