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.D13⋊8C2, C26.29(C4○D4), C26.D4⋊14C2, (C2×C26).50C23, (C2×C52).61C22, (C22×Dic13)⋊5C2, C22.4(C13⋊D4), C13⋊5(C22.D4), C2.15(D4⋊2D13), (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
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, C2, C4, C22, C22, C22, C2×C4, C2×C4, D4, C23, C13, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C26, C26, C26, C22.D4, Dic13, C52, C2×C26, C2×C26, C2×C26, C2×Dic13, C2×Dic13, C2×C52, D4×C13, C22×C26, C26.D4, C23.D13, C23.D13, C22×Dic13, D4×C26, C23.18D26
Quotients: C1, C2, C22, D4, C23, C2×D4, C4○D4, D13, C22.D4, D26, C13⋊D4, C22×D13, D4⋊2D13, C2×C13⋊D4, C23.18D26
►On 208 points
Generators in S208
(2 190)(4 192)(6 194)(8 196)(10 198)(12 200)(14 202)(16 204)(18 206)(20 208)(22 184)(24 186)(26 188)(28 110)(30 112)(32 114)(34 116)(36 118)(38 120)(40 122)(42 124)(44 126)(46 128)(48 130)(50 106)(52 108)(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)(132 159)(134 161)(136 163)(138 165)(140 167)(142 169)(144 171)(146 173)(148 175)(150 177)(152 179)(154 181)(156 157)
(1 174)(2 175)(3 176)(4 177)(5 178)(6 179)(7 180)(8 181)(9 182)(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)(27 100)(28 101)(29 102)(30 103)(31 104)(32 79)(33 80)(34 81)(35 82)(36 83)(37 84)(38 85)(39 86)(40 87)(41 88)(42 89)(43 90)(44 91)(45 92)(46 93)(47 94)(48 95)(49 96)(50 97)(51 98)(52 99)(53 114)(54 115)(55 116)(56 117)(57 118)(58 119)(59 120)(60 121)(61 122)(62 123)(63 124)(64 125)(65 126)(66 127)(67 128)(68 129)(69 130)(70 105)(71 106)(72 107)(73 108)(74 109)(75 110)(76 111)(77 112)(78 113)(131 199)(132 200)(133 201)(134 202)(135 203)(136 204)(137 205)(138 206)(139 207)(140 208)(141 183)(142 184)(143 185)(144 186)(145 187)(146 188)(147 189)(148 190)(149 191)(150 192)(151 193)(152 194)(153 195)(154 196)(155 197)(156 198)
(1 189)(2 190)(3 191)(4 192)(5 193)(6 194)(7 195)(8 196)(9 197)(10 198)(11 199)(12 200)(13 201)(14 202)(15 203)(16 204)(17 205)(18 206)(19 207)(20 208)(21 183)(22 184)(23 185)(24 186)(25 187)(26 188)(27 109)(28 110)(29 111)(30 112)(31 113)(32 114)(33 115)(34 116)(35 117)(36 118)(37 119)(38 120)(39 121)(40 122)(41 123)(42 124)(43 125)(44 126)(45 127)(46 128)(47 129)(48 130)(49 105)(50 106)(51 107)(52 108)(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)(131 158)(132 159)(133 160)(134 161)(135 162)(136 163)(137 164)(138 165)(139 166)(140 167)(141 168)(142 169)(143 170)(144 171)(145 172)(146 173)(147 174)(148 175)(149 176)(150 177)(151 178)(152 179)(153 180)(154 181)(155 182)(156 157)
(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 36 147 57)(2 82 148 117)(3 34 149 55)(4 80 150 115)(5 32 151 53)(6 104 152 113)(7 30 153 77)(8 102 154 111)(9 28 155 75)(10 100 156 109)(11 52 131 73)(12 98 132 107)(13 50 133 71)(14 96 134 105)(15 48 135 69)(16 94 136 129)(17 46 137 67)(18 92 138 127)(19 44 139 65)(20 90 140 125)(21 42 141 63)(22 88 142 123)(23 40 143 61)(24 86 144 121)(25 38 145 59)(26 84 146 119)(27 198 74 157)(29 196 76 181)(31 194 78 179)(33 192 54 177)(35 190 56 175)(37 188 58 173)(39 186 60 171)(41 184 62 169)(43 208 64 167)(45 206 66 165)(47 204 68 163)(49 202 70 161)(51 200 72 159)(79 193 114 178)(81 191 116 176)(83 189 118 174)(85 187 120 172)(87 185 122 170)(89 183 124 168)(91 207 126 166)(93 205 128 164)(95 203 130 162)(97 201 106 160)(99 199 108 158)(101 197 110 182)(103 195 112 180)
G:=sub<Sym(208)| (2,190)(4,192)(6,194)(8,196)(10,198)(12,200)(14,202)(16,204)(18,206)(20,208)(22,184)(24,186)(26,188)(28,110)(30,112)(32,114)(34,116)(36,118)(38,120)(40,122)(42,124)(44,126)(46,128)(48,130)(50,106)(52,108)(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)(132,159)(134,161)(136,163)(138,165)(140,167)(142,169)(144,171)(146,173)(148,175)(150,177)(152,179)(154,181)(156,157), (1,174)(2,175)(3,176)(4,177)(5,178)(6,179)(7,180)(8,181)(9,182)(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)(27,100)(28,101)(29,102)(30,103)(31,104)(32,79)(33,80)(34,81)(35,82)(36,83)(37,84)(38,85)(39,86)(40,87)(41,88)(42,89)(43,90)(44,91)(45,92)(46,93)(47,94)(48,95)(49,96)(50,97)(51,98)(52,99)(53,114)(54,115)(55,116)(56,117)(57,118)(58,119)(59,120)(60,121)(61,122)(62,123)(63,124)(64,125)(65,126)(66,127)(67,128)(68,129)(69,130)(70,105)(71,106)(72,107)(73,108)(74,109)(75,110)(76,111)(77,112)(78,113)(131,199)(132,200)(133,201)(134,202)(135,203)(136,204)(137,205)(138,206)(139,207)(140,208)(141,183)(142,184)(143,185)(144,186)(145,187)(146,188)(147,189)(148,190)(149,191)(150,192)(151,193)(152,194)(153,195)(154,196)(155,197)(156,198), (1,189)(2,190)(3,191)(4,192)(5,193)(6,194)(7,195)(8,196)(9,197)(10,198)(11,199)(12,200)(13,201)(14,202)(15,203)(16,204)(17,205)(18,206)(19,207)(20,208)(21,183)(22,184)(23,185)(24,186)(25,187)(26,188)(27,109)(28,110)(29,111)(30,112)(31,113)(32,114)(33,115)(34,116)(35,117)(36,118)(37,119)(38,120)(39,121)(40,122)(41,123)(42,124)(43,125)(44,126)(45,127)(46,128)(47,129)(48,130)(49,105)(50,106)(51,107)(52,108)(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)(131,158)(132,159)(133,160)(134,161)(135,162)(136,163)(137,164)(138,165)(139,166)(140,167)(141,168)(142,169)(143,170)(144,171)(145,172)(146,173)(147,174)(148,175)(149,176)(150,177)(151,178)(152,179)(153,180)(154,181)(155,182)(156,157), (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), (1,36,147,57)(2,82,148,117)(3,34,149,55)(4,80,150,115)(5,32,151,53)(6,104,152,113)(7,30,153,77)(8,102,154,111)(9,28,155,75)(10,100,156,109)(11,52,131,73)(12,98,132,107)(13,50,133,71)(14,96,134,105)(15,48,135,69)(16,94,136,129)(17,46,137,67)(18,92,138,127)(19,44,139,65)(20,90,140,125)(21,42,141,63)(22,88,142,123)(23,40,143,61)(24,86,144,121)(25,38,145,59)(26,84,146,119)(27,198,74,157)(29,196,76,181)(31,194,78,179)(33,192,54,177)(35,190,56,175)(37,188,58,173)(39,186,60,171)(41,184,62,169)(43,208,64,167)(45,206,66,165)(47,204,68,163)(49,202,70,161)(51,200,72,159)(79,193,114,178)(81,191,116,176)(83,189,118,174)(85,187,120,172)(87,185,122,170)(89,183,124,168)(91,207,126,166)(93,205,128,164)(95,203,130,162)(97,201,106,160)(99,199,108,158)(101,197,110,182)(103,195,112,180)>;
G:=Group( (2,190)(4,192)(6,194)(8,196)(10,198)(12,200)(14,202)(16,204)(18,206)(20,208)(22,184)(24,186)(26,188)(28,110)(30,112)(32,114)(34,116)(36,118)(38,120)(40,122)(42,124)(44,126)(46,128)(48,130)(50,106)(52,108)(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)(132,159)(134,161)(136,163)(138,165)(140,167)(142,169)(144,171)(146,173)(148,175)(150,177)(152,179)(154,181)(156,157), (1,174)(2,175)(3,176)(4,177)(5,178)(6,179)(7,180)(8,181)(9,182)(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)(27,100)(28,101)(29,102)(30,103)(31,104)(32,79)(33,80)(34,81)(35,82)(36,83)(37,84)(38,85)(39,86)(40,87)(41,88)(42,89)(43,90)(44,91)(45,92)(46,93)(47,94)(48,95)(49,96)(50,97)(51,98)(52,99)(53,114)(54,115)(55,116)(56,117)(57,118)(58,119)(59,120)(60,121)(61,122)(62,123)(63,124)(64,125)(65,126)(66,127)(67,128)(68,129)(69,130)(70,105)(71,106)(72,107)(73,108)(74,109)(75,110)(76,111)(77,112)(78,113)(131,199)(132,200)(133,201)(134,202)(135,203)(136,204)(137,205)(138,206)(139,207)(140,208)(141,183)(142,184)(143,185)(144,186)(145,187)(146,188)(147,189)(148,190)(149,191)(150,192)(151,193)(152,194)(153,195)(154,196)(155,197)(156,198), (1,189)(2,190)(3,191)(4,192)(5,193)(6,194)(7,195)(8,196)(9,197)(10,198)(11,199)(12,200)(13,201)(14,202)(15,203)(16,204)(17,205)(18,206)(19,207)(20,208)(21,183)(22,184)(23,185)(24,186)(25,187)(26,188)(27,109)(28,110)(29,111)(30,112)(31,113)(32,114)(33,115)(34,116)(35,117)(36,118)(37,119)(38,120)(39,121)(40,122)(41,123)(42,124)(43,125)(44,126)(45,127)(46,128)(47,129)(48,130)(49,105)(50,106)(51,107)(52,108)(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)(131,158)(132,159)(133,160)(134,161)(135,162)(136,163)(137,164)(138,165)(139,166)(140,167)(141,168)(142,169)(143,170)(144,171)(145,172)(146,173)(147,174)(148,175)(149,176)(150,177)(151,178)(152,179)(153,180)(154,181)(155,182)(156,157), (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), (1,36,147,57)(2,82,148,117)(3,34,149,55)(4,80,150,115)(5,32,151,53)(6,104,152,113)(7,30,153,77)(8,102,154,111)(9,28,155,75)(10,100,156,109)(11,52,131,73)(12,98,132,107)(13,50,133,71)(14,96,134,105)(15,48,135,69)(16,94,136,129)(17,46,137,67)(18,92,138,127)(19,44,139,65)(20,90,140,125)(21,42,141,63)(22,88,142,123)(23,40,143,61)(24,86,144,121)(25,38,145,59)(26,84,146,119)(27,198,74,157)(29,196,76,181)(31,194,78,179)(33,192,54,177)(35,190,56,175)(37,188,58,173)(39,186,60,171)(41,184,62,169)(43,208,64,167)(45,206,66,165)(47,204,68,163)(49,202,70,161)(51,200,72,159)(79,193,114,178)(81,191,116,176)(83,189,118,174)(85,187,120,172)(87,185,122,170)(89,183,124,168)(91,207,126,166)(93,205,128,164)(95,203,130,162)(97,201,106,160)(99,199,108,158)(101,197,110,182)(103,195,112,180) );
G=PermutationGroup([[(2,190),(4,192),(6,194),(8,196),(10,198),(12,200),(14,202),(16,204),(18,206),(20,208),(22,184),(24,186),(26,188),(28,110),(30,112),(32,114),(34,116),(36,118),(38,120),(40,122),(42,124),(44,126),(46,128),(48,130),(50,106),(52,108),(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),(132,159),(134,161),(136,163),(138,165),(140,167),(142,169),(144,171),(146,173),(148,175),(150,177),(152,179),(154,181),(156,157)], [(1,174),(2,175),(3,176),(4,177),(5,178),(6,179),(7,180),(8,181),(9,182),(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),(27,100),(28,101),(29,102),(30,103),(31,104),(32,79),(33,80),(34,81),(35,82),(36,83),(37,84),(38,85),(39,86),(40,87),(41,88),(42,89),(43,90),(44,91),(45,92),(46,93),(47,94),(48,95),(49,96),(50,97),(51,98),(52,99),(53,114),(54,115),(55,116),(56,117),(57,118),(58,119),(59,120),(60,121),(61,122),(62,123),(63,124),(64,125),(65,126),(66,127),(67,128),(68,129),(69,130),(70,105),(71,106),(72,107),(73,108),(74,109),(75,110),(76,111),(77,112),(78,113),(131,199),(132,200),(133,201),(134,202),(135,203),(136,204),(137,205),(138,206),(139,207),(140,208),(141,183),(142,184),(143,185),(144,186),(145,187),(146,188),(147,189),(148,190),(149,191),(150,192),(151,193),(152,194),(153,195),(154,196),(155,197),(156,198)], [(1,189),(2,190),(3,191),(4,192),(5,193),(6,194),(7,195),(8,196),(9,197),(10,198),(11,199),(12,200),(13,201),(14,202),(15,203),(16,204),(17,205),(18,206),(19,207),(20,208),(21,183),(22,184),(23,185),(24,186),(25,187),(26,188),(27,109),(28,110),(29,111),(30,112),(31,113),(32,114),(33,115),(34,116),(35,117),(36,118),(37,119),(38,120),(39,121),(40,122),(41,123),(42,124),(43,125),(44,126),(45,127),(46,128),(47,129),(48,130),(49,105),(50,106),(51,107),(52,108),(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),(131,158),(132,159),(133,160),(134,161),(135,162),(136,163),(137,164),(138,165),(139,166),(140,167),(141,168),(142,169),(143,170),(144,171),(145,172),(146,173),(147,174),(148,175),(149,176),(150,177),(151,178),(152,179),(153,180),(154,181),(155,182),(156,157)], [(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)], [(1,36,147,57),(2,82,148,117),(3,34,149,55),(4,80,150,115),(5,32,151,53),(6,104,152,113),(7,30,153,77),(8,102,154,111),(9,28,155,75),(10,100,156,109),(11,52,131,73),(12,98,132,107),(13,50,133,71),(14,96,134,105),(15,48,135,69),(16,94,136,129),(17,46,137,67),(18,92,138,127),(19,44,139,65),(20,90,140,125),(21,42,141,63),(22,88,142,123),(23,40,143,61),(24,86,144,121),(25,38,145,59),(26,84,146,119),(27,198,74,157),(29,196,76,181),(31,194,78,179),(33,192,54,177),(35,190,56,175),(37,188,58,173),(39,186,60,171),(41,184,62,169),(43,208,64,167),(45,206,66,165),(47,204,68,163),(49,202,70,161),(51,200,72,159),(79,193,114,178),(81,191,116,176),(83,189,118,174),(85,187,120,172),(87,185,122,170),(89,183,124,168),(91,207,126,166),(93,205,128,164),(95,203,130,162),(97,201,106,160),(99,199,108,158),(101,197,110,182),(103,195,112,180)]])
74 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 13A | ··· | 13F | 26A | ··· | 26R | 26S | ··· | 26AP | 52A | ··· | 52L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 13 | ··· | 13 | 26 | ··· | 26 | 26 | ··· | 26 | 52 | ··· | 52 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 26 | 26 | 26 | 26 | 52 | 52 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
74 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | D4 | C4○D4 | D13 | D26 | D26 | C13⋊D4 | D4⋊2D13 |
| kernel | C23.18D26 | C26.D4 | C23.D13 | C22×Dic13 | D4×C26 | C2×C26 | C26 | C2×D4 | C2×C4 | C23 | C22 | C2 |
| # reps | 1 | 2 | 3 | 1 | 1 | 2 | 4 | 6 | 6 | 12 | 24 | 12 |
Matrix representation of C23.18D26 ►in GL4(𝔽53) generated by
| 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 | 12 | 0 | 0 |
| 51 | 16 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
| 30 | 0 | 0 | 0 |
| 29 | 23 | 0 | 0 |
| 0 | 0 | 0 | 30 |
| 0 | 0 | 23 | 0 |
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