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G = C23.18D26order 416 = 25·13

8th non-split extension by C23 of D26 acting via D26/D13=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C23.18D26, (C2×C26).7D4, (C2×D4).5D13, C26.47(C2×D4), (C2×C4).18D26, (D4×C26).10C2, C23.D138C2, C26.29(C4○D4), C26.D414C2, (C2×C26).50C23, (C2×C52).61C22, (C22×Dic13)⋊5C2, C22.4(C13⋊D4), C135(C22.D4), C2.15(D42D13), (C22×C26).18C22, C22.57(C22×D13), (C2×Dic13).17C22, C2.11(C2×C13⋊D4), SmallGroup(416,156)

Series: Derived Chief Lower central Upper central

C1C2×C26 — C23.18D26
C1C13C26C2×C26C2×Dic13C22×Dic13 — C23.18D26
C13C2×C26 — C23.18D26
C1C22C2×D4

Generators and relations for C23.18D26
 G = < a,b,c,d,e | a2=b2=c2=d26=1, e2=cb=bc, ab=ba, dad-1=eae-1=ac=ca, bd=db, be=eb, cd=dc, ce=ec, ede-1=bd-1 >

Subgroups: 392 in 78 conjugacy classes, 33 normal (17 characteristic)
C1, C2, C2 [×2], C2 [×3], C4 [×5], C22, C22 [×2], C22 [×5], C2×C4, C2×C4 [×6], D4 [×2], C23 [×2], C13, C22⋊C4 [×3], C4⋊C4 [×2], C22×C4, C2×D4, C26, C26 [×2], C26 [×3], C22.D4, Dic13 [×4], C52, C2×C26, C2×C26 [×2], C2×C26 [×5], C2×Dic13 [×4], C2×Dic13 [×2], C2×C52, D4×C13 [×2], C22×C26 [×2], C26.D4 [×2], C23.D13, C23.D13 [×2], C22×Dic13, D4×C26, C23.18D26
Quotients: C1, C2 [×7], C22 [×7], D4 [×2], C23, C2×D4, C4○D4 [×2], D13, C22.D4, D26 [×3], C13⋊D4 [×2], C22×D13, D42D13 [×2], C2×C13⋊D4, C23.18D26

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

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

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

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

74 conjugacy classes

class 1 2A2B2C2D2E2F4A4B4C4D4E4F4G13A···13F26A···26R26S···26AP52A···52L
order1222222444444413···1326···2626···2652···52
size111122442626262652522···22···24···44···4

74 irreducible representations

dim111112222224
type+++++++++-
imageC1C2C2C2C2D4C4○D4D13D26D26C13⋊D4D42D13
kernelC23.18D26C26.D4C23.D13C22×Dic13D4×C26C2×C26C26C2×D4C2×C4C23C22C2
# reps123112466122412

Matrix representation of C23.18D26 in GL4(𝔽53) generated by

1000
0100
0010
00052
,
52000
05200
00520
00052
,
1000
0100
00520
00052
,
151200
511600
0001
0010
,
30000
292300
00030
00230
G:=sub<GL(4,GF(53))| [1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,52],[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],[15,51,0,0,12,16,0,0,0,0,0,1,0,0,1,0],[30,29,0,0,0,23,0,0,0,0,0,23,0,0,30,0] >;

C23.18D26 in GAP, Magma, Sage, TeX

C_2^3._{18}D_{26}
% in TeX

G:=Group("C2^3.18D26");
// GroupNames label

G:=SmallGroup(416,156);
// by ID

G=gap.SmallGroup(416,156);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-2,-13,96,218,188,13829]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^26=1,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=b*d^-1>;
// generators/relations

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