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G = C13×C22.D4order 416 = 25·13

Direct product of C13 and C22.D4

direct product, metabelian, nilpotent (class 2), monomial, 2-elementary

Aliases: C13×C22.D4, C4⋊C44C26, C2.7(D4×C26), C22⋊C44C26, (C22×C4)⋊3C26, (C22×C52)⋊5C2, (C2×D4).4C26, C26.70(C2×D4), (C2×C26).23D4, (D4×C26).11C2, C22.4(D4×C13), C26.43(C4○D4), (C2×C52).65C22, C23.10(C2×C26), (C2×C26).78C23, (C22×C26).29C22, C22.13(C22×C26), (C13×C4⋊C4)⋊13C2, (C2×C4).5(C2×C26), C2.6(C13×C4○D4), (C13×C22⋊C4)⋊12C2, SmallGroup(416,184)

Series: Derived Chief Lower central Upper central

C1C22 — C13×C22.D4
C1C2C22C2×C26C22×C26D4×C26 — C13×C22.D4
C1C22 — C13×C22.D4
C1C2×C26 — C13×C22.D4

Generators and relations for C13×C22.D4
 G = < a,b,c,d,e | a13=b2=c2=d4=e2=1, ab=ba, ac=ca, ad=da, ae=ea, dbd-1=ebe=bc=cb, cd=dc, ce=ec, ede=cd-1 >

Subgroups: 116 in 78 conjugacy classes, 44 normal (20 characteristic)
C1, C2, C2 [×2], C2 [×3], C4 [×5], C22, C22 [×2], C22 [×5], C2×C4, C2×C4 [×4], C2×C4 [×2], D4 [×2], C23 [×2], C13, C22⋊C4, C22⋊C4 [×2], C4⋊C4 [×2], C22×C4, C2×D4, C26, C26 [×2], C26 [×3], C22.D4, C52 [×5], C2×C26, C2×C26 [×2], C2×C26 [×5], C2×C52, C2×C52 [×4], C2×C52 [×2], D4×C13 [×2], C22×C26 [×2], C13×C22⋊C4, C13×C22⋊C4 [×2], C13×C4⋊C4 [×2], C22×C52, D4×C26, C13×C22.D4
Quotients: C1, C2 [×7], C22 [×7], D4 [×2], C23, C13, C2×D4, C4○D4 [×2], C26 [×7], C22.D4, C2×C26 [×7], D4×C13 [×2], C22×C26, D4×C26, C13×C4○D4 [×2], C13×C22.D4

Smallest permutation representation of C13×C22.D4
On 208 points
Generators in S208
(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 52)(2 40)(3 41)(4 42)(5 43)(6 44)(7 45)(8 46)(9 47)(10 48)(11 49)(12 50)(13 51)(14 28)(15 29)(16 30)(17 31)(18 32)(19 33)(20 34)(21 35)(22 36)(23 37)(24 38)(25 39)(26 27)(53 124)(54 125)(55 126)(56 127)(57 128)(58 129)(59 130)(60 118)(61 119)(62 120)(63 121)(64 122)(65 123)(66 193)(67 194)(68 195)(69 183)(70 184)(71 185)(72 186)(73 187)(74 188)(75 189)(76 190)(77 191)(78 192)(79 167)(80 168)(81 169)(82 157)(83 158)(84 159)(85 160)(86 161)(87 162)(88 163)(89 164)(90 165)(91 166)(92 150)(93 151)(94 152)(95 153)(96 154)(97 155)(98 156)(99 144)(100 145)(101 146)(102 147)(103 148)(104 149)(105 143)(106 131)(107 132)(108 133)(109 134)(110 135)(111 136)(112 137)(113 138)(114 139)(115 140)(116 141)(117 142)(170 207)(171 208)(172 196)(173 197)(174 198)(175 199)(176 200)(177 201)(178 202)(179 203)(180 204)(181 205)(182 206)
(1 129)(2 130)(3 118)(4 119)(5 120)(6 121)(7 122)(8 123)(9 124)(10 125)(11 126)(12 127)(13 128)(14 138)(15 139)(16 140)(17 141)(18 142)(19 143)(20 131)(21 132)(22 133)(23 134)(24 135)(25 136)(26 137)(27 112)(28 113)(29 114)(30 115)(31 116)(32 117)(33 105)(34 106)(35 107)(36 108)(37 109)(38 110)(39 111)(40 59)(41 60)(42 61)(43 62)(44 63)(45 64)(46 65)(47 53)(48 54)(49 55)(50 56)(51 57)(52 58)(66 175)(67 176)(68 177)(69 178)(70 179)(71 180)(72 181)(73 182)(74 170)(75 171)(76 172)(77 173)(78 174)(79 99)(80 100)(81 101)(82 102)(83 103)(84 104)(85 92)(86 93)(87 94)(88 95)(89 96)(90 97)(91 98)(144 167)(145 168)(146 169)(147 157)(148 158)(149 159)(150 160)(151 161)(152 162)(153 163)(154 164)(155 165)(156 166)(183 202)(184 203)(185 204)(186 205)(187 206)(188 207)(189 208)(190 196)(191 197)(192 198)(193 199)(194 200)(195 201)
(1 156 58 98)(2 144 59 99)(3 145 60 100)(4 146 61 101)(5 147 62 102)(6 148 63 103)(7 149 64 104)(8 150 65 92)(9 151 53 93)(10 152 54 94)(11 153 55 95)(12 154 56 96)(13 155 57 97)(14 76 28 196)(15 77 29 197)(16 78 30 198)(17 66 31 199)(18 67 32 200)(19 68 33 201)(20 69 34 202)(21 70 35 203)(22 71 36 204)(23 72 37 205)(24 73 38 206)(25 74 39 207)(26 75 27 208)(40 79 130 167)(41 80 118 168)(42 81 119 169)(43 82 120 157)(44 83 121 158)(45 84 122 159)(46 85 123 160)(47 86 124 161)(48 87 125 162)(49 88 126 163)(50 89 127 164)(51 90 128 165)(52 91 129 166)(105 195 143 177)(106 183 131 178)(107 184 132 179)(108 185 133 180)(109 186 134 181)(110 187 135 182)(111 188 136 170)(112 189 137 171)(113 190 138 172)(114 191 139 173)(115 192 140 174)(116 193 141 175)(117 194 142 176)
(1 116)(2 117)(3 105)(4 106)(5 107)(6 108)(7 109)(8 110)(9 111)(10 112)(11 113)(12 114)(13 115)(14 49)(15 50)(16 51)(17 52)(18 40)(19 41)(20 42)(21 43)(22 44)(23 45)(24 46)(25 47)(26 48)(27 125)(28 126)(29 127)(30 128)(31 129)(32 130)(33 118)(34 119)(35 120)(36 121)(37 122)(38 123)(39 124)(53 136)(54 137)(55 138)(56 139)(57 140)(58 141)(59 142)(60 143)(61 131)(62 132)(63 133)(64 134)(65 135)(66 156)(67 144)(68 145)(69 146)(70 147)(71 148)(72 149)(73 150)(74 151)(75 152)(76 153)(77 154)(78 155)(79 194)(80 195)(81 183)(82 184)(83 185)(84 186)(85 187)(86 188)(87 189)(88 190)(89 191)(90 192)(91 193)(92 206)(93 207)(94 208)(95 196)(96 197)(97 198)(98 199)(99 200)(100 201)(101 202)(102 203)(103 204)(104 205)(157 179)(158 180)(159 181)(160 182)(161 170)(162 171)(163 172)(164 173)(165 174)(166 175)(167 176)(168 177)(169 178)

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

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

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

182 conjugacy classes

class 1 2A2B2C2D2E2F4A4B4C4D4E4F4G13A···13L26A···26AJ26AK···26BH26BI···26BT52A···52AV52AW···52CF
order1222222444444413···1326···2626···2626···2652···5252···52
size111122422224441···11···12···24···42···24···4

182 irreducible representations

dim11111111112222
type++++++
imageC1C2C2C2C2C13C26C26C26C26D4C4○D4D4×C13C13×C4○D4
kernelC13×C22.D4C13×C22⋊C4C13×C4⋊C4C22×C52D4×C26C22.D4C22⋊C4C4⋊C4C22×C4C2×D4C2×C26C26C22C2
# reps132111236241212242448

Matrix representation of C13×C22.D4 in GL4(𝔽53) generated by

16000
01600
00460
00046
,
1000
05200
00520
00052
,
52000
05200
0010
0001
,
03000
30000
00175
004836
,
0100
1000
004836
00175
G:=sub<GL(4,GF(53))| [16,0,0,0,0,16,0,0,0,0,46,0,0,0,0,46],[1,0,0,0,0,52,0,0,0,0,52,0,0,0,0,52],[52,0,0,0,0,52,0,0,0,0,1,0,0,0,0,1],[0,30,0,0,30,0,0,0,0,0,17,48,0,0,5,36],[0,1,0,0,1,0,0,0,0,0,48,17,0,0,36,5] >;

C13×C22.D4 in GAP, Magma, Sage, TeX

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

G:=Group("C13xC2^2.D4");
// GroupNames label

G:=SmallGroup(416,184);
// by ID

G=gap.SmallGroup(416,184);
# by ID

G:=PCGroup([6,-2,-2,-2,-13,-2,-2,1273,3818,482]);
// Polycyclic

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

׿
×
𝔽