Copied to
clipboard

G = C22×C4×D13order 416 = 25·13

Direct product of C22×C4 and D13

direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary

Aliases: C22×C4×D13, C523C23, C26.2C24, C23.34D26, Dic133C23, D26.16C23, C132(C23×C4), C262(C22×C4), (C22×C52)⋊10C2, (C2×C52)⋊14C22, C2.1(C23×D13), (C2×C26).63C23, (C23×D13).5C2, (C2×Dic13)⋊12C22, (C22×Dic13)⋊10C2, (C22×C26).44C22, C22.29(C22×D13), (C22×D13).44C22, (C2×C26)⋊9(C2×C4), SmallGroup(416,213)

Series: Derived Chief Lower central Upper central

C1C13 — C22×C4×D13
C1C13C26D26C22×D13C23×D13 — C22×C4×D13
C13 — C22×C4×D13
C1C22×C4

Generators and relations for C22×C4×D13
 G = < a,b,c,d,e | a2=b2=c4=d13=e2=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede=d-1 >

Subgroups: 1328 in 236 conjugacy classes, 145 normal (11 characteristic)
C1, C2, C2 [×6], C2 [×8], C4 [×4], C4 [×4], C22 [×7], C22 [×28], C2×C4 [×6], C2×C4 [×22], C23, C23 [×14], C13, C22×C4, C22×C4 [×13], C24, D13 [×8], C26, C26 [×6], C23×C4, Dic13 [×4], C52 [×4], D26 [×28], C2×C26 [×7], C4×D13 [×16], C2×Dic13 [×6], C2×C52 [×6], C22×D13 [×14], C22×C26, C2×C4×D13 [×12], C22×Dic13, C22×C52, C23×D13, C22×C4×D13
Quotients: C1, C2 [×15], C4 [×8], C22 [×35], C2×C4 [×28], C23 [×15], C22×C4 [×14], C24, D13, C23×C4, D26 [×7], C4×D13 [×4], C22×D13 [×7], C2×C4×D13 [×6], C23×D13, C22×C4×D13

Smallest permutation representation of C22×C4×D13
On 208 points
Generators in S208
(1 118)(2 119)(3 120)(4 121)(5 122)(6 123)(7 124)(8 125)(9 126)(10 127)(11 128)(12 129)(13 130)(14 113)(15 114)(16 115)(17 116)(18 117)(19 105)(20 106)(21 107)(22 108)(23 109)(24 110)(25 111)(26 112)(27 148)(28 149)(29 150)(30 151)(31 152)(32 153)(33 154)(34 155)(35 156)(36 144)(37 145)(38 146)(39 147)(40 143)(41 131)(42 132)(43 133)(44 134)(45 135)(46 136)(47 137)(48 138)(49 139)(50 140)(51 141)(52 142)(53 179)(54 180)(55 181)(56 182)(57 170)(58 171)(59 172)(60 173)(61 174)(62 175)(63 176)(64 177)(65 178)(66 168)(67 169)(68 157)(69 158)(70 159)(71 160)(72 161)(73 162)(74 163)(75 164)(76 165)(77 166)(78 167)(79 206)(80 207)(81 208)(82 196)(83 197)(84 198)(85 199)(86 200)(87 201)(88 202)(89 203)(90 204)(91 205)(92 194)(93 195)(94 183)(95 184)(96 185)(97 186)(98 187)(99 188)(100 189)(101 190)(102 191)(103 192)(104 193)
(1 76)(2 77)(3 78)(4 66)(5 67)(6 68)(7 69)(8 70)(9 71)(10 72)(11 73)(12 74)(13 75)(14 61)(15 62)(16 63)(17 64)(18 65)(19 53)(20 54)(21 55)(22 56)(23 57)(24 58)(25 59)(26 60)(27 94)(28 95)(29 96)(30 97)(31 98)(32 99)(33 100)(34 101)(35 102)(36 103)(37 104)(38 92)(39 93)(40 87)(41 88)(42 89)(43 90)(44 91)(45 79)(46 80)(47 81)(48 82)(49 83)(50 84)(51 85)(52 86)(105 179)(106 180)(107 181)(108 182)(109 170)(110 171)(111 172)(112 173)(113 174)(114 175)(115 176)(116 177)(117 178)(118 165)(119 166)(120 167)(121 168)(122 169)(123 157)(124 158)(125 159)(126 160)(127 161)(128 162)(129 163)(130 164)(131 202)(132 203)(133 204)(134 205)(135 206)(136 207)(137 208)(138 196)(139 197)(140 198)(141 199)(142 200)(143 201)(144 192)(145 193)(146 194)(147 195)(148 183)(149 184)(150 185)(151 186)(152 187)(153 188)(154 189)(155 190)(156 191)
(1 30 15 40)(2 31 16 41)(3 32 17 42)(4 33 18 43)(5 34 19 44)(6 35 20 45)(7 36 21 46)(8 37 22 47)(9 38 23 48)(10 39 24 49)(11 27 25 50)(12 28 26 51)(13 29 14 52)(53 91 67 101)(54 79 68 102)(55 80 69 103)(56 81 70 104)(57 82 71 92)(58 83 72 93)(59 84 73 94)(60 85 74 95)(61 86 75 96)(62 87 76 97)(63 88 77 98)(64 89 78 99)(65 90 66 100)(105 134 122 155)(106 135 123 156)(107 136 124 144)(108 137 125 145)(109 138 126 146)(110 139 127 147)(111 140 128 148)(112 141 129 149)(113 142 130 150)(114 143 118 151)(115 131 119 152)(116 132 120 153)(117 133 121 154)(157 191 180 206)(158 192 181 207)(159 193 182 208)(160 194 170 196)(161 195 171 197)(162 183 172 198)(163 184 173 199)(164 185 174 200)(165 186 175 201)(166 187 176 202)(167 188 177 203)(168 189 178 204)(169 190 179 205)
(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)
(1 164)(2 163)(3 162)(4 161)(5 160)(6 159)(7 158)(8 157)(9 169)(10 168)(11 167)(12 166)(13 165)(14 175)(15 174)(16 173)(17 172)(18 171)(19 170)(20 182)(21 181)(22 180)(23 179)(24 178)(25 177)(26 176)(27 188)(28 187)(29 186)(30 185)(31 184)(32 183)(33 195)(34 194)(35 193)(36 192)(37 191)(38 190)(39 189)(40 200)(41 199)(42 198)(43 197)(44 196)(45 208)(46 207)(47 206)(48 205)(49 204)(50 203)(51 202)(52 201)(53 109)(54 108)(55 107)(56 106)(57 105)(58 117)(59 116)(60 115)(61 114)(62 113)(63 112)(64 111)(65 110)(66 127)(67 126)(68 125)(69 124)(70 123)(71 122)(72 121)(73 120)(74 119)(75 118)(76 130)(77 129)(78 128)(79 137)(80 136)(81 135)(82 134)(83 133)(84 132)(85 131)(86 143)(87 142)(88 141)(89 140)(90 139)(91 138)(92 155)(93 154)(94 153)(95 152)(96 151)(97 150)(98 149)(99 148)(100 147)(101 146)(102 145)(103 144)(104 156)

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

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

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

128 conjugacy classes

class 1 2A···2G2H···2O4A···4H4I···4P13A···13F26A···26AP52A···52AV
order12···22···24···44···413···1326···2652···52
size11···113···131···113···132···22···22···2

128 irreducible representations

dim1111112222
type++++++++
imageC1C2C2C2C2C4D13D26D26C4×D13
kernelC22×C4×D13C2×C4×D13C22×Dic13C22×C52C23×D13C22×D13C22×C4C2×C4C23C22
# reps11211116636648

Matrix representation of C22×C4×D13 in GL5(𝔽53)

520000
052000
00100
00010
00001
,
10000
01000
005200
00010
00001
,
520000
023000
00100
000520
000052
,
10000
01000
00100
00001
000529
,
10000
01000
00100
00001
00010

G:=sub<GL(5,GF(53))| [52,0,0,0,0,0,52,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0,0,0,52,0,0,0,0,0,1,0,0,0,0,0,1],[52,0,0,0,0,0,23,0,0,0,0,0,1,0,0,0,0,0,52,0,0,0,0,0,52],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,52,0,0,0,1,9],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0] >;

C22×C4×D13 in GAP, Magma, Sage, TeX

C_2^2\times C_4\times D_{13}
% in TeX

G:=Group("C2^2xC4xD13");
// GroupNames label

G:=SmallGroup(416,213);
// by ID

G=gap.SmallGroup(416,213);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-2,-13,69,13829]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^2=c^4=d^13=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e=d^-1>;
// generators/relations

׿
×
𝔽