metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.105D14, C14.562- 1+4, (C4×D4).12D7, C4⋊C4.280D14, (D4×C28).13C2, Dic7.Q8⋊7C2, (C4×Dic14)⋊27C2, (C2×D4).209D14, C28.48D4⋊8C2, (C2×C14).85C24, C28.6Q8⋊15C2, C28.291(C4○D4), (C4×C28).147C22, (C2×C28).585C23, C22⋊C4.130D14, (C22×C4).204D14, C23.D14⋊6C2, C4.115(D4⋊2D7), C23.D7.9C22, (D4×C14).303C22, C22.11(C4○D28), C23.21D14⋊6C2, C4⋊Dic7.296C22, (C22×C28).79C22, (C2×Dic7).35C23, C23.165(C22×D7), C22.113(C23×D7), C23.11D14⋊27C2, Dic7⋊C4.153C22, (C22×C14).155C23, C7⋊4(C22.46C24), (C4×Dic7).202C22, C23.18D14.5C2, C2.14(D4.10D14), (C2×Dic14).236C22, (C22×Dic7).93C22, (C2×C4⋊Dic7)⋊23C2, C14.37(C2×C4○D4), C2.41(C2×C4○D28), C2.19(C2×D4⋊2D7), (C2×C14).15(C4○D4), (C7×C4⋊C4).321C22, (C2×C4).155(C22×D7), (C7×C22⋊C4).142C22, SmallGroup(448,994)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.105D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2, ab=ba, cac-1=a-1, dad-1=a-1b2, bc=cb, dbd-1=b-1, dcd-1=c-1 >
Subgroups: 756 in 214 conjugacy classes, 99 normal (51 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, Q8, C23, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C2×C14, C2×C4⋊C4, C42⋊C2, C4×D4, C4×Q8, C22⋊Q8, C22.D4, C42.C2, C42⋊2C2, Dic14, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×D4, C22×C14, C22.46C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C22×Dic7, C22×C28, D4×C14, C4×Dic14, C28.6Q8, C23.11D14, C23.D14, Dic7.Q8, C28.48D4, C2×C4⋊Dic7, C23.21D14, C23.18D14, D4×C28, C42.105D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2- 1+4, C22×D7, C22.46C24, C4○D28, D4⋊2D7, C23×D7, C2×C4○D28, C2×D4⋊2D7, D4.10D14, C42.105D14
►On 224 points
Generators in S224
(1 211 12 218)(2 219 13 212)(3 213 14 220)(4 221 8 214)(5 215 9 222)(6 223 10 216)(7 217 11 224)(15 113 22 120)(16 121 23 114)(17 115 24 122)(18 123 25 116)(19 117 26 124)(20 125 27 118)(21 119 28 126)(29 185 39 192)(30 193 40 186)(31 187 41 194)(32 195 42 188)(33 189 36 196)(34 183 37 190)(35 191 38 184)(43 154 54 147)(44 148 55 141)(45 142 56 149)(46 150 50 143)(47 144 51 151)(48 152 52 145)(49 146 53 153)(57 173 72 180)(58 181 73 174)(59 175 74 182)(60 169 75 176)(61 177 76 170)(62 171 77 178)(63 179 71 172)(64 131 84 138)(65 139 78 132)(66 133 79 140)(67 127 80 134)(68 135 81 128)(69 129 82 136)(70 137 83 130)(85 209 92 202)(86 203 93 210)(87 197 94 204)(88 205 95 198)(89 199 96 206)(90 207 97 200)(91 201 98 208)(99 167 106 160)(100 161 107 168)(101 155 108 162)(102 163 109 156)(103 157 110 164)(104 165 111 158)(105 159 112 166)
(1 103 19 89)(2 104 20 90)(3 105 21 91)(4 99 15 85)(5 100 16 86)(6 101 17 87)(7 102 18 88)(8 106 22 92)(9 107 23 93)(10 108 24 94)(11 109 25 95)(12 110 26 96)(13 111 27 97)(14 112 28 98)(29 78 55 74)(30 79 56 75)(31 80 50 76)(32 81 51 77)(33 82 52 71)(34 83 53 72)(35 84 54 73)(36 69 48 63)(37 70 49 57)(38 64 43 58)(39 65 44 59)(40 66 45 60)(41 67 46 61)(42 68 47 62)(113 209 221 167)(114 210 222 168)(115 197 223 155)(116 198 224 156)(117 199 211 157)(118 200 212 158)(119 201 213 159)(120 202 214 160)(121 203 215 161)(122 204 216 162)(123 205 217 163)(124 206 218 164)(125 207 219 165)(126 208 220 166)(127 150 177 194)(128 151 178 195)(129 152 179 196)(130 153 180 183)(131 154 181 184)(132 141 182 185)(133 142 169 186)(134 143 170 187)(135 144 171 188)(136 145 172 189)(137 146 173 190)(138 147 174 191)(139 148 175 192)(140 149 176 193)
(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 50 12 46)(2 56 13 45)(3 55 14 44)(4 54 8 43)(5 53 9 49)(6 52 10 48)(7 51 11 47)(15 35 22 38)(16 34 23 37)(17 33 24 36)(18 32 25 42)(19 31 26 41)(20 30 27 40)(21 29 28 39)(57 86 72 93)(58 85 73 92)(59 91 74 98)(60 90 75 97)(61 89 76 96)(62 88 77 95)(63 87 71 94)(64 99 84 106)(65 105 78 112)(66 104 79 111)(67 103 80 110)(68 102 81 109)(69 101 82 108)(70 100 83 107)(113 154 120 147)(114 153 121 146)(115 152 122 145)(116 151 123 144)(117 150 124 143)(118 149 125 142)(119 148 126 141)(127 206 134 199)(128 205 135 198)(129 204 136 197)(130 203 137 210)(131 202 138 209)(132 201 139 208)(133 200 140 207)(155 179 162 172)(156 178 163 171)(157 177 164 170)(158 176 165 169)(159 175 166 182)(160 174 167 181)(161 173 168 180)(183 215 190 222)(184 214 191 221)(185 213 192 220)(186 212 193 219)(187 211 194 218)(188 224 195 217)(189 223 196 216)
G:=sub<Sym(224)| (1,211,12,218)(2,219,13,212)(3,213,14,220)(4,221,8,214)(5,215,9,222)(6,223,10,216)(7,217,11,224)(15,113,22,120)(16,121,23,114)(17,115,24,122)(18,123,25,116)(19,117,26,124)(20,125,27,118)(21,119,28,126)(29,185,39,192)(30,193,40,186)(31,187,41,194)(32,195,42,188)(33,189,36,196)(34,183,37,190)(35,191,38,184)(43,154,54,147)(44,148,55,141)(45,142,56,149)(46,150,50,143)(47,144,51,151)(48,152,52,145)(49,146,53,153)(57,173,72,180)(58,181,73,174)(59,175,74,182)(60,169,75,176)(61,177,76,170)(62,171,77,178)(63,179,71,172)(64,131,84,138)(65,139,78,132)(66,133,79,140)(67,127,80,134)(68,135,81,128)(69,129,82,136)(70,137,83,130)(85,209,92,202)(86,203,93,210)(87,197,94,204)(88,205,95,198)(89,199,96,206)(90,207,97,200)(91,201,98,208)(99,167,106,160)(100,161,107,168)(101,155,108,162)(102,163,109,156)(103,157,110,164)(104,165,111,158)(105,159,112,166), (1,103,19,89)(2,104,20,90)(3,105,21,91)(4,99,15,85)(5,100,16,86)(6,101,17,87)(7,102,18,88)(8,106,22,92)(9,107,23,93)(10,108,24,94)(11,109,25,95)(12,110,26,96)(13,111,27,97)(14,112,28,98)(29,78,55,74)(30,79,56,75)(31,80,50,76)(32,81,51,77)(33,82,52,71)(34,83,53,72)(35,84,54,73)(36,69,48,63)(37,70,49,57)(38,64,43,58)(39,65,44,59)(40,66,45,60)(41,67,46,61)(42,68,47,62)(113,209,221,167)(114,210,222,168)(115,197,223,155)(116,198,224,156)(117,199,211,157)(118,200,212,158)(119,201,213,159)(120,202,214,160)(121,203,215,161)(122,204,216,162)(123,205,217,163)(124,206,218,164)(125,207,219,165)(126,208,220,166)(127,150,177,194)(128,151,178,195)(129,152,179,196)(130,153,180,183)(131,154,181,184)(132,141,182,185)(133,142,169,186)(134,143,170,187)(135,144,171,188)(136,145,172,189)(137,146,173,190)(138,147,174,191)(139,148,175,192)(140,149,176,193), (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), (1,50,12,46)(2,56,13,45)(3,55,14,44)(4,54,8,43)(5,53,9,49)(6,52,10,48)(7,51,11,47)(15,35,22,38)(16,34,23,37)(17,33,24,36)(18,32,25,42)(19,31,26,41)(20,30,27,40)(21,29,28,39)(57,86,72,93)(58,85,73,92)(59,91,74,98)(60,90,75,97)(61,89,76,96)(62,88,77,95)(63,87,71,94)(64,99,84,106)(65,105,78,112)(66,104,79,111)(67,103,80,110)(68,102,81,109)(69,101,82,108)(70,100,83,107)(113,154,120,147)(114,153,121,146)(115,152,122,145)(116,151,123,144)(117,150,124,143)(118,149,125,142)(119,148,126,141)(127,206,134,199)(128,205,135,198)(129,204,136,197)(130,203,137,210)(131,202,138,209)(132,201,139,208)(133,200,140,207)(155,179,162,172)(156,178,163,171)(157,177,164,170)(158,176,165,169)(159,175,166,182)(160,174,167,181)(161,173,168,180)(183,215,190,222)(184,214,191,221)(185,213,192,220)(186,212,193,219)(187,211,194,218)(188,224,195,217)(189,223,196,216)>;
G:=Group( (1,211,12,218)(2,219,13,212)(3,213,14,220)(4,221,8,214)(5,215,9,222)(6,223,10,216)(7,217,11,224)(15,113,22,120)(16,121,23,114)(17,115,24,122)(18,123,25,116)(19,117,26,124)(20,125,27,118)(21,119,28,126)(29,185,39,192)(30,193,40,186)(31,187,41,194)(32,195,42,188)(33,189,36,196)(34,183,37,190)(35,191,38,184)(43,154,54,147)(44,148,55,141)(45,142,56,149)(46,150,50,143)(47,144,51,151)(48,152,52,145)(49,146,53,153)(57,173,72,180)(58,181,73,174)(59,175,74,182)(60,169,75,176)(61,177,76,170)(62,171,77,178)(63,179,71,172)(64,131,84,138)(65,139,78,132)(66,133,79,140)(67,127,80,134)(68,135,81,128)(69,129,82,136)(70,137,83,130)(85,209,92,202)(86,203,93,210)(87,197,94,204)(88,205,95,198)(89,199,96,206)(90,207,97,200)(91,201,98,208)(99,167,106,160)(100,161,107,168)(101,155,108,162)(102,163,109,156)(103,157,110,164)(104,165,111,158)(105,159,112,166), (1,103,19,89)(2,104,20,90)(3,105,21,91)(4,99,15,85)(5,100,16,86)(6,101,17,87)(7,102,18,88)(8,106,22,92)(9,107,23,93)(10,108,24,94)(11,109,25,95)(12,110,26,96)(13,111,27,97)(14,112,28,98)(29,78,55,74)(30,79,56,75)(31,80,50,76)(32,81,51,77)(33,82,52,71)(34,83,53,72)(35,84,54,73)(36,69,48,63)(37,70,49,57)(38,64,43,58)(39,65,44,59)(40,66,45,60)(41,67,46,61)(42,68,47,62)(113,209,221,167)(114,210,222,168)(115,197,223,155)(116,198,224,156)(117,199,211,157)(118,200,212,158)(119,201,213,159)(120,202,214,160)(121,203,215,161)(122,204,216,162)(123,205,217,163)(124,206,218,164)(125,207,219,165)(126,208,220,166)(127,150,177,194)(128,151,178,195)(129,152,179,196)(130,153,180,183)(131,154,181,184)(132,141,182,185)(133,142,169,186)(134,143,170,187)(135,144,171,188)(136,145,172,189)(137,146,173,190)(138,147,174,191)(139,148,175,192)(140,149,176,193), (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), (1,50,12,46)(2,56,13,45)(3,55,14,44)(4,54,8,43)(5,53,9,49)(6,52,10,48)(7,51,11,47)(15,35,22,38)(16,34,23,37)(17,33,24,36)(18,32,25,42)(19,31,26,41)(20,30,27,40)(21,29,28,39)(57,86,72,93)(58,85,73,92)(59,91,74,98)(60,90,75,97)(61,89,76,96)(62,88,77,95)(63,87,71,94)(64,99,84,106)(65,105,78,112)(66,104,79,111)(67,103,80,110)(68,102,81,109)(69,101,82,108)(70,100,83,107)(113,154,120,147)(114,153,121,146)(115,152,122,145)(116,151,123,144)(117,150,124,143)(118,149,125,142)(119,148,126,141)(127,206,134,199)(128,205,135,198)(129,204,136,197)(130,203,137,210)(131,202,138,209)(132,201,139,208)(133,200,140,207)(155,179,162,172)(156,178,163,171)(157,177,164,170)(158,176,165,169)(159,175,166,182)(160,174,167,181)(161,173,168,180)(183,215,190,222)(184,214,191,221)(185,213,192,220)(186,212,193,219)(187,211,194,218)(188,224,195,217)(189,223,196,216) );
G=PermutationGroup([[(1,211,12,218),(2,219,13,212),(3,213,14,220),(4,221,8,214),(5,215,9,222),(6,223,10,216),(7,217,11,224),(15,113,22,120),(16,121,23,114),(17,115,24,122),(18,123,25,116),(19,117,26,124),(20,125,27,118),(21,119,28,126),(29,185,39,192),(30,193,40,186),(31,187,41,194),(32,195,42,188),(33,189,36,196),(34,183,37,190),(35,191,38,184),(43,154,54,147),(44,148,55,141),(45,142,56,149),(46,150,50,143),(47,144,51,151),(48,152,52,145),(49,146,53,153),(57,173,72,180),(58,181,73,174),(59,175,74,182),(60,169,75,176),(61,177,76,170),(62,171,77,178),(63,179,71,172),(64,131,84,138),(65,139,78,132),(66,133,79,140),(67,127,80,134),(68,135,81,128),(69,129,82,136),(70,137,83,130),(85,209,92,202),(86,203,93,210),(87,197,94,204),(88,205,95,198),(89,199,96,206),(90,207,97,200),(91,201,98,208),(99,167,106,160),(100,161,107,168),(101,155,108,162),(102,163,109,156),(103,157,110,164),(104,165,111,158),(105,159,112,166)], [(1,103,19,89),(2,104,20,90),(3,105,21,91),(4,99,15,85),(5,100,16,86),(6,101,17,87),(7,102,18,88),(8,106,22,92),(9,107,23,93),(10,108,24,94),(11,109,25,95),(12,110,26,96),(13,111,27,97),(14,112,28,98),(29,78,55,74),(30,79,56,75),(31,80,50,76),(32,81,51,77),(33,82,52,71),(34,83,53,72),(35,84,54,73),(36,69,48,63),(37,70,49,57),(38,64,43,58),(39,65,44,59),(40,66,45,60),(41,67,46,61),(42,68,47,62),(113,209,221,167),(114,210,222,168),(115,197,223,155),(116,198,224,156),(117,199,211,157),(118,200,212,158),(119,201,213,159),(120,202,214,160),(121,203,215,161),(122,204,216,162),(123,205,217,163),(124,206,218,164),(125,207,219,165),(126,208,220,166),(127,150,177,194),(128,151,178,195),(129,152,179,196),(130,153,180,183),(131,154,181,184),(132,141,182,185),(133,142,169,186),(134,143,170,187),(135,144,171,188),(136,145,172,189),(137,146,173,190),(138,147,174,191),(139,148,175,192),(140,149,176,193)], [(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)], [(1,50,12,46),(2,56,13,45),(3,55,14,44),(4,54,8,43),(5,53,9,49),(6,52,10,48),(7,51,11,47),(15,35,22,38),(16,34,23,37),(17,33,24,36),(18,32,25,42),(19,31,26,41),(20,30,27,40),(21,29,28,39),(57,86,72,93),(58,85,73,92),(59,91,74,98),(60,90,75,97),(61,89,76,96),(62,88,77,95),(63,87,71,94),(64,99,84,106),(65,105,78,112),(66,104,79,111),(67,103,80,110),(68,102,81,109),(69,101,82,108),(70,100,83,107),(113,154,120,147),(114,153,121,146),(115,152,122,145),(116,151,123,144),(117,150,124,143),(118,149,125,142),(119,148,126,141),(127,206,134,199),(128,205,135,198),(129,204,136,197),(130,203,137,210),(131,202,138,209),(132,201,139,208),(133,200,140,207),(155,179,162,172),(156,178,163,171),(157,177,164,170),(158,176,165,169),(159,175,166,182),(160,174,167,181),(161,173,168,180),(183,215,190,222),(184,214,191,221),(185,213,192,220),(186,212,193,219),(187,211,194,218),(188,224,195,217),(189,223,196,216)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | ··· | 4R | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 2 | ··· | 2 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | D14 | D14 | C4○D28 | 2- 1+4 | D4⋊2D7 | D4.10D14 |
| kernel | C42.105D14 | C4×Dic14 | C28.6Q8 | C23.11D14 | C23.D14 | Dic7.Q8 | C28.48D4 | C2×C4⋊Dic7 | C23.21D14 | C23.18D14 | D4×C28 | C4×D4 | C28 | C2×C14 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C22 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 2 | 1 | 3 | 4 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of C42.105D14 ►in GL6(𝔽29)
| 28 | 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 18 |
| 0 | 0 | 0 | 0 | 16 | 28 |
| 17 | 12 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 0 | 0 | 0 |
| 0 | 0 | 18 | 20 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 16 | 28 |
| 14 | 21 | 0 | 0 | 0 | 0 |
| 28 | 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 4 | 0 | 0 |
| 0 | 0 | 28 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 11 | 12 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,16,0,0,0,0,18,28],[17,0,0,0,0,0,12,12,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,16,18,0,0,0,0,0,20,0,0,0,0,0,0,1,16,0,0,0,0,0,28],[14,28,0,0,0,0,21,15,0,0,0,0,0,0,18,28,0,0,0,0,4,11,0,0,0,0,0,0,17,11,0,0,0,0,0,12] >;
C42.105D14 in GAP, Magma, Sage, TeX
C_4^2._{105}D_{14} % in TeX
G:=Group("C4^2.105D14"); // GroupNames label
G:=SmallGroup(448,994);
// by ID
G=gap.SmallGroup(448,994);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,387,100,675,570,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2,a*b=b*a,c*a*c^-1=a^-1,d*a*d^-1=a^-1*b^2,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=c^-1>;
// generators/relations