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## G = C2×D4.D13order 416 = 25·13

### Direct product of C2 and D4.D13

Series: Derived Chief Lower central Upper central

 Derived series C1 — C52 — C2×D4.D13
 Chief series C1 — C13 — C26 — C52 — Dic26 — C2×Dic26 — C2×D4.D13
 Lower central C13 — C26 — C52 — C2×D4.D13
 Upper central C1 — C22 — C2×C4 — C2×D4

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 [×2], C2 [×2], C4 [×2], C4 [×2], C22, C22 [×4], C8 [×2], C2×C4, C2×C4, D4 [×2], D4, Q8 [×3], C23, C13, C2×C8, SD16 [×4], C2×D4, C2×Q8, C26, C26 [×2], C26 [×2], C2×SD16, Dic13 [×2], C52 [×2], C2×C26, C2×C26 [×4], C132C8 [×2], Dic26 [×2], Dic26, C2×Dic13, C2×C52, D4×C13 [×2], D4×C13, C22×C26, C2×C132C8, D4.D13 [×4], C2×Dic26, D4×C26, C2×D4.D13
Quotients: C1, C2 [×7], C22 [×7], D4 [×2], C23, SD16 [×2], C2×D4, D13, C2×SD16, D26 [×3], C13⋊D4 [×2], C22×D13, D4.D13 [×2], C2×C13⋊D4, C2×D4.D13

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

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

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

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

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

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