metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.49(C2×D8), (C2×C14).40D8, C4⋊C4.227D14, C28⋊7D4.9C2, (C2×C28).283D4, C14.D8⋊25C2, C4.86(C4○D28), C28.Q8⋊25C2, C28.55D4⋊4C2, C22.9(D4⋊D7), (C22×C4).94D14, C7⋊4(C22.D8), C28.174(C4○D4), (C2×C28).320C23, (C2×D28).90C22, (C22×C14).185D4, C23.77(C7⋊D4), C2.6(C28.C23), C14.84(C8.C22), C4⋊Dic7.130C22, (C22×C28).135C22, C2.8(C23.23D14), C14.58(C22.D4), (C2×C4⋊C4)⋊3D7, (C14×C4⋊C4)⋊3C2, C2.5(C2×D4⋊D7), (C2×C7⋊C8).81C22, (C2×C14).440(C2×D4), (C2×C4).31(C7⋊D4), (C7×C4⋊C4).258C22, (C2×C4).420(C22×D7), C22.130(C2×C7⋊D4), SmallGroup(448,501)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.(C2×D8)
G = < a,b,c,d | a14=b2=c8=1, d2=a7, ab=ba, cac-1=a-1, ad=da, cbc-1=a7b, bd=db, dcd-1=c-1 >
Subgroups: 580 in 114 conjugacy classes, 43 normal (25 characteristic)
C1, C2 [×3], C2 [×3], C4 [×2], C4 [×4], C22, C22 [×2], C22 [×5], C7, C8 [×2], C2×C4 [×2], C2×C4 [×7], D4 [×4], C23, C23, D7, C14 [×3], C14 [×2], C22⋊C4, C4⋊C4 [×2], C4⋊C4 [×2], C2×C8 [×2], C22×C4, C22×C4, C2×D4 [×2], Dic7, C28 [×2], C28 [×3], D14 [×3], C2×C14, C2×C14 [×2], C2×C14 [×2], C22⋊C8, D4⋊C4 [×2], C2.D8 [×2], C2×C4⋊C4, C4⋊D4, C7⋊C8 [×2], D28 [×2], C2×Dic7, C7⋊D4 [×2], C2×C28 [×2], C2×C28 [×6], C22×D7, C22×C14, C22.D8, C2×C7⋊C8 [×2], C4⋊Dic7, D14⋊C4, C7×C4⋊C4 [×2], C7×C4⋊C4, C2×D28, C2×C7⋊D4, C22×C28, C22×C28, C28.Q8 [×2], C14.D8 [×2], C28.55D4, C28⋊7D4, C14×C4⋊C4, C14.(C2×D8)
Quotients: C1, C2 [×7], C22 [×7], D4 [×2], C23, D7, D8 [×2], C2×D4, C4○D4 [×2], D14 [×3], C22.D4, C2×D8, C8.C22, C7⋊D4 [×2], C22×D7, C22.D8, D4⋊D7 [×2], C4○D28 [×2], C2×C7⋊D4, C23.23D14, C2×D4⋊D7, C28.C23, C14.(C2×D8)
►On 224 points
Generators in S224
(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)
(1 155)(2 156)(3 157)(4 158)(5 159)(6 160)(7 161)(8 162)(9 163)(10 164)(11 165)(12 166)(13 167)(14 168)(15 86)(16 87)(17 88)(18 89)(19 90)(20 91)(21 92)(22 93)(23 94)(24 95)(25 96)(26 97)(27 98)(28 85)(29 201)(30 202)(31 203)(32 204)(33 205)(34 206)(35 207)(36 208)(37 209)(38 210)(39 197)(40 198)(41 199)(42 200)(43 214)(44 215)(45 216)(46 217)(47 218)(48 219)(49 220)(50 221)(51 222)(52 223)(53 224)(54 211)(55 212)(56 213)(57 128)(58 129)(59 130)(60 131)(61 132)(62 133)(63 134)(64 135)(65 136)(66 137)(67 138)(68 139)(69 140)(70 127)(71 187)(72 188)(73 189)(74 190)(75 191)(76 192)(77 193)(78 194)(79 195)(80 196)(81 183)(82 184)(83 185)(84 186)(99 178)(100 179)(101 180)(102 181)(103 182)(104 169)(105 170)(106 171)(107 172)(108 173)(109 174)(110 175)(111 176)(112 177)(113 148)(114 149)(115 150)(116 151)(117 152)(118 153)(119 154)(120 141)(121 142)(122 143)(123 144)(124 145)(125 146)(126 147)
(1 204 145 182 155 39 124 110)(2 203 146 181 156 38 125 109)(3 202 147 180 157 37 126 108)(4 201 148 179 158 36 113 107)(5 200 149 178 159 35 114 106)(6 199 150 177 160 34 115 105)(7 198 151 176 161 33 116 104)(8 197 152 175 162 32 117 103)(9 210 153 174 163 31 118 102)(10 209 154 173 164 30 119 101)(11 208 141 172 165 29 120 100)(12 207 142 171 166 42 121 99)(13 206 143 170 167 41 122 112)(14 205 144 169 168 40 123 111)(15 84 130 44 93 186 66 215)(16 83 131 43 94 185 67 214)(17 82 132 56 95 184 68 213)(18 81 133 55 96 183 69 212)(19 80 134 54 97 196 70 211)(20 79 135 53 98 195 57 224)(21 78 136 52 85 194 58 223)(22 77 137 51 86 193 59 222)(23 76 138 50 87 192 60 221)(24 75 139 49 88 191 61 220)(25 74 140 48 89 190 62 219)(26 73 127 47 90 189 63 218)(27 72 128 46 91 188 64 217)(28 71 129 45 92 187 65 216)
(1 184 8 191)(2 185 9 192)(3 186 10 193)(4 187 11 194)(5 188 12 195)(6 189 13 196)(7 190 14 183)(15 30 22 37)(16 31 23 38)(17 32 24 39)(18 33 25 40)(19 34 26 41)(20 35 27 42)(21 36 28 29)(43 153 50 146)(44 154 51 147)(45 141 52 148)(46 142 53 149)(47 143 54 150)(48 144 55 151)(49 145 56 152)(57 106 64 99)(58 107 65 100)(59 108 66 101)(60 109 67 102)(61 110 68 103)(62 111 69 104)(63 112 70 105)(71 165 78 158)(72 166 79 159)(73 167 80 160)(74 168 81 161)(75 155 82 162)(76 156 83 163)(77 157 84 164)(85 201 92 208)(86 202 93 209)(87 203 94 210)(88 204 95 197)(89 205 96 198)(90 206 97 199)(91 207 98 200)(113 216 120 223)(114 217 121 224)(115 218 122 211)(116 219 123 212)(117 220 124 213)(118 221 125 214)(119 222 126 215)(127 170 134 177)(128 171 135 178)(129 172 136 179)(130 173 137 180)(131 174 138 181)(132 175 139 182)(133 176 140 169)
G:=sub<Sym(224)| (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), (1,155)(2,156)(3,157)(4,158)(5,159)(6,160)(7,161)(8,162)(9,163)(10,164)(11,165)(12,166)(13,167)(14,168)(15,86)(16,87)(17,88)(18,89)(19,90)(20,91)(21,92)(22,93)(23,94)(24,95)(25,96)(26,97)(27,98)(28,85)(29,201)(30,202)(31,203)(32,204)(33,205)(34,206)(35,207)(36,208)(37,209)(38,210)(39,197)(40,198)(41,199)(42,200)(43,214)(44,215)(45,216)(46,217)(47,218)(48,219)(49,220)(50,221)(51,222)(52,223)(53,224)(54,211)(55,212)(56,213)(57,128)(58,129)(59,130)(60,131)(61,132)(62,133)(63,134)(64,135)(65,136)(66,137)(67,138)(68,139)(69,140)(70,127)(71,187)(72,188)(73,189)(74,190)(75,191)(76,192)(77,193)(78,194)(79,195)(80,196)(81,183)(82,184)(83,185)(84,186)(99,178)(100,179)(101,180)(102,181)(103,182)(104,169)(105,170)(106,171)(107,172)(108,173)(109,174)(110,175)(111,176)(112,177)(113,148)(114,149)(115,150)(116,151)(117,152)(118,153)(119,154)(120,141)(121,142)(122,143)(123,144)(124,145)(125,146)(126,147), (1,204,145,182,155,39,124,110)(2,203,146,181,156,38,125,109)(3,202,147,180,157,37,126,108)(4,201,148,179,158,36,113,107)(5,200,149,178,159,35,114,106)(6,199,150,177,160,34,115,105)(7,198,151,176,161,33,116,104)(8,197,152,175,162,32,117,103)(9,210,153,174,163,31,118,102)(10,209,154,173,164,30,119,101)(11,208,141,172,165,29,120,100)(12,207,142,171,166,42,121,99)(13,206,143,170,167,41,122,112)(14,205,144,169,168,40,123,111)(15,84,130,44,93,186,66,215)(16,83,131,43,94,185,67,214)(17,82,132,56,95,184,68,213)(18,81,133,55,96,183,69,212)(19,80,134,54,97,196,70,211)(20,79,135,53,98,195,57,224)(21,78,136,52,85,194,58,223)(22,77,137,51,86,193,59,222)(23,76,138,50,87,192,60,221)(24,75,139,49,88,191,61,220)(25,74,140,48,89,190,62,219)(26,73,127,47,90,189,63,218)(27,72,128,46,91,188,64,217)(28,71,129,45,92,187,65,216), (1,184,8,191)(2,185,9,192)(3,186,10,193)(4,187,11,194)(5,188,12,195)(6,189,13,196)(7,190,14,183)(15,30,22,37)(16,31,23,38)(17,32,24,39)(18,33,25,40)(19,34,26,41)(20,35,27,42)(21,36,28,29)(43,153,50,146)(44,154,51,147)(45,141,52,148)(46,142,53,149)(47,143,54,150)(48,144,55,151)(49,145,56,152)(57,106,64,99)(58,107,65,100)(59,108,66,101)(60,109,67,102)(61,110,68,103)(62,111,69,104)(63,112,70,105)(71,165,78,158)(72,166,79,159)(73,167,80,160)(74,168,81,161)(75,155,82,162)(76,156,83,163)(77,157,84,164)(85,201,92,208)(86,202,93,209)(87,203,94,210)(88,204,95,197)(89,205,96,198)(90,206,97,199)(91,207,98,200)(113,216,120,223)(114,217,121,224)(115,218,122,211)(116,219,123,212)(117,220,124,213)(118,221,125,214)(119,222,126,215)(127,170,134,177)(128,171,135,178)(129,172,136,179)(130,173,137,180)(131,174,138,181)(132,175,139,182)(133,176,140,169)>;
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)(197,198,199,200,201,202,203,204,205,206,207,208,209,210)(211,212,213,214,215,216,217,218,219,220,221,222,223,224), (1,155)(2,156)(3,157)(4,158)(5,159)(6,160)(7,161)(8,162)(9,163)(10,164)(11,165)(12,166)(13,167)(14,168)(15,86)(16,87)(17,88)(18,89)(19,90)(20,91)(21,92)(22,93)(23,94)(24,95)(25,96)(26,97)(27,98)(28,85)(29,201)(30,202)(31,203)(32,204)(33,205)(34,206)(35,207)(36,208)(37,209)(38,210)(39,197)(40,198)(41,199)(42,200)(43,214)(44,215)(45,216)(46,217)(47,218)(48,219)(49,220)(50,221)(51,222)(52,223)(53,224)(54,211)(55,212)(56,213)(57,128)(58,129)(59,130)(60,131)(61,132)(62,133)(63,134)(64,135)(65,136)(66,137)(67,138)(68,139)(69,140)(70,127)(71,187)(72,188)(73,189)(74,190)(75,191)(76,192)(77,193)(78,194)(79,195)(80,196)(81,183)(82,184)(83,185)(84,186)(99,178)(100,179)(101,180)(102,181)(103,182)(104,169)(105,170)(106,171)(107,172)(108,173)(109,174)(110,175)(111,176)(112,177)(113,148)(114,149)(115,150)(116,151)(117,152)(118,153)(119,154)(120,141)(121,142)(122,143)(123,144)(124,145)(125,146)(126,147), (1,204,145,182,155,39,124,110)(2,203,146,181,156,38,125,109)(3,202,147,180,157,37,126,108)(4,201,148,179,158,36,113,107)(5,200,149,178,159,35,114,106)(6,199,150,177,160,34,115,105)(7,198,151,176,161,33,116,104)(8,197,152,175,162,32,117,103)(9,210,153,174,163,31,118,102)(10,209,154,173,164,30,119,101)(11,208,141,172,165,29,120,100)(12,207,142,171,166,42,121,99)(13,206,143,170,167,41,122,112)(14,205,144,169,168,40,123,111)(15,84,130,44,93,186,66,215)(16,83,131,43,94,185,67,214)(17,82,132,56,95,184,68,213)(18,81,133,55,96,183,69,212)(19,80,134,54,97,196,70,211)(20,79,135,53,98,195,57,224)(21,78,136,52,85,194,58,223)(22,77,137,51,86,193,59,222)(23,76,138,50,87,192,60,221)(24,75,139,49,88,191,61,220)(25,74,140,48,89,190,62,219)(26,73,127,47,90,189,63,218)(27,72,128,46,91,188,64,217)(28,71,129,45,92,187,65,216), (1,184,8,191)(2,185,9,192)(3,186,10,193)(4,187,11,194)(5,188,12,195)(6,189,13,196)(7,190,14,183)(15,30,22,37)(16,31,23,38)(17,32,24,39)(18,33,25,40)(19,34,26,41)(20,35,27,42)(21,36,28,29)(43,153,50,146)(44,154,51,147)(45,141,52,148)(46,142,53,149)(47,143,54,150)(48,144,55,151)(49,145,56,152)(57,106,64,99)(58,107,65,100)(59,108,66,101)(60,109,67,102)(61,110,68,103)(62,111,69,104)(63,112,70,105)(71,165,78,158)(72,166,79,159)(73,167,80,160)(74,168,81,161)(75,155,82,162)(76,156,83,163)(77,157,84,164)(85,201,92,208)(86,202,93,209)(87,203,94,210)(88,204,95,197)(89,205,96,198)(90,206,97,199)(91,207,98,200)(113,216,120,223)(114,217,121,224)(115,218,122,211)(116,219,123,212)(117,220,124,213)(118,221,125,214)(119,222,126,215)(127,170,134,177)(128,171,135,178)(129,172,136,179)(130,173,137,180)(131,174,138,181)(132,175,139,182)(133,176,140,169) );
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),(197,198,199,200,201,202,203,204,205,206,207,208,209,210),(211,212,213,214,215,216,217,218,219,220,221,222,223,224)], [(1,155),(2,156),(3,157),(4,158),(5,159),(6,160),(7,161),(8,162),(9,163),(10,164),(11,165),(12,166),(13,167),(14,168),(15,86),(16,87),(17,88),(18,89),(19,90),(20,91),(21,92),(22,93),(23,94),(24,95),(25,96),(26,97),(27,98),(28,85),(29,201),(30,202),(31,203),(32,204),(33,205),(34,206),(35,207),(36,208),(37,209),(38,210),(39,197),(40,198),(41,199),(42,200),(43,214),(44,215),(45,216),(46,217),(47,218),(48,219),(49,220),(50,221),(51,222),(52,223),(53,224),(54,211),(55,212),(56,213),(57,128),(58,129),(59,130),(60,131),(61,132),(62,133),(63,134),(64,135),(65,136),(66,137),(67,138),(68,139),(69,140),(70,127),(71,187),(72,188),(73,189),(74,190),(75,191),(76,192),(77,193),(78,194),(79,195),(80,196),(81,183),(82,184),(83,185),(84,186),(99,178),(100,179),(101,180),(102,181),(103,182),(104,169),(105,170),(106,171),(107,172),(108,173),(109,174),(110,175),(111,176),(112,177),(113,148),(114,149),(115,150),(116,151),(117,152),(118,153),(119,154),(120,141),(121,142),(122,143),(123,144),(124,145),(125,146),(126,147)], [(1,204,145,182,155,39,124,110),(2,203,146,181,156,38,125,109),(3,202,147,180,157,37,126,108),(4,201,148,179,158,36,113,107),(5,200,149,178,159,35,114,106),(6,199,150,177,160,34,115,105),(7,198,151,176,161,33,116,104),(8,197,152,175,162,32,117,103),(9,210,153,174,163,31,118,102),(10,209,154,173,164,30,119,101),(11,208,141,172,165,29,120,100),(12,207,142,171,166,42,121,99),(13,206,143,170,167,41,122,112),(14,205,144,169,168,40,123,111),(15,84,130,44,93,186,66,215),(16,83,131,43,94,185,67,214),(17,82,132,56,95,184,68,213),(18,81,133,55,96,183,69,212),(19,80,134,54,97,196,70,211),(20,79,135,53,98,195,57,224),(21,78,136,52,85,194,58,223),(22,77,137,51,86,193,59,222),(23,76,138,50,87,192,60,221),(24,75,139,49,88,191,61,220),(25,74,140,48,89,190,62,219),(26,73,127,47,90,189,63,218),(27,72,128,46,91,188,64,217),(28,71,129,45,92,187,65,216)], [(1,184,8,191),(2,185,9,192),(3,186,10,193),(4,187,11,194),(5,188,12,195),(6,189,13,196),(7,190,14,183),(15,30,22,37),(16,31,23,38),(17,32,24,39),(18,33,25,40),(19,34,26,41),(20,35,27,42),(21,36,28,29),(43,153,50,146),(44,154,51,147),(45,141,52,148),(46,142,53,149),(47,143,54,150),(48,144,55,151),(49,145,56,152),(57,106,64,99),(58,107,65,100),(59,108,66,101),(60,109,67,102),(61,110,68,103),(62,111,69,104),(63,112,70,105),(71,165,78,158),(72,166,79,159),(73,167,80,160),(74,168,81,161),(75,155,82,162),(76,156,83,163),(77,157,84,164),(85,201,92,208),(86,202,93,209),(87,203,94,210),(88,204,95,197),(89,205,96,198),(90,206,97,199),(91,207,98,200),(113,216,120,223),(114,217,121,224),(115,218,122,211),(116,219,123,212),(117,220,124,213),(118,221,125,214),(119,222,126,215),(127,170,134,177),(128,171,135,178),(129,172,136,179),(130,173,137,180),(131,174,138,181),(132,175,139,182),(133,176,140,169)])
79 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | ··· | 4G | 4H | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 56 | 2 | 2 | 4 | ··· | 4 | 56 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 |
79 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | + | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | C4○D4 | D8 | D14 | D14 | C7⋊D4 | C7⋊D4 | C4○D28 | C8.C22 | D4⋊D7 | C28.C23 |
| kernel | C14.(C2×D8) | C28.Q8 | C14.D8 | C28.55D4 | C28⋊7D4 | C14×C4⋊C4 | C2×C28 | C22×C14 | C2×C4⋊C4 | C28 | C2×C14 | C4⋊C4 | C22×C4 | C2×C4 | C23 | C4 | C14 | C22 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 4 | 6 | 3 | 6 | 6 | 24 | 1 | 6 | 6 |
Matrix representation of C14.(C2×D8) ►in GL4(𝔽113) generated by
| 83 | 0 | 0 | 0 |
| 56 | 64 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 107 | 112 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 90 | 30 | 0 | 0 |
| 5 | 23 | 0 | 0 |
| 0 | 0 | 82 | 82 |
| 0 | 0 | 31 | 82 |
| 98 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 3 | 61 |
| 0 | 0 | 61 | 110 |
G:=sub<GL(4,GF(113))| [83,56,0,0,0,64,0,0,0,0,1,0,0,0,0,1],[1,107,0,0,0,112,0,0,0,0,112,0,0,0,0,112],[90,5,0,0,30,23,0,0,0,0,82,31,0,0,82,82],[98,0,0,0,0,98,0,0,0,0,3,61,0,0,61,110] >;
C14.(C2×D8) in GAP, Magma, Sage, TeX
C_{14}.(C_2\times D_8) % in TeX
G:=Group("C14.(C2xD8)"); // GroupNames label
G:=SmallGroup(448,501);
// by ID
G=gap.SmallGroup(448,501);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,254,100,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^2=c^8=1,d^2=a^7,a*b=b*a,c*a*c^-1=a^-1,a*d=d*a,c*b*c^-1=a^7*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations