direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C8.Dic7, C23.14Dic14, C56.74(C2×C4), (C2×C56).19C4, C4.84(C2×D28), C28.48(C4⋊C4), (C2×C28).62Q8, (C2×C8).314D14, C28.304(C2×D4), (C2×C28).402D4, (C2×C4).170D28, (C2×C8).11Dic7, C8.19(C2×Dic7), C14⋊1(C8.C4), (C22×C8).12D7, (C22×C56).18C2, C4.24(C4⋊Dic7), (C2×C4).51Dic14, (C22×C14).23Q8, (C2×C56).386C22, C28.172(C22×C4), (C2×C28).795C23, (C22×C4).426D14, C22.8(C2×Dic14), C4.26(C22×Dic7), C22.14(C4⋊Dic7), C4.Dic7.35C22, (C22×C28).540C22, C7⋊2(C2×C8.C4), C14.47(C2×C4⋊C4), C2.13(C2×C4⋊Dic7), (C2×C14).40(C2×Q8), (C2×C14).52(C4⋊C4), (C2×C28).307(C2×C4), (C2×C4).84(C2×Dic7), (C2×C4.Dic7).5C2, (C2×C4).713(C22×D7), SmallGroup(448,641)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C8.Dic7
G = < a,b,c,d | a2=b8=1, c14=b4, d2=b4c7, ab=ba, ac=ca, ad=da, bc=cb, dbd-1=b-1, dcd-1=c13 >
Subgroups: 292 in 106 conjugacy classes, 71 normal (41 characteristic)
C1, C2, C2 [×2], C2 [×2], C4 [×4], C22 [×3], C22 [×2], C7, C8 [×4], C8 [×4], C2×C4 [×6], C23, C14, C14 [×2], C14 [×2], C2×C8 [×2], C2×C8 [×4], C2×C8 [×2], M4(2) [×6], C22×C4, C28 [×4], C2×C14 [×3], C2×C14 [×2], C8.C4 [×4], C22×C8, C2×M4(2) [×2], C7⋊C8 [×4], C56 [×4], C2×C28 [×6], C22×C14, C2×C8.C4, C2×C7⋊C8 [×2], C4.Dic7 [×4], C4.Dic7 [×2], C2×C56 [×2], C2×C56 [×4], C22×C28, C8.Dic7 [×4], C2×C4.Dic7 [×2], C22×C56, C2×C8.Dic7
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], D4 [×2], Q8 [×2], C23, D7, C4⋊C4 [×4], C22×C4, C2×D4, C2×Q8, Dic7 [×4], D14 [×3], C8.C4 [×2], C2×C4⋊C4, Dic14 [×2], D28 [×2], C2×Dic7 [×6], C22×D7, C2×C8.C4, C4⋊Dic7 [×4], C2×Dic14, C2×D28, C22×Dic7, C8.Dic7 [×2], C2×C4⋊Dic7, C2×C8.Dic7
►On 224 points
Generators in S224
(1 111)(2 112)(3 85)(4 86)(5 87)(6 88)(7 89)(8 90)(9 91)(10 92)(11 93)(12 94)(13 95)(14 96)(15 97)(16 98)(17 99)(18 100)(19 101)(20 102)(21 103)(22 104)(23 105)(24 106)(25 107)(26 108)(27 109)(28 110)(29 149)(30 150)(31 151)(32 152)(33 153)(34 154)(35 155)(36 156)(37 157)(38 158)(39 159)(40 160)(41 161)(42 162)(43 163)(44 164)(45 165)(46 166)(47 167)(48 168)(49 141)(50 142)(51 143)(52 144)(53 145)(54 146)(55 147)(56 148)(57 216)(58 217)(59 218)(60 219)(61 220)(62 221)(63 222)(64 223)(65 224)(66 197)(67 198)(68 199)(69 200)(70 201)(71 202)(72 203)(73 204)(74 205)(75 206)(76 207)(77 208)(78 209)(79 210)(80 211)(81 212)(82 213)(83 214)(84 215)(113 188)(114 189)(115 190)(116 191)(117 192)(118 193)(119 194)(120 195)(121 196)(122 169)(123 170)(124 171)(125 172)(126 173)(127 174)(128 175)(129 176)(130 177)(131 178)(132 179)(133 180)(134 181)(135 182)(136 183)(137 184)(138 185)(139 186)(140 187)
(1 160 90 47 15 146 104 33)(2 161 91 48 16 147 105 34)(3 162 92 49 17 148 106 35)(4 163 93 50 18 149 107 36)(5 164 94 51 19 150 108 37)(6 165 95 52 20 151 109 38)(7 166 96 53 21 152 110 39)(8 167 97 54 22 153 111 40)(9 168 98 55 23 154 112 41)(10 141 99 56 24 155 85 42)(11 142 100 29 25 156 86 43)(12 143 101 30 26 157 87 44)(13 144 102 31 27 158 88 45)(14 145 103 32 28 159 89 46)(57 188 209 134 71 174 223 120)(58 189 210 135 72 175 224 121)(59 190 211 136 73 176 197 122)(60 191 212 137 74 177 198 123)(61 192 213 138 75 178 199 124)(62 193 214 139 76 179 200 125)(63 194 215 140 77 180 201 126)(64 195 216 113 78 181 202 127)(65 196 217 114 79 182 203 128)(66 169 218 115 80 183 204 129)(67 170 219 116 81 184 205 130)(68 171 220 117 82 185 206 131)(69 172 221 118 83 186 207 132)(70 173 222 119 84 187 208 133)
(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)(197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224)
(1 224 22 217 15 210 8 203)(2 209 23 202 16 223 9 216)(3 222 24 215 17 208 10 201)(4 207 25 200 18 221 11 214)(5 220 26 213 19 206 12 199)(6 205 27 198 20 219 13 212)(7 218 28 211 21 204 14 197)(29 125 50 118 43 139 36 132)(30 138 51 131 44 124 37 117)(31 123 52 116 45 137 38 130)(32 136 53 129 46 122 39 115)(33 121 54 114 47 135 40 128)(34 134 55 127 48 120 41 113)(35 119 56 140 49 133 42 126)(57 112 78 105 71 98 64 91)(58 97 79 90 72 111 65 104)(59 110 80 103 73 96 66 89)(60 95 81 88 74 109 67 102)(61 108 82 101 75 94 68 87)(62 93 83 86 76 107 69 100)(63 106 84 99 77 92 70 85)(141 180 162 173 155 194 148 187)(142 193 163 186 156 179 149 172)(143 178 164 171 157 192 150 185)(144 191 165 184 158 177 151 170)(145 176 166 169 159 190 152 183)(146 189 167 182 160 175 153 196)(147 174 168 195 161 188 154 181)
G:=sub<Sym(224)| (1,111)(2,112)(3,85)(4,86)(5,87)(6,88)(7,89)(8,90)(9,91)(10,92)(11,93)(12,94)(13,95)(14,96)(15,97)(16,98)(17,99)(18,100)(19,101)(20,102)(21,103)(22,104)(23,105)(24,106)(25,107)(26,108)(27,109)(28,110)(29,149)(30,150)(31,151)(32,152)(33,153)(34,154)(35,155)(36,156)(37,157)(38,158)(39,159)(40,160)(41,161)(42,162)(43,163)(44,164)(45,165)(46,166)(47,167)(48,168)(49,141)(50,142)(51,143)(52,144)(53,145)(54,146)(55,147)(56,148)(57,216)(58,217)(59,218)(60,219)(61,220)(62,221)(63,222)(64,223)(65,224)(66,197)(67,198)(68,199)(69,200)(70,201)(71,202)(72,203)(73,204)(74,205)(75,206)(76,207)(77,208)(78,209)(79,210)(80,211)(81,212)(82,213)(83,214)(84,215)(113,188)(114,189)(115,190)(116,191)(117,192)(118,193)(119,194)(120,195)(121,196)(122,169)(123,170)(124,171)(125,172)(126,173)(127,174)(128,175)(129,176)(130,177)(131,178)(132,179)(133,180)(134,181)(135,182)(136,183)(137,184)(138,185)(139,186)(140,187), (1,160,90,47,15,146,104,33)(2,161,91,48,16,147,105,34)(3,162,92,49,17,148,106,35)(4,163,93,50,18,149,107,36)(5,164,94,51,19,150,108,37)(6,165,95,52,20,151,109,38)(7,166,96,53,21,152,110,39)(8,167,97,54,22,153,111,40)(9,168,98,55,23,154,112,41)(10,141,99,56,24,155,85,42)(11,142,100,29,25,156,86,43)(12,143,101,30,26,157,87,44)(13,144,102,31,27,158,88,45)(14,145,103,32,28,159,89,46)(57,188,209,134,71,174,223,120)(58,189,210,135,72,175,224,121)(59,190,211,136,73,176,197,122)(60,191,212,137,74,177,198,123)(61,192,213,138,75,178,199,124)(62,193,214,139,76,179,200,125)(63,194,215,140,77,180,201,126)(64,195,216,113,78,181,202,127)(65,196,217,114,79,182,203,128)(66,169,218,115,80,183,204,129)(67,170,219,116,81,184,205,130)(68,171,220,117,82,185,206,131)(69,172,221,118,83,186,207,132)(70,173,222,119,84,187,208,133), (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)(197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224), (1,224,22,217,15,210,8,203)(2,209,23,202,16,223,9,216)(3,222,24,215,17,208,10,201)(4,207,25,200,18,221,11,214)(5,220,26,213,19,206,12,199)(6,205,27,198,20,219,13,212)(7,218,28,211,21,204,14,197)(29,125,50,118,43,139,36,132)(30,138,51,131,44,124,37,117)(31,123,52,116,45,137,38,130)(32,136,53,129,46,122,39,115)(33,121,54,114,47,135,40,128)(34,134,55,127,48,120,41,113)(35,119,56,140,49,133,42,126)(57,112,78,105,71,98,64,91)(58,97,79,90,72,111,65,104)(59,110,80,103,73,96,66,89)(60,95,81,88,74,109,67,102)(61,108,82,101,75,94,68,87)(62,93,83,86,76,107,69,100)(63,106,84,99,77,92,70,85)(141,180,162,173,155,194,148,187)(142,193,163,186,156,179,149,172)(143,178,164,171,157,192,150,185)(144,191,165,184,158,177,151,170)(145,176,166,169,159,190,152,183)(146,189,167,182,160,175,153,196)(147,174,168,195,161,188,154,181)>;
G:=Group( (1,111)(2,112)(3,85)(4,86)(5,87)(6,88)(7,89)(8,90)(9,91)(10,92)(11,93)(12,94)(13,95)(14,96)(15,97)(16,98)(17,99)(18,100)(19,101)(20,102)(21,103)(22,104)(23,105)(24,106)(25,107)(26,108)(27,109)(28,110)(29,149)(30,150)(31,151)(32,152)(33,153)(34,154)(35,155)(36,156)(37,157)(38,158)(39,159)(40,160)(41,161)(42,162)(43,163)(44,164)(45,165)(46,166)(47,167)(48,168)(49,141)(50,142)(51,143)(52,144)(53,145)(54,146)(55,147)(56,148)(57,216)(58,217)(59,218)(60,219)(61,220)(62,221)(63,222)(64,223)(65,224)(66,197)(67,198)(68,199)(69,200)(70,201)(71,202)(72,203)(73,204)(74,205)(75,206)(76,207)(77,208)(78,209)(79,210)(80,211)(81,212)(82,213)(83,214)(84,215)(113,188)(114,189)(115,190)(116,191)(117,192)(118,193)(119,194)(120,195)(121,196)(122,169)(123,170)(124,171)(125,172)(126,173)(127,174)(128,175)(129,176)(130,177)(131,178)(132,179)(133,180)(134,181)(135,182)(136,183)(137,184)(138,185)(139,186)(140,187), (1,160,90,47,15,146,104,33)(2,161,91,48,16,147,105,34)(3,162,92,49,17,148,106,35)(4,163,93,50,18,149,107,36)(5,164,94,51,19,150,108,37)(6,165,95,52,20,151,109,38)(7,166,96,53,21,152,110,39)(8,167,97,54,22,153,111,40)(9,168,98,55,23,154,112,41)(10,141,99,56,24,155,85,42)(11,142,100,29,25,156,86,43)(12,143,101,30,26,157,87,44)(13,144,102,31,27,158,88,45)(14,145,103,32,28,159,89,46)(57,188,209,134,71,174,223,120)(58,189,210,135,72,175,224,121)(59,190,211,136,73,176,197,122)(60,191,212,137,74,177,198,123)(61,192,213,138,75,178,199,124)(62,193,214,139,76,179,200,125)(63,194,215,140,77,180,201,126)(64,195,216,113,78,181,202,127)(65,196,217,114,79,182,203,128)(66,169,218,115,80,183,204,129)(67,170,219,116,81,184,205,130)(68,171,220,117,82,185,206,131)(69,172,221,118,83,186,207,132)(70,173,222,119,84,187,208,133), (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)(197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224), (1,224,22,217,15,210,8,203)(2,209,23,202,16,223,9,216)(3,222,24,215,17,208,10,201)(4,207,25,200,18,221,11,214)(5,220,26,213,19,206,12,199)(6,205,27,198,20,219,13,212)(7,218,28,211,21,204,14,197)(29,125,50,118,43,139,36,132)(30,138,51,131,44,124,37,117)(31,123,52,116,45,137,38,130)(32,136,53,129,46,122,39,115)(33,121,54,114,47,135,40,128)(34,134,55,127,48,120,41,113)(35,119,56,140,49,133,42,126)(57,112,78,105,71,98,64,91)(58,97,79,90,72,111,65,104)(59,110,80,103,73,96,66,89)(60,95,81,88,74,109,67,102)(61,108,82,101,75,94,68,87)(62,93,83,86,76,107,69,100)(63,106,84,99,77,92,70,85)(141,180,162,173,155,194,148,187)(142,193,163,186,156,179,149,172)(143,178,164,171,157,192,150,185)(144,191,165,184,158,177,151,170)(145,176,166,169,159,190,152,183)(146,189,167,182,160,175,153,196)(147,174,168,195,161,188,154,181) );
G=PermutationGroup([(1,111),(2,112),(3,85),(4,86),(5,87),(6,88),(7,89),(8,90),(9,91),(10,92),(11,93),(12,94),(13,95),(14,96),(15,97),(16,98),(17,99),(18,100),(19,101),(20,102),(21,103),(22,104),(23,105),(24,106),(25,107),(26,108),(27,109),(28,110),(29,149),(30,150),(31,151),(32,152),(33,153),(34,154),(35,155),(36,156),(37,157),(38,158),(39,159),(40,160),(41,161),(42,162),(43,163),(44,164),(45,165),(46,166),(47,167),(48,168),(49,141),(50,142),(51,143),(52,144),(53,145),(54,146),(55,147),(56,148),(57,216),(58,217),(59,218),(60,219),(61,220),(62,221),(63,222),(64,223),(65,224),(66,197),(67,198),(68,199),(69,200),(70,201),(71,202),(72,203),(73,204),(74,205),(75,206),(76,207),(77,208),(78,209),(79,210),(80,211),(81,212),(82,213),(83,214),(84,215),(113,188),(114,189),(115,190),(116,191),(117,192),(118,193),(119,194),(120,195),(121,196),(122,169),(123,170),(124,171),(125,172),(126,173),(127,174),(128,175),(129,176),(130,177),(131,178),(132,179),(133,180),(134,181),(135,182),(136,183),(137,184),(138,185),(139,186),(140,187)], [(1,160,90,47,15,146,104,33),(2,161,91,48,16,147,105,34),(3,162,92,49,17,148,106,35),(4,163,93,50,18,149,107,36),(5,164,94,51,19,150,108,37),(6,165,95,52,20,151,109,38),(7,166,96,53,21,152,110,39),(8,167,97,54,22,153,111,40),(9,168,98,55,23,154,112,41),(10,141,99,56,24,155,85,42),(11,142,100,29,25,156,86,43),(12,143,101,30,26,157,87,44),(13,144,102,31,27,158,88,45),(14,145,103,32,28,159,89,46),(57,188,209,134,71,174,223,120),(58,189,210,135,72,175,224,121),(59,190,211,136,73,176,197,122),(60,191,212,137,74,177,198,123),(61,192,213,138,75,178,199,124),(62,193,214,139,76,179,200,125),(63,194,215,140,77,180,201,126),(64,195,216,113,78,181,202,127),(65,196,217,114,79,182,203,128),(66,169,218,115,80,183,204,129),(67,170,219,116,81,184,205,130),(68,171,220,117,82,185,206,131),(69,172,221,118,83,186,207,132),(70,173,222,119,84,187,208,133)], [(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),(197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224)], [(1,224,22,217,15,210,8,203),(2,209,23,202,16,223,9,216),(3,222,24,215,17,208,10,201),(4,207,25,200,18,221,11,214),(5,220,26,213,19,206,12,199),(6,205,27,198,20,219,13,212),(7,218,28,211,21,204,14,197),(29,125,50,118,43,139,36,132),(30,138,51,131,44,124,37,117),(31,123,52,116,45,137,38,130),(32,136,53,129,46,122,39,115),(33,121,54,114,47,135,40,128),(34,134,55,127,48,120,41,113),(35,119,56,140,49,133,42,126),(57,112,78,105,71,98,64,91),(58,97,79,90,72,111,65,104),(59,110,80,103,73,96,66,89),(60,95,81,88,74,109,67,102),(61,108,82,101,75,94,68,87),(62,93,83,86,76,107,69,100),(63,106,84,99,77,92,70,85),(141,180,162,173,155,194,148,187),(142,193,163,186,156,179,149,172),(143,178,164,171,157,192,150,185),(144,191,165,184,158,177,151,170),(145,176,166,169,159,190,152,183),(146,189,167,182,160,175,153,196),(147,174,168,195,161,188,154,181)])
124 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 7A | 7B | 7C | 8A | ··· | 8H | 8I | ··· | 8P | 14A | ··· | 14U | 28A | ··· | 28X | 56A | ··· | 56AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 8 | ··· | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 28 | ··· | 28 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
124 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | - | + | - | + | + | - | + | - | |||
| image | C1 | C2 | C2 | C2 | C4 | D4 | Q8 | Q8 | D7 | Dic7 | D14 | D14 | C8.C4 | Dic14 | D28 | Dic14 | C8.Dic7 |
| kernel | C2×C8.Dic7 | C8.Dic7 | C2×C4.Dic7 | C22×C56 | C2×C56 | C2×C28 | C2×C28 | C22×C14 | C22×C8 | C2×C8 | C2×C8 | C22×C4 | C14 | C2×C4 | C2×C4 | C23 | C2 |
| # reps | 1 | 4 | 2 | 1 | 8 | 2 | 1 | 1 | 3 | 12 | 6 | 3 | 8 | 6 | 12 | 6 | 48 |
Matrix representation of C2×C8.Dic7 ►in GL3(𝔽113) generated by
| 112 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 1 |
| 1 | 0 | 0 |
| 0 | 95 | 0 |
| 0 | 0 | 69 |
| 1 | 0 | 0 |
| 0 | 53 | 0 |
| 0 | 0 | 81 |
| 1 | 0 | 0 |
| 0 | 0 | 44 |
| 0 | 44 | 0 |
G:=sub<GL(3,GF(113))| [112,0,0,0,1,0,0,0,1],[1,0,0,0,95,0,0,0,69],[1,0,0,0,53,0,0,0,81],[1,0,0,0,0,44,0,44,0] >;
C2×C8.Dic7 in GAP, Magma, Sage, TeX
C_2\times C_8.{\rm Dic}_7 % in TeX
G:=Group("C2xC8.Dic7"); // GroupNames label
G:=SmallGroup(448,641);
// by ID
G=gap.SmallGroup(448,641);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,56,422,100,136,1684,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^8=1,c^14=b^4,d^2=b^4*c^7,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=c^13>;
// generators/relations