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## G = C22×C13⋊D4order 416 = 25·13

### Direct product of C22 and C13⋊D4

Series: Derived Chief Lower central Upper central

 Derived series C1 — C26 — C22×C13⋊D4
 Chief series C1 — C13 — C26 — D26 — C22×D13 — C23×D13 — C22×C13⋊D4
 Lower central C13 — C26 — C22×C13⋊D4
 Upper central C1 — C23 — C24

Generators and relations for C22×C13⋊D4
G = < a,b,c,d,e | a2=b2=c13=d4=e2=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, dcd-1=ece=c-1, ede=d-1 >

Subgroups: 1408 in 236 conjugacy classes, 105 normal (11 characteristic)
C1, C2, C2, C2, C4, C22, C22, C2×C4, D4, C23, C23, C23, C13, C22×C4, C2×D4, C24, C24, D13, C26, C26, C26, C22×D4, Dic13, D26, D26, C2×C26, C2×C26, C2×Dic13, C13⋊D4, C22×D13, C22×D13, C22×C26, C22×C26, C22×C26, C22×Dic13, C2×C13⋊D4, C23×D13, C23×C26, C22×C13⋊D4
Quotients: C1, C2, C22, D4, C23, C2×D4, C24, D13, C22×D4, D26, C13⋊D4, C22×D13, C2×C13⋊D4, C23×D13, C22×C13⋊D4

Smallest permutation representation of C22×C13⋊D4
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)(14 105)(15 106)(16 107)(17 108)(18 109)(19 110)(20 111)(21 112)(22 113)(23 114)(24 115)(25 116)(26 117)(27 144)(28 145)(29 146)(30 147)(31 148)(32 149)(33 150)(34 151)(35 152)(36 153)(37 154)(38 155)(39 156)(40 131)(41 132)(42 133)(43 134)(44 135)(45 136)(46 137)(47 138)(48 139)(49 140)(50 141)(51 142)(52 143)(53 170)(54 171)(55 172)(56 173)(57 174)(58 175)(59 176)(60 177)(61 178)(62 179)(63 180)(64 181)(65 182)(66 157)(67 158)(68 159)(69 160)(70 161)(71 162)(72 163)(73 164)(74 165)(75 166)(76 167)(77 168)(78 169)(79 196)(80 197)(81 198)(82 199)(83 200)(84 201)(85 202)(86 203)(87 204)(88 205)(89 206)(90 207)(91 208)(92 183)(93 184)(94 185)(95 186)(96 187)(97 188)(98 189)(99 190)(100 191)(101 192)(102 193)(103 194)(104 195)
(1 66)(2 67)(3 68)(4 69)(5 70)(6 71)(7 72)(8 73)(9 74)(10 75)(11 76)(12 77)(13 78)(14 53)(15 54)(16 55)(17 56)(18 57)(19 58)(20 59)(21 60)(22 61)(23 62)(24 63)(25 64)(26 65)(27 92)(28 93)(29 94)(30 95)(31 96)(32 97)(33 98)(34 99)(35 100)(36 101)(37 102)(38 103)(39 104)(40 79)(41 80)(42 81)(43 82)(44 83)(45 84)(46 85)(47 86)(48 87)(49 88)(50 89)(51 90)(52 91)(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)(118 157)(119 158)(120 159)(121 160)(122 161)(123 162)(124 163)(125 164)(126 165)(127 166)(128 167)(129 168)(130 169)(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)(144 183)(145 184)(146 185)(147 186)(148 187)(149 188)(150 189)(151 190)(152 191)(153 192)(154 193)(155 194)(156 195)
(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 27 14 40)(2 39 15 52)(3 38 16 51)(4 37 17 50)(5 36 18 49)(6 35 19 48)(7 34 20 47)(8 33 21 46)(9 32 22 45)(10 31 23 44)(11 30 24 43)(12 29 25 42)(13 28 26 41)(53 79 66 92)(54 91 67 104)(55 90 68 103)(56 89 69 102)(57 88 70 101)(58 87 71 100)(59 86 72 99)(60 85 73 98)(61 84 74 97)(62 83 75 96)(63 82 76 95)(64 81 77 94)(65 80 78 93)(105 131 118 144)(106 143 119 156)(107 142 120 155)(108 141 121 154)(109 140 122 153)(110 139 123 152)(111 138 124 151)(112 137 125 150)(113 136 126 149)(114 135 127 148)(115 134 128 147)(116 133 129 146)(117 132 130 145)(157 183 170 196)(158 195 171 208)(159 194 172 207)(160 193 173 206)(161 192 174 205)(162 191 175 204)(163 190 176 203)(164 189 177 202)(165 188 178 201)(166 187 179 200)(167 186 180 199)(168 185 181 198)(169 184 182 197)
(1 53)(2 65)(3 64)(4 63)(5 62)(6 61)(7 60)(8 59)(9 58)(10 57)(11 56)(12 55)(13 54)(14 66)(15 78)(16 77)(17 76)(18 75)(19 74)(20 73)(21 72)(22 71)(23 70)(24 69)(25 68)(26 67)(27 92)(28 104)(29 103)(30 102)(31 101)(32 100)(33 99)(34 98)(35 97)(36 96)(37 95)(38 94)(39 93)(40 79)(41 91)(42 90)(43 89)(44 88)(45 87)(46 86)(47 85)(48 84)(49 83)(50 82)(51 81)(52 80)(105 157)(106 169)(107 168)(108 167)(109 166)(110 165)(111 164)(112 163)(113 162)(114 161)(115 160)(116 159)(117 158)(118 170)(119 182)(120 181)(121 180)(122 179)(123 178)(124 177)(125 176)(126 175)(127 174)(128 173)(129 172)(130 171)(131 196)(132 208)(133 207)(134 206)(135 205)(136 204)(137 203)(138 202)(139 201)(140 200)(141 199)(142 198)(143 197)(144 183)(145 195)(146 194)(147 193)(148 192)(149 191)(150 190)(151 189)(152 188)(153 187)(154 186)(155 185)(156 184)

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

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

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

116 conjugacy classes

 class 1 2A ··· 2G 2H 2I 2J 2K 2L 2M 2N 2O 4A 4B 4C 4D 13A ··· 13F 26A ··· 26CL order 1 2 ··· 2 2 2 2 2 2 2 2 2 4 4 4 4 13 ··· 13 26 ··· 26 size 1 1 ··· 1 2 2 2 2 26 26 26 26 26 26 26 26 2 ··· 2 2 ··· 2

116 irreducible representations

 dim 1 1 1 1 1 2 2 2 2 type + + + + + + + + image C1 C2 C2 C2 C2 D4 D13 D26 C13⋊D4 kernel C22×C13⋊D4 C22×Dic13 C2×C13⋊D4 C23×D13 C23×C26 C2×C26 C24 C23 C22 # reps 1 1 12 1 1 4 6 42 48

Matrix representation of C22×C13⋊D4 in GL6(𝔽53)

 1 0 0 0 0 0 0 1 0 0 0 0 0 0 52 0 0 0 0 0 0 52 0 0 0 0 0 0 52 0 0 0 0 0 0 52
,
 52 0 0 0 0 0 0 52 0 0 0 0 0 0 52 0 0 0 0 0 0 52 0 0 0 0 0 0 52 0 0 0 0 0 0 52
,
 51 52 0 0 0 0 27 13 0 0 0 0 0 0 7 52 0 0 0 0 40 2 0 0 0 0 0 0 26 52 0 0 0 0 1 0
,
 28 22 0 0 0 0 15 25 0 0 0 0 0 0 52 20 0 0 0 0 0 1 0 0 0 0 0 0 22 35 0 0 0 0 24 31
,
 25 31 0 0 0 0 38 28 0 0 0 0 0 0 1 33 0 0 0 0 0 52 0 0 0 0 0 0 1 0 0 0 0 0 26 52

G:=sub<GL(6,GF(53))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,52,0,0,0,0,0,0,52,0,0,0,0,0,0,52,0,0,0,0,0,0,52],[52,0,0,0,0,0,0,52,0,0,0,0,0,0,52,0,0,0,0,0,0,52,0,0,0,0,0,0,52,0,0,0,0,0,0,52],[51,27,0,0,0,0,52,13,0,0,0,0,0,0,7,40,0,0,0,0,52,2,0,0,0,0,0,0,26,1,0,0,0,0,52,0],[28,15,0,0,0,0,22,25,0,0,0,0,0,0,52,0,0,0,0,0,20,1,0,0,0,0,0,0,22,24,0,0,0,0,35,31],[25,38,0,0,0,0,31,28,0,0,0,0,0,0,1,0,0,0,0,0,33,52,0,0,0,0,0,0,1,26,0,0,0,0,0,52] >;

C22×C13⋊D4 in GAP, Magma, Sage, TeX

C_2^2\times C_{13}\rtimes D_4
% in TeX

G:=Group("C2^2xC13:D4");
// GroupNames label

G:=SmallGroup(416,226);
// by ID

G=gap.SmallGroup(416,226);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-2,-13,579,13829]);
// Polycyclic

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

׿
×
𝔽