metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.126D14, C14.102- 1+4, C14.1092+ 1+4, Q8⋊9(C4×D7), (C4×Q8)⋊7D7, (Q8×C28)⋊9C2, (C4×D28)⋊37C2, D28⋊15(C2×C4), Q8⋊2D7⋊5C4, (Q8×Dic7)⋊9C2, C4⋊C4.325D14, D28⋊C4⋊17C2, C42⋊D7⋊16C2, C28.37(C22×C4), C14.27(C23×C4), (C2×Q8).202D14, C2.4(D4⋊8D14), (C4×C28).170C22, (C2×C14).118C24, (C2×C28).497C23, D14.11(C22×C4), C22.37(C23×D7), D14⋊C4.163C22, (C2×D28).262C22, C4⋊Dic7.368C22, (Q8×C14).218C22, Dic7.20(C22×C4), (C4×Dic7).85C22, Dic7⋊C4.138C22, C2.3(Q8.10D14), C7⋊4(C23.33C23), (C2×Dic7).214C23, (C22×D7).177C23, C4.37(C2×C4×D7), (D7×C4⋊C4)⋊17C2, (C4×D7)⋊5(C2×C4), (C7×Q8)⋊12(C2×C4), C2.29(D7×C22×C4), (C2×C4×D7).70C22, (C2×Q8⋊2D7).6C2, (C7×C4⋊C4).346C22, (C2×C4).654(C22×D7), SmallGroup(448,1027)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.126D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2b2, ab=ba, cac-1=dad-1=a-1, bc=cb, dbd-1=a2b, dcd-1=c13 >
Subgroups: 1252 in 294 conjugacy classes, 151 normal (22 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C4⋊C4, C42⋊C2, C4×D4, C4×Q8, C4×Q8, C2×C4○D4, C4×D7, C4×D7, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C23.33C23, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C4×C28, C7×C4⋊C4, C2×C4×D7, C2×D28, Q8⋊2D7, Q8×C14, C42⋊D7, C4×D28, D7×C4⋊C4, D28⋊C4, Q8×Dic7, Q8×C28, C2×Q8⋊2D7, C42.126D14
Quotients: C1, C2, C4, C22, C2×C4, C23, D7, C22×C4, C24, D14, C23×C4, 2+ 1+4, 2- 1+4, C4×D7, C22×D7, C23.33C23, C2×C4×D7, C23×D7, D7×C22×C4, Q8.10D14, D4⋊8D14, C42.126D14
►On 224 points
Generators in S224
(1 174 89 141)(2 142 90 175)(3 176 91 143)(4 144 92 177)(5 178 93 145)(6 146 94 179)(7 180 95 147)(8 148 96 181)(9 182 97 149)(10 150 98 183)(11 184 99 151)(12 152 100 185)(13 186 101 153)(14 154 102 187)(15 188 103 155)(16 156 104 189)(17 190 105 157)(18 158 106 191)(19 192 107 159)(20 160 108 193)(21 194 109 161)(22 162 110 195)(23 196 111 163)(24 164 112 169)(25 170 85 165)(26 166 86 171)(27 172 87 167)(28 168 88 173)(29 60 135 198)(30 199 136 61)(31 62 137 200)(32 201 138 63)(33 64 139 202)(34 203 140 65)(35 66 113 204)(36 205 114 67)(37 68 115 206)(38 207 116 69)(39 70 117 208)(40 209 118 71)(41 72 119 210)(42 211 120 73)(43 74 121 212)(44 213 122 75)(45 76 123 214)(46 215 124 77)(47 78 125 216)(48 217 126 79)(49 80 127 218)(50 219 128 81)(51 82 129 220)(52 221 130 83)(53 84 131 222)(54 223 132 57)(55 58 133 224)(56 197 134 59)
(1 201 103 77)(2 202 104 78)(3 203 105 79)(4 204 106 80)(5 205 107 81)(6 206 108 82)(7 207 109 83)(8 208 110 84)(9 209 111 57)(10 210 112 58)(11 211 85 59)(12 212 86 60)(13 213 87 61)(14 214 88 62)(15 215 89 63)(16 216 90 64)(17 217 91 65)(18 218 92 66)(19 219 93 67)(20 220 94 68)(21 221 95 69)(22 222 96 70)(23 223 97 71)(24 224 98 72)(25 197 99 73)(26 198 100 74)(27 199 101 75)(28 200 102 76)(29 185 121 166)(30 186 122 167)(31 187 123 168)(32 188 124 141)(33 189 125 142)(34 190 126 143)(35 191 127 144)(36 192 128 145)(37 193 129 146)(38 194 130 147)(39 195 131 148)(40 196 132 149)(41 169 133 150)(42 170 134 151)(43 171 135 152)(44 172 136 153)(45 173 137 154)(46 174 138 155)(47 175 139 156)(48 176 140 157)(49 177 113 158)(50 178 114 159)(51 179 115 160)(52 180 116 161)(53 181 117 162)(54 182 118 163)(55 183 119 164)(56 184 120 165)
(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)
(1 130 15 116)(2 115 16 129)(3 128 17 114)(4 113 18 127)(5 126 19 140)(6 139 20 125)(7 124 21 138)(8 137 22 123)(9 122 23 136)(10 135 24 121)(11 120 25 134)(12 133 26 119)(13 118 27 132)(14 131 28 117)(29 112 43 98)(30 97 44 111)(31 110 45 96)(32 95 46 109)(33 108 47 94)(34 93 48 107)(35 106 49 92)(36 91 50 105)(37 104 51 90)(38 89 52 103)(39 102 53 88)(40 87 54 101)(41 100 55 86)(42 85 56 99)(57 153 71 167)(58 166 72 152)(59 151 73 165)(60 164 74 150)(61 149 75 163)(62 162 76 148)(63 147 77 161)(64 160 78 146)(65 145 79 159)(66 158 80 144)(67 143 81 157)(68 156 82 142)(69 141 83 155)(70 154 84 168)(169 212 183 198)(170 197 184 211)(171 210 185 224)(172 223 186 209)(173 208 187 222)(174 221 188 207)(175 206 189 220)(176 219 190 205)(177 204 191 218)(178 217 192 203)(179 202 193 216)(180 215 194 201)(181 200 195 214)(182 213 196 199)
G:=sub<Sym(224)| (1,174,89,141)(2,142,90,175)(3,176,91,143)(4,144,92,177)(5,178,93,145)(6,146,94,179)(7,180,95,147)(8,148,96,181)(9,182,97,149)(10,150,98,183)(11,184,99,151)(12,152,100,185)(13,186,101,153)(14,154,102,187)(15,188,103,155)(16,156,104,189)(17,190,105,157)(18,158,106,191)(19,192,107,159)(20,160,108,193)(21,194,109,161)(22,162,110,195)(23,196,111,163)(24,164,112,169)(25,170,85,165)(26,166,86,171)(27,172,87,167)(28,168,88,173)(29,60,135,198)(30,199,136,61)(31,62,137,200)(32,201,138,63)(33,64,139,202)(34,203,140,65)(35,66,113,204)(36,205,114,67)(37,68,115,206)(38,207,116,69)(39,70,117,208)(40,209,118,71)(41,72,119,210)(42,211,120,73)(43,74,121,212)(44,213,122,75)(45,76,123,214)(46,215,124,77)(47,78,125,216)(48,217,126,79)(49,80,127,218)(50,219,128,81)(51,82,129,220)(52,221,130,83)(53,84,131,222)(54,223,132,57)(55,58,133,224)(56,197,134,59), (1,201,103,77)(2,202,104,78)(3,203,105,79)(4,204,106,80)(5,205,107,81)(6,206,108,82)(7,207,109,83)(8,208,110,84)(9,209,111,57)(10,210,112,58)(11,211,85,59)(12,212,86,60)(13,213,87,61)(14,214,88,62)(15,215,89,63)(16,216,90,64)(17,217,91,65)(18,218,92,66)(19,219,93,67)(20,220,94,68)(21,221,95,69)(22,222,96,70)(23,223,97,71)(24,224,98,72)(25,197,99,73)(26,198,100,74)(27,199,101,75)(28,200,102,76)(29,185,121,166)(30,186,122,167)(31,187,123,168)(32,188,124,141)(33,189,125,142)(34,190,126,143)(35,191,127,144)(36,192,128,145)(37,193,129,146)(38,194,130,147)(39,195,131,148)(40,196,132,149)(41,169,133,150)(42,170,134,151)(43,171,135,152)(44,172,136,153)(45,173,137,154)(46,174,138,155)(47,175,139,156)(48,176,140,157)(49,177,113,158)(50,178,114,159)(51,179,115,160)(52,180,116,161)(53,181,117,162)(54,182,118,163)(55,183,119,164)(56,184,120,165), (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), (1,130,15,116)(2,115,16,129)(3,128,17,114)(4,113,18,127)(5,126,19,140)(6,139,20,125)(7,124,21,138)(8,137,22,123)(9,122,23,136)(10,135,24,121)(11,120,25,134)(12,133,26,119)(13,118,27,132)(14,131,28,117)(29,112,43,98)(30,97,44,111)(31,110,45,96)(32,95,46,109)(33,108,47,94)(34,93,48,107)(35,106,49,92)(36,91,50,105)(37,104,51,90)(38,89,52,103)(39,102,53,88)(40,87,54,101)(41,100,55,86)(42,85,56,99)(57,153,71,167)(58,166,72,152)(59,151,73,165)(60,164,74,150)(61,149,75,163)(62,162,76,148)(63,147,77,161)(64,160,78,146)(65,145,79,159)(66,158,80,144)(67,143,81,157)(68,156,82,142)(69,141,83,155)(70,154,84,168)(169,212,183,198)(170,197,184,211)(171,210,185,224)(172,223,186,209)(173,208,187,222)(174,221,188,207)(175,206,189,220)(176,219,190,205)(177,204,191,218)(178,217,192,203)(179,202,193,216)(180,215,194,201)(181,200,195,214)(182,213,196,199)>;
G:=Group( (1,174,89,141)(2,142,90,175)(3,176,91,143)(4,144,92,177)(5,178,93,145)(6,146,94,179)(7,180,95,147)(8,148,96,181)(9,182,97,149)(10,150,98,183)(11,184,99,151)(12,152,100,185)(13,186,101,153)(14,154,102,187)(15,188,103,155)(16,156,104,189)(17,190,105,157)(18,158,106,191)(19,192,107,159)(20,160,108,193)(21,194,109,161)(22,162,110,195)(23,196,111,163)(24,164,112,169)(25,170,85,165)(26,166,86,171)(27,172,87,167)(28,168,88,173)(29,60,135,198)(30,199,136,61)(31,62,137,200)(32,201,138,63)(33,64,139,202)(34,203,140,65)(35,66,113,204)(36,205,114,67)(37,68,115,206)(38,207,116,69)(39,70,117,208)(40,209,118,71)(41,72,119,210)(42,211,120,73)(43,74,121,212)(44,213,122,75)(45,76,123,214)(46,215,124,77)(47,78,125,216)(48,217,126,79)(49,80,127,218)(50,219,128,81)(51,82,129,220)(52,221,130,83)(53,84,131,222)(54,223,132,57)(55,58,133,224)(56,197,134,59), (1,201,103,77)(2,202,104,78)(3,203,105,79)(4,204,106,80)(5,205,107,81)(6,206,108,82)(7,207,109,83)(8,208,110,84)(9,209,111,57)(10,210,112,58)(11,211,85,59)(12,212,86,60)(13,213,87,61)(14,214,88,62)(15,215,89,63)(16,216,90,64)(17,217,91,65)(18,218,92,66)(19,219,93,67)(20,220,94,68)(21,221,95,69)(22,222,96,70)(23,223,97,71)(24,224,98,72)(25,197,99,73)(26,198,100,74)(27,199,101,75)(28,200,102,76)(29,185,121,166)(30,186,122,167)(31,187,123,168)(32,188,124,141)(33,189,125,142)(34,190,126,143)(35,191,127,144)(36,192,128,145)(37,193,129,146)(38,194,130,147)(39,195,131,148)(40,196,132,149)(41,169,133,150)(42,170,134,151)(43,171,135,152)(44,172,136,153)(45,173,137,154)(46,174,138,155)(47,175,139,156)(48,176,140,157)(49,177,113,158)(50,178,114,159)(51,179,115,160)(52,180,116,161)(53,181,117,162)(54,182,118,163)(55,183,119,164)(56,184,120,165), (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), (1,130,15,116)(2,115,16,129)(3,128,17,114)(4,113,18,127)(5,126,19,140)(6,139,20,125)(7,124,21,138)(8,137,22,123)(9,122,23,136)(10,135,24,121)(11,120,25,134)(12,133,26,119)(13,118,27,132)(14,131,28,117)(29,112,43,98)(30,97,44,111)(31,110,45,96)(32,95,46,109)(33,108,47,94)(34,93,48,107)(35,106,49,92)(36,91,50,105)(37,104,51,90)(38,89,52,103)(39,102,53,88)(40,87,54,101)(41,100,55,86)(42,85,56,99)(57,153,71,167)(58,166,72,152)(59,151,73,165)(60,164,74,150)(61,149,75,163)(62,162,76,148)(63,147,77,161)(64,160,78,146)(65,145,79,159)(66,158,80,144)(67,143,81,157)(68,156,82,142)(69,141,83,155)(70,154,84,168)(169,212,183,198)(170,197,184,211)(171,210,185,224)(172,223,186,209)(173,208,187,222)(174,221,188,207)(175,206,189,220)(176,219,190,205)(177,204,191,218)(178,217,192,203)(179,202,193,216)(180,215,194,201)(181,200,195,214)(182,213,196,199) );
G=PermutationGroup([[(1,174,89,141),(2,142,90,175),(3,176,91,143),(4,144,92,177),(5,178,93,145),(6,146,94,179),(7,180,95,147),(8,148,96,181),(9,182,97,149),(10,150,98,183),(11,184,99,151),(12,152,100,185),(13,186,101,153),(14,154,102,187),(15,188,103,155),(16,156,104,189),(17,190,105,157),(18,158,106,191),(19,192,107,159),(20,160,108,193),(21,194,109,161),(22,162,110,195),(23,196,111,163),(24,164,112,169),(25,170,85,165),(26,166,86,171),(27,172,87,167),(28,168,88,173),(29,60,135,198),(30,199,136,61),(31,62,137,200),(32,201,138,63),(33,64,139,202),(34,203,140,65),(35,66,113,204),(36,205,114,67),(37,68,115,206),(38,207,116,69),(39,70,117,208),(40,209,118,71),(41,72,119,210),(42,211,120,73),(43,74,121,212),(44,213,122,75),(45,76,123,214),(46,215,124,77),(47,78,125,216),(48,217,126,79),(49,80,127,218),(50,219,128,81),(51,82,129,220),(52,221,130,83),(53,84,131,222),(54,223,132,57),(55,58,133,224),(56,197,134,59)], [(1,201,103,77),(2,202,104,78),(3,203,105,79),(4,204,106,80),(5,205,107,81),(6,206,108,82),(7,207,109,83),(8,208,110,84),(9,209,111,57),(10,210,112,58),(11,211,85,59),(12,212,86,60),(13,213,87,61),(14,214,88,62),(15,215,89,63),(16,216,90,64),(17,217,91,65),(18,218,92,66),(19,219,93,67),(20,220,94,68),(21,221,95,69),(22,222,96,70),(23,223,97,71),(24,224,98,72),(25,197,99,73),(26,198,100,74),(27,199,101,75),(28,200,102,76),(29,185,121,166),(30,186,122,167),(31,187,123,168),(32,188,124,141),(33,189,125,142),(34,190,126,143),(35,191,127,144),(36,192,128,145),(37,193,129,146),(38,194,130,147),(39,195,131,148),(40,196,132,149),(41,169,133,150),(42,170,134,151),(43,171,135,152),(44,172,136,153),(45,173,137,154),(46,174,138,155),(47,175,139,156),(48,176,140,157),(49,177,113,158),(50,178,114,159),(51,179,115,160),(52,180,116,161),(53,181,117,162),(54,182,118,163),(55,183,119,164),(56,184,120,165)], [(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)], [(1,130,15,116),(2,115,16,129),(3,128,17,114),(4,113,18,127),(5,126,19,140),(6,139,20,125),(7,124,21,138),(8,137,22,123),(9,122,23,136),(10,135,24,121),(11,120,25,134),(12,133,26,119),(13,118,27,132),(14,131,28,117),(29,112,43,98),(30,97,44,111),(31,110,45,96),(32,95,46,109),(33,108,47,94),(34,93,48,107),(35,106,49,92),(36,91,50,105),(37,104,51,90),(38,89,52,103),(39,102,53,88),(40,87,54,101),(41,100,55,86),(42,85,56,99),(57,153,71,167),(58,166,72,152),(59,151,73,165),(60,164,74,150),(61,149,75,163),(62,162,76,148),(63,147,77,161),(64,160,78,146),(65,145,79,159),(66,158,80,144),(67,143,81,157),(68,156,82,142),(69,141,83,155),(70,154,84,168),(169,212,183,198),(170,197,184,211),(171,210,185,224),(172,223,186,209),(173,208,187,222),(174,221,188,207),(175,206,189,220),(176,219,190,205),(177,204,191,218),(178,217,192,203),(179,202,193,216),(180,215,194,201),(181,200,195,214),(182,213,196,199)]])
94 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | ··· | 2I | 4A | ··· | 4N | 4O | ··· | 4X | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28AV |
| order | 1 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 14 | ··· | 14 | 2 | ··· | 2 | 14 | ··· | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
94 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | D7 | D14 | D14 | D14 | C4×D7 | 2+ 1+4 | 2- 1+4 | Q8.10D14 | D4⋊8D14 |
| kernel | C42.126D14 | C42⋊D7 | C4×D28 | D7×C4⋊C4 | D28⋊C4 | Q8×Dic7 | Q8×C28 | C2×Q8⋊2D7 | Q8⋊2D7 | C4×Q8 | C42 | C4⋊C4 | C2×Q8 | Q8 | C14 | C14 | C2 | C2 |
| # reps | 1 | 3 | 3 | 3 | 3 | 1 | 1 | 1 | 16 | 3 | 9 | 9 | 3 | 24 | 1 | 1 | 6 | 6 |
Matrix representation of C42.126D14 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 24 | 0 |
| 0 | 0 | 0 | 17 | 0 | 24 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 16 | 0 | 0 |
| 0 | 0 | 13 | 24 | 0 | 0 |
| 0 | 0 | 0 | 0 | 5 | 16 |
| 0 | 0 | 0 | 0 | 13 | 24 |
| 16 | 10 | 0 | 0 | 0 | 0 |
| 19 | 10 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 21 | 16 | 16 |
| 0 | 0 | 8 | 26 | 13 | 6 |
| 0 | 0 | 21 | 21 | 8 | 8 |
| 0 | 0 | 8 | 26 | 21 | 3 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 12 | 24 | 5 |
| 0 | 0 | 5 | 12 | 19 | 5 |
| 0 | 0 | 17 | 12 | 12 | 17 |
| 0 | 0 | 5 | 12 | 24 | 17 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,0,0,24,0,12,0,0,0,0,24,0,12],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,5,13,0,0,0,0,16,24,0,0,0,0,0,0,5,13,0,0,0,0,16,24],[16,19,0,0,0,0,10,10,0,0,0,0,0,0,21,8,21,8,0,0,21,26,21,26,0,0,16,13,8,21,0,0,16,6,8,3],[0,17,0,0,0,0,17,0,0,0,0,0,0,0,17,5,17,5,0,0,12,12,12,12,0,0,24,19,12,24,0,0,5,5,17,17] >;
C42.126D14 in GAP, Magma, Sage, TeX
C_4^2._{126}D_{14} % in TeX
G:=Group("C4^2.126D14"); // GroupNames label
G:=SmallGroup(448,1027);
// by ID
G=gap.SmallGroup(448,1027);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,268,675,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^2*b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,b*c=c*b,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations