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