direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×D4.D13, D4.7D26, C26⋊2SD16, C52.16D4, C52.13C23, Dic26⋊6C22, C13⋊3(C2×SD16), (C2×D4).4D13, (D4×C26).3C2, (C2×C4).48D26, C26.46(C2×D4), (C2×C26).40D4, C13⋊2C8⋊8C22, (C2×Dic26)⋊9C2, C4.6(C13⋊D4), (C2×C52).31C22, (D4×C13).7C22, C4.13(C22×D13), C22.22(C13⋊D4), (C2×C13⋊2C8)⋊5C2, C2.10(C2×C13⋊D4), SmallGroup(416,154)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×D4.D13
G = < a,b,c,d,e | a2=b4=c2=d13=1, e2=b2, ab=ba, ac=ca, ad=da, ae=ea, cbc=ebe-1=b-1, bd=db, cd=dc, ece-1=bc, ede-1=d-1 >
Subgroups: 336 in 68 conjugacy classes, 33 normal (17 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C8, C2×C4, C2×C4, D4, D4, Q8, C23, C13, C2×C8, SD16, C2×D4, C2×Q8, C26, C26, C26, C2×SD16, Dic13, C52, C2×C26, C2×C26, C13⋊2C8, Dic26, Dic26, C2×Dic13, C2×C52, D4×C13, D4×C13, C22×C26, C2×C13⋊2C8, D4.D13, C2×Dic26, D4×C26, C2×D4.D13
Quotients: C1, C2, C22, D4, C23, SD16, C2×D4, D13, C2×SD16, D26, C13⋊D4, C22×D13, D4.D13, C2×C13⋊D4, C2×D4.D13
►On 208 points
Generators in S208
(1 53)(2 54)(3 55)(4 56)(5 57)(6 58)(7 59)(8 60)(9 61)(10 62)(11 63)(12 64)(13 65)(14 66)(15 67)(16 68)(17 69)(18 70)(19 71)(20 72)(21 73)(22 74)(23 75)(24 76)(25 77)(26 78)(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)(105 164)(106 165)(107 166)(108 167)(109 168)(110 169)(111 157)(112 158)(113 159)(114 160)(115 161)(116 162)(117 163)(118 173)(119 174)(120 175)(121 176)(122 177)(123 178)(124 179)(125 180)(126 181)(127 182)(128 170)(129 171)(130 172)(131 199)(132 200)(133 201)(134 202)(135 203)(136 204)(137 205)(138 206)(139 207)(140 208)(141 196)(142 197)(143 198)(144 187)(145 188)(146 189)(147 190)(148 191)(149 192)(150 193)(151 194)(152 195)(153 183)(154 184)(155 185)(156 186)
(1 40 14 27)(2 41 15 28)(3 42 16 29)(4 43 17 30)(5 44 18 31)(6 45 19 32)(7 46 20 33)(8 47 21 34)(9 48 22 35)(10 49 23 36)(11 50 24 37)(12 51 25 38)(13 52 26 39)(53 79 66 92)(54 80 67 93)(55 81 68 94)(56 82 69 95)(57 83 70 96)(58 84 71 97)(59 85 72 98)(60 86 73 99)(61 87 74 100)(62 88 75 101)(63 89 76 102)(64 90 77 103)(65 91 78 104)(105 142 125 145)(106 143 126 146)(107 131 127 147)(108 132 128 148)(109 133 129 149)(110 134 130 150)(111 135 118 151)(112 136 119 152)(113 137 120 153)(114 138 121 154)(115 139 122 155)(116 140 123 156)(117 141 124 144)(157 203 173 194)(158 204 174 195)(159 205 175 183)(160 206 176 184)(161 207 177 185)(162 208 178 186)(163 196 179 187)(164 197 180 188)(165 198 181 189)(166 199 182 190)(167 200 170 191)(168 201 171 192)(169 202 172 193)
(1 27)(2 28)(3 29)(4 30)(5 31)(6 32)(7 33)(8 34)(9 35)(10 36)(11 37)(12 38)(13 39)(14 40)(15 41)(16 42)(17 43)(18 44)(19 45)(20 46)(21 47)(22 48)(23 49)(24 50)(25 51)(26 52)(53 92)(54 93)(55 94)(56 95)(57 96)(58 97)(59 98)(60 99)(61 100)(62 101)(63 102)(64 103)(65 104)(66 79)(67 80)(68 81)(69 82)(70 83)(71 84)(72 85)(73 86)(74 87)(75 88)(76 89)(77 90)(78 91)(105 125)(106 126)(107 127)(108 128)(109 129)(110 130)(111 118)(112 119)(113 120)(114 121)(115 122)(116 123)(117 124)(157 173)(158 174)(159 175)(160 176)(161 177)(162 178)(163 179)(164 180)(165 181)(166 182)(167 170)(168 171)(169 172)
(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)
(1 175 14 159)(2 174 15 158)(3 173 16 157)(4 172 17 169)(5 171 18 168)(6 170 19 167)(7 182 20 166)(8 181 21 165)(9 180 22 164)(10 179 23 163)(11 178 24 162)(12 177 25 161)(13 176 26 160)(27 183 40 205)(28 195 41 204)(29 194 42 203)(30 193 43 202)(31 192 44 201)(32 191 45 200)(33 190 46 199)(34 189 47 198)(35 188 48 197)(36 187 49 196)(37 186 50 208)(38 185 51 207)(39 184 52 206)(53 120 66 113)(54 119 67 112)(55 118 68 111)(56 130 69 110)(57 129 70 109)(58 128 71 108)(59 127 72 107)(60 126 73 106)(61 125 74 105)(62 124 75 117)(63 123 76 116)(64 122 77 115)(65 121 78 114)(79 137 92 153)(80 136 93 152)(81 135 94 151)(82 134 95 150)(83 133 96 149)(84 132 97 148)(85 131 98 147)(86 143 99 146)(87 142 100 145)(88 141 101 144)(89 140 102 156)(90 139 103 155)(91 138 104 154)
G:=sub<Sym(208)| (1,53)(2,54)(3,55)(4,56)(5,57)(6,58)(7,59)(8,60)(9,61)(10,62)(11,63)(12,64)(13,65)(14,66)(15,67)(16,68)(17,69)(18,70)(19,71)(20,72)(21,73)(22,74)(23,75)(24,76)(25,77)(26,78)(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)(105,164)(106,165)(107,166)(108,167)(109,168)(110,169)(111,157)(112,158)(113,159)(114,160)(115,161)(116,162)(117,163)(118,173)(119,174)(120,175)(121,176)(122,177)(123,178)(124,179)(125,180)(126,181)(127,182)(128,170)(129,171)(130,172)(131,199)(132,200)(133,201)(134,202)(135,203)(136,204)(137,205)(138,206)(139,207)(140,208)(141,196)(142,197)(143,198)(144,187)(145,188)(146,189)(147,190)(148,191)(149,192)(150,193)(151,194)(152,195)(153,183)(154,184)(155,185)(156,186), (1,40,14,27)(2,41,15,28)(3,42,16,29)(4,43,17,30)(5,44,18,31)(6,45,19,32)(7,46,20,33)(8,47,21,34)(9,48,22,35)(10,49,23,36)(11,50,24,37)(12,51,25,38)(13,52,26,39)(53,79,66,92)(54,80,67,93)(55,81,68,94)(56,82,69,95)(57,83,70,96)(58,84,71,97)(59,85,72,98)(60,86,73,99)(61,87,74,100)(62,88,75,101)(63,89,76,102)(64,90,77,103)(65,91,78,104)(105,142,125,145)(106,143,126,146)(107,131,127,147)(108,132,128,148)(109,133,129,149)(110,134,130,150)(111,135,118,151)(112,136,119,152)(113,137,120,153)(114,138,121,154)(115,139,122,155)(116,140,123,156)(117,141,124,144)(157,203,173,194)(158,204,174,195)(159,205,175,183)(160,206,176,184)(161,207,177,185)(162,208,178,186)(163,196,179,187)(164,197,180,188)(165,198,181,189)(166,199,182,190)(167,200,170,191)(168,201,171,192)(169,202,172,193), (1,27)(2,28)(3,29)(4,30)(5,31)(6,32)(7,33)(8,34)(9,35)(10,36)(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52)(53,92)(54,93)(55,94)(56,95)(57,96)(58,97)(59,98)(60,99)(61,100)(62,101)(63,102)(64,103)(65,104)(66,79)(67,80)(68,81)(69,82)(70,83)(71,84)(72,85)(73,86)(74,87)(75,88)(76,89)(77,90)(78,91)(105,125)(106,126)(107,127)(108,128)(109,129)(110,130)(111,118)(112,119)(113,120)(114,121)(115,122)(116,123)(117,124)(157,173)(158,174)(159,175)(160,176)(161,177)(162,178)(163,179)(164,180)(165,181)(166,182)(167,170)(168,171)(169,172), (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), (1,175,14,159)(2,174,15,158)(3,173,16,157)(4,172,17,169)(5,171,18,168)(6,170,19,167)(7,182,20,166)(8,181,21,165)(9,180,22,164)(10,179,23,163)(11,178,24,162)(12,177,25,161)(13,176,26,160)(27,183,40,205)(28,195,41,204)(29,194,42,203)(30,193,43,202)(31,192,44,201)(32,191,45,200)(33,190,46,199)(34,189,47,198)(35,188,48,197)(36,187,49,196)(37,186,50,208)(38,185,51,207)(39,184,52,206)(53,120,66,113)(54,119,67,112)(55,118,68,111)(56,130,69,110)(57,129,70,109)(58,128,71,108)(59,127,72,107)(60,126,73,106)(61,125,74,105)(62,124,75,117)(63,123,76,116)(64,122,77,115)(65,121,78,114)(79,137,92,153)(80,136,93,152)(81,135,94,151)(82,134,95,150)(83,133,96,149)(84,132,97,148)(85,131,98,147)(86,143,99,146)(87,142,100,145)(88,141,101,144)(89,140,102,156)(90,139,103,155)(91,138,104,154)>;
G:=Group( (1,53)(2,54)(3,55)(4,56)(5,57)(6,58)(7,59)(8,60)(9,61)(10,62)(11,63)(12,64)(13,65)(14,66)(15,67)(16,68)(17,69)(18,70)(19,71)(20,72)(21,73)(22,74)(23,75)(24,76)(25,77)(26,78)(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)(105,164)(106,165)(107,166)(108,167)(109,168)(110,169)(111,157)(112,158)(113,159)(114,160)(115,161)(116,162)(117,163)(118,173)(119,174)(120,175)(121,176)(122,177)(123,178)(124,179)(125,180)(126,181)(127,182)(128,170)(129,171)(130,172)(131,199)(132,200)(133,201)(134,202)(135,203)(136,204)(137,205)(138,206)(139,207)(140,208)(141,196)(142,197)(143,198)(144,187)(145,188)(146,189)(147,190)(148,191)(149,192)(150,193)(151,194)(152,195)(153,183)(154,184)(155,185)(156,186), (1,40,14,27)(2,41,15,28)(3,42,16,29)(4,43,17,30)(5,44,18,31)(6,45,19,32)(7,46,20,33)(8,47,21,34)(9,48,22,35)(10,49,23,36)(11,50,24,37)(12,51,25,38)(13,52,26,39)(53,79,66,92)(54,80,67,93)(55,81,68,94)(56,82,69,95)(57,83,70,96)(58,84,71,97)(59,85,72,98)(60,86,73,99)(61,87,74,100)(62,88,75,101)(63,89,76,102)(64,90,77,103)(65,91,78,104)(105,142,125,145)(106,143,126,146)(107,131,127,147)(108,132,128,148)(109,133,129,149)(110,134,130,150)(111,135,118,151)(112,136,119,152)(113,137,120,153)(114,138,121,154)(115,139,122,155)(116,140,123,156)(117,141,124,144)(157,203,173,194)(158,204,174,195)(159,205,175,183)(160,206,176,184)(161,207,177,185)(162,208,178,186)(163,196,179,187)(164,197,180,188)(165,198,181,189)(166,199,182,190)(167,200,170,191)(168,201,171,192)(169,202,172,193), (1,27)(2,28)(3,29)(4,30)(5,31)(6,32)(7,33)(8,34)(9,35)(10,36)(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52)(53,92)(54,93)(55,94)(56,95)(57,96)(58,97)(59,98)(60,99)(61,100)(62,101)(63,102)(64,103)(65,104)(66,79)(67,80)(68,81)(69,82)(70,83)(71,84)(72,85)(73,86)(74,87)(75,88)(76,89)(77,90)(78,91)(105,125)(106,126)(107,127)(108,128)(109,129)(110,130)(111,118)(112,119)(113,120)(114,121)(115,122)(116,123)(117,124)(157,173)(158,174)(159,175)(160,176)(161,177)(162,178)(163,179)(164,180)(165,181)(166,182)(167,170)(168,171)(169,172), (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), (1,175,14,159)(2,174,15,158)(3,173,16,157)(4,172,17,169)(5,171,18,168)(6,170,19,167)(7,182,20,166)(8,181,21,165)(9,180,22,164)(10,179,23,163)(11,178,24,162)(12,177,25,161)(13,176,26,160)(27,183,40,205)(28,195,41,204)(29,194,42,203)(30,193,43,202)(31,192,44,201)(32,191,45,200)(33,190,46,199)(34,189,47,198)(35,188,48,197)(36,187,49,196)(37,186,50,208)(38,185,51,207)(39,184,52,206)(53,120,66,113)(54,119,67,112)(55,118,68,111)(56,130,69,110)(57,129,70,109)(58,128,71,108)(59,127,72,107)(60,126,73,106)(61,125,74,105)(62,124,75,117)(63,123,76,116)(64,122,77,115)(65,121,78,114)(79,137,92,153)(80,136,93,152)(81,135,94,151)(82,134,95,150)(83,133,96,149)(84,132,97,148)(85,131,98,147)(86,143,99,146)(87,142,100,145)(88,141,101,144)(89,140,102,156)(90,139,103,155)(91,138,104,154) );
G=PermutationGroup([[(1,53),(2,54),(3,55),(4,56),(5,57),(6,58),(7,59),(8,60),(9,61),(10,62),(11,63),(12,64),(13,65),(14,66),(15,67),(16,68),(17,69),(18,70),(19,71),(20,72),(21,73),(22,74),(23,75),(24,76),(25,77),(26,78),(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),(105,164),(106,165),(107,166),(108,167),(109,168),(110,169),(111,157),(112,158),(113,159),(114,160),(115,161),(116,162),(117,163),(118,173),(119,174),(120,175),(121,176),(122,177),(123,178),(124,179),(125,180),(126,181),(127,182),(128,170),(129,171),(130,172),(131,199),(132,200),(133,201),(134,202),(135,203),(136,204),(137,205),(138,206),(139,207),(140,208),(141,196),(142,197),(143,198),(144,187),(145,188),(146,189),(147,190),(148,191),(149,192),(150,193),(151,194),(152,195),(153,183),(154,184),(155,185),(156,186)], [(1,40,14,27),(2,41,15,28),(3,42,16,29),(4,43,17,30),(5,44,18,31),(6,45,19,32),(7,46,20,33),(8,47,21,34),(9,48,22,35),(10,49,23,36),(11,50,24,37),(12,51,25,38),(13,52,26,39),(53,79,66,92),(54,80,67,93),(55,81,68,94),(56,82,69,95),(57,83,70,96),(58,84,71,97),(59,85,72,98),(60,86,73,99),(61,87,74,100),(62,88,75,101),(63,89,76,102),(64,90,77,103),(65,91,78,104),(105,142,125,145),(106,143,126,146),(107,131,127,147),(108,132,128,148),(109,133,129,149),(110,134,130,150),(111,135,118,151),(112,136,119,152),(113,137,120,153),(114,138,121,154),(115,139,122,155),(116,140,123,156),(117,141,124,144),(157,203,173,194),(158,204,174,195),(159,205,175,183),(160,206,176,184),(161,207,177,185),(162,208,178,186),(163,196,179,187),(164,197,180,188),(165,198,181,189),(166,199,182,190),(167,200,170,191),(168,201,171,192),(169,202,172,193)], [(1,27),(2,28),(3,29),(4,30),(5,31),(6,32),(7,33),(8,34),(9,35),(10,36),(11,37),(12,38),(13,39),(14,40),(15,41),(16,42),(17,43),(18,44),(19,45),(20,46),(21,47),(22,48),(23,49),(24,50),(25,51),(26,52),(53,92),(54,93),(55,94),(56,95),(57,96),(58,97),(59,98),(60,99),(61,100),(62,101),(63,102),(64,103),(65,104),(66,79),(67,80),(68,81),(69,82),(70,83),(71,84),(72,85),(73,86),(74,87),(75,88),(76,89),(77,90),(78,91),(105,125),(106,126),(107,127),(108,128),(109,129),(110,130),(111,118),(112,119),(113,120),(114,121),(115,122),(116,123),(117,124),(157,173),(158,174),(159,175),(160,176),(161,177),(162,178),(163,179),(164,180),(165,181),(166,182),(167,170),(168,171),(169,172)], [(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)], [(1,175,14,159),(2,174,15,158),(3,173,16,157),(4,172,17,169),(5,171,18,168),(6,170,19,167),(7,182,20,166),(8,181,21,165),(9,180,22,164),(10,179,23,163),(11,178,24,162),(12,177,25,161),(13,176,26,160),(27,183,40,205),(28,195,41,204),(29,194,42,203),(30,193,43,202),(31,192,44,201),(32,191,45,200),(33,190,46,199),(34,189,47,198),(35,188,48,197),(36,187,49,196),(37,186,50,208),(38,185,51,207),(39,184,52,206),(53,120,66,113),(54,119,67,112),(55,118,68,111),(56,130,69,110),(57,129,70,109),(58,128,71,108),(59,127,72,107),(60,126,73,106),(61,125,74,105),(62,124,75,117),(63,123,76,116),(64,122,77,115),(65,121,78,114),(79,137,92,153),(80,136,93,152),(81,135,94,151),(82,134,95,150),(83,133,96,149),(84,132,97,148),(85,131,98,147),(86,143,99,146),(87,142,100,145),(88,141,101,144),(89,140,102,156),(90,139,103,155),(91,138,104,154)]])
74 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 8A | 8B | 8C | 8D | 13A | ··· | 13F | 26A | ··· | 26R | 26S | ··· | 26AP | 52A | ··· | 52L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 13 | ··· | 13 | 26 | ··· | 26 | 26 | ··· | 26 | 52 | ··· | 52 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 2 | 2 | 52 | 52 | 26 | 26 | 26 | 26 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
74 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | D4 | D4 | SD16 | D13 | D26 | D26 | C13⋊D4 | C13⋊D4 | D4.D13 |
| kernel | C2×D4.D13 | C2×C13⋊2C8 | D4.D13 | C2×Dic26 | D4×C26 | C52 | C2×C26 | C26 | C2×D4 | C2×C4 | D4 | C4 | C22 | C2 |
| # reps | 1 | 1 | 4 | 1 | 1 | 1 | 1 | 4 | 6 | 6 | 12 | 12 | 12 | 12 |
Matrix representation of C2×D4.D13 ►in GL4(𝔽313) generated by
| 312 | 0 | 0 | 0 |
| 0 | 312 | 0 | 0 |
| 0 | 0 | 312 | 0 |
| 0 | 0 | 0 | 312 |
| 0 | 1 | 0 | 0 |
| 312 | 0 | 0 | 0 |
| 0 | 0 | 312 | 0 |
| 0 | 0 | 0 | 312 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 312 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 150 | 0 |
| 0 | 0 | 0 | 48 |
| 65 | 248 | 0 | 0 |
| 248 | 248 | 0 | 0 |
| 0 | 0 | 0 | 265 |
| 0 | 0 | 163 | 0 |
G:=sub<GL(4,GF(313))| [312,0,0,0,0,312,0,0,0,0,312,0,0,0,0,312],[0,312,0,0,1,0,0,0,0,0,312,0,0,0,0,312],[0,1,0,0,1,0,0,0,0,0,312,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,150,0,0,0,0,48],[65,248,0,0,248,248,0,0,0,0,0,163,0,0,265,0] >;
C2×D4.D13 in GAP, Magma, Sage, TeX
C_2\times D_4.D_{13} % in TeX
G:=Group("C2xD4.D13"); // GroupNames label
G:=SmallGroup(416,154);
// by ID
G=gap.SmallGroup(416,154);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-13,96,218,579,159,69,13829]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^4=c^2=d^13=1,e^2=b^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=e*b*e^-1=b^-1,b*d=d*b,c*d=d*c,e*c*e^-1=b*c,e*d*e^-1=d^-1>;
// generators/relations