metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.51D14, D4.D7⋊5C4, (C4×D4).8D7, D4.6(C4×D7), (D4×C28).9C2, C14.72(C4×D4), C4⋊C4.246D14, (C2×C28).256D4, (C4×Dic14)⋊20C2, Dic14⋊11(C2×C4), (C2×D4).193D14, C4.39(C4○D28), C28.53(C4○D4), C14.Q16⋊30C2, C28.Q8⋊32C2, C7⋊5(SD16⋊C4), (C4×C28).89C22, C28.24(C22×C4), C42.D7⋊6C2, C14.88(C8⋊C22), (C2×C28).340C23, D4⋊Dic7.10C2, C2.4(D4.D14), C2.3(D4.9D14), (D4×C14).235C22, C4⋊Dic7.329C22, C14.108(C8.C22), (C2×Dic14).265C22, C7⋊C8⋊9(C2×C4), C4.24(C2×C4×D7), C2.18(C4×C7⋊D4), (C7×D4).13(C2×C4), (C2×C7⋊C8).95C22, (C2×D4.D7).4C2, (C2×C14).471(C2×D4), C22.78(C2×C7⋊D4), (C2×C4).219(C7⋊D4), (C7×C4⋊C4).277C22, (C2×C4).440(C22×D7), SmallGroup(448,552)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.51D14
G = < a,b,c,d | a4=b4=c14=1, d2=b, ab=ba, cac-1=dad-1=ab2, cbc-1=b-1, bd=db, dcd-1=b-1c-1 >
Subgroups: 436 in 120 conjugacy classes, 51 normal (39 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, D4, Q8, C23, C14, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, SD16, C22×C4, C2×D4, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C8⋊C4, D4⋊C4, Q8⋊C4, C2.D8, C4×D4, C4×Q8, C2×SD16, C7⋊C8, C7⋊C8, Dic14, Dic14, C2×Dic7, C2×C28, C2×C28, C7×D4, C7×D4, C22×C14, SD16⋊C4, C2×C7⋊C8, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D4.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C22×C28, D4×C14, C42.D7, C28.Q8, C14.Q16, D4⋊Dic7, C4×Dic14, C2×D4.D7, D4×C28, C42.51D14
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22×C4, C2×D4, C4○D4, D14, C4×D4, C8⋊C22, C8.C22, C4×D7, C7⋊D4, C22×D7, SD16⋊C4, C2×C4×D7, C4○D28, C2×C7⋊D4, C4×C7⋊D4, D4.D14, D4.9D14, C42.51D14
►On 224 points
Generators in S224
(1 199 44 73)(2 207 45 81)(3 201 46 75)(4 209 47 83)(5 203 48 77)(6 197 49 71)(7 205 43 79)(8 104 41 94)(9 112 42 88)(10 106 36 96)(11 100 37 90)(12 108 38 98)(13 102 39 92)(14 110 40 86)(15 80 53 206)(16 74 54 200)(17 82 55 208)(18 76 56 202)(19 84 50 210)(20 78 51 204)(21 72 52 198)(22 105 29 95)(23 99 30 89)(24 107 31 97)(25 101 32 91)(26 109 33 85)(27 103 34 93)(28 111 35 87)(57 179 123 166)(58 141 124 183)(59 181 125 168)(60 143 126 185)(61 169 113 156)(62 145 114 187)(63 171 115 158)(64 147 116 189)(65 173 117 160)(66 149 118 191)(67 175 119 162)(68 151 120 193)(69 177 121 164)(70 153 122 195)(127 182 220 155)(128 144 221 186)(129 170 222 157)(130 146 223 188)(131 172 224 159)(132 148 211 190)(133 174 212 161)(134 150 213 192)(135 176 214 163)(136 152 215 194)(137 178 216 165)(138 154 217 196)(139 180 218 167)(140 142 219 184)
(1 95 53 88)(2 89 54 96)(3 97 55 90)(4 91 56 98)(5 85 50 92)(6 93 51 86)(7 87 52 94)(8 205 28 198)(9 199 22 206)(10 207 23 200)(11 201 24 208)(12 209 25 202)(13 203 26 210)(14 197 27 204)(15 112 44 105)(16 106 45 99)(17 100 46 107)(18 108 47 101)(19 102 48 109)(20 110 49 103)(21 104 43 111)(29 80 42 73)(30 74 36 81)(31 82 37 75)(32 76 38 83)(33 84 39 77)(34 78 40 71)(35 72 41 79)(57 64 138 131)(58 132 139 65)(59 66 140 133)(60 134 127 67)(61 68 128 135)(62 136 129 69)(63 70 130 137)(113 120 221 214)(114 215 222 121)(115 122 223 216)(116 217 224 123)(117 124 211 218)(118 219 212 125)(119 126 213 220)(141 148 180 173)(142 174 181 149)(143 150 182 175)(144 176 169 151)(145 152 170 177)(146 178 171 153)(147 154 172 179)(155 162 185 192)(156 193 186 163)(157 164 187 194)(158 195 188 165)(159 166 189 196)(160 183 190 167)(161 168 191 184)
(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)
(1 149 95 142 53 174 88 181)(2 141 89 148 54 180 96 173)(3 147 97 154 55 172 90 179)(4 153 91 146 56 178 98 171)(5 145 85 152 50 170 92 177)(6 151 93 144 51 176 86 169)(7 143 87 150 52 182 94 175)(8 213 205 220 28 119 198 126)(9 219 199 212 22 125 206 118)(10 211 207 218 23 117 200 124)(11 217 201 224 24 123 208 116)(12 223 209 216 25 115 202 122)(13 215 203 222 26 121 210 114)(14 221 197 214 27 113 204 120)(15 161 112 168 44 191 105 184)(16 167 106 160 45 183 99 190)(17 159 100 166 46 189 107 196)(18 165 108 158 47 195 101 188)(19 157 102 164 48 187 109 194)(20 163 110 156 49 193 103 186)(21 155 104 162 43 185 111 192)(29 59 80 66 42 140 73 133)(30 65 74 58 36 132 81 139)(31 57 82 64 37 138 75 131)(32 63 76 70 38 130 83 137)(33 69 84 62 39 136 77 129)(34 61 78 68 40 128 71 135)(35 67 72 60 41 134 79 127)
G:=sub<Sym(224)| (1,199,44,73)(2,207,45,81)(3,201,46,75)(4,209,47,83)(5,203,48,77)(6,197,49,71)(7,205,43,79)(8,104,41,94)(9,112,42,88)(10,106,36,96)(11,100,37,90)(12,108,38,98)(13,102,39,92)(14,110,40,86)(15,80,53,206)(16,74,54,200)(17,82,55,208)(18,76,56,202)(19,84,50,210)(20,78,51,204)(21,72,52,198)(22,105,29,95)(23,99,30,89)(24,107,31,97)(25,101,32,91)(26,109,33,85)(27,103,34,93)(28,111,35,87)(57,179,123,166)(58,141,124,183)(59,181,125,168)(60,143,126,185)(61,169,113,156)(62,145,114,187)(63,171,115,158)(64,147,116,189)(65,173,117,160)(66,149,118,191)(67,175,119,162)(68,151,120,193)(69,177,121,164)(70,153,122,195)(127,182,220,155)(128,144,221,186)(129,170,222,157)(130,146,223,188)(131,172,224,159)(132,148,211,190)(133,174,212,161)(134,150,213,192)(135,176,214,163)(136,152,215,194)(137,178,216,165)(138,154,217,196)(139,180,218,167)(140,142,219,184), (1,95,53,88)(2,89,54,96)(3,97,55,90)(4,91,56,98)(5,85,50,92)(6,93,51,86)(7,87,52,94)(8,205,28,198)(9,199,22,206)(10,207,23,200)(11,201,24,208)(12,209,25,202)(13,203,26,210)(14,197,27,204)(15,112,44,105)(16,106,45,99)(17,100,46,107)(18,108,47,101)(19,102,48,109)(20,110,49,103)(21,104,43,111)(29,80,42,73)(30,74,36,81)(31,82,37,75)(32,76,38,83)(33,84,39,77)(34,78,40,71)(35,72,41,79)(57,64,138,131)(58,132,139,65)(59,66,140,133)(60,134,127,67)(61,68,128,135)(62,136,129,69)(63,70,130,137)(113,120,221,214)(114,215,222,121)(115,122,223,216)(116,217,224,123)(117,124,211,218)(118,219,212,125)(119,126,213,220)(141,148,180,173)(142,174,181,149)(143,150,182,175)(144,176,169,151)(145,152,170,177)(146,178,171,153)(147,154,172,179)(155,162,185,192)(156,193,186,163)(157,164,187,194)(158,195,188,165)(159,166,189,196)(160,183,190,167)(161,168,191,184), (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), (1,149,95,142,53,174,88,181)(2,141,89,148,54,180,96,173)(3,147,97,154,55,172,90,179)(4,153,91,146,56,178,98,171)(5,145,85,152,50,170,92,177)(6,151,93,144,51,176,86,169)(7,143,87,150,52,182,94,175)(8,213,205,220,28,119,198,126)(9,219,199,212,22,125,206,118)(10,211,207,218,23,117,200,124)(11,217,201,224,24,123,208,116)(12,223,209,216,25,115,202,122)(13,215,203,222,26,121,210,114)(14,221,197,214,27,113,204,120)(15,161,112,168,44,191,105,184)(16,167,106,160,45,183,99,190)(17,159,100,166,46,189,107,196)(18,165,108,158,47,195,101,188)(19,157,102,164,48,187,109,194)(20,163,110,156,49,193,103,186)(21,155,104,162,43,185,111,192)(29,59,80,66,42,140,73,133)(30,65,74,58,36,132,81,139)(31,57,82,64,37,138,75,131)(32,63,76,70,38,130,83,137)(33,69,84,62,39,136,77,129)(34,61,78,68,40,128,71,135)(35,67,72,60,41,134,79,127)>;
G:=Group( (1,199,44,73)(2,207,45,81)(3,201,46,75)(4,209,47,83)(5,203,48,77)(6,197,49,71)(7,205,43,79)(8,104,41,94)(9,112,42,88)(10,106,36,96)(11,100,37,90)(12,108,38,98)(13,102,39,92)(14,110,40,86)(15,80,53,206)(16,74,54,200)(17,82,55,208)(18,76,56,202)(19,84,50,210)(20,78,51,204)(21,72,52,198)(22,105,29,95)(23,99,30,89)(24,107,31,97)(25,101,32,91)(26,109,33,85)(27,103,34,93)(28,111,35,87)(57,179,123,166)(58,141,124,183)(59,181,125,168)(60,143,126,185)(61,169,113,156)(62,145,114,187)(63,171,115,158)(64,147,116,189)(65,173,117,160)(66,149,118,191)(67,175,119,162)(68,151,120,193)(69,177,121,164)(70,153,122,195)(127,182,220,155)(128,144,221,186)(129,170,222,157)(130,146,223,188)(131,172,224,159)(132,148,211,190)(133,174,212,161)(134,150,213,192)(135,176,214,163)(136,152,215,194)(137,178,216,165)(138,154,217,196)(139,180,218,167)(140,142,219,184), (1,95,53,88)(2,89,54,96)(3,97,55,90)(4,91,56,98)(5,85,50,92)(6,93,51,86)(7,87,52,94)(8,205,28,198)(9,199,22,206)(10,207,23,200)(11,201,24,208)(12,209,25,202)(13,203,26,210)(14,197,27,204)(15,112,44,105)(16,106,45,99)(17,100,46,107)(18,108,47,101)(19,102,48,109)(20,110,49,103)(21,104,43,111)(29,80,42,73)(30,74,36,81)(31,82,37,75)(32,76,38,83)(33,84,39,77)(34,78,40,71)(35,72,41,79)(57,64,138,131)(58,132,139,65)(59,66,140,133)(60,134,127,67)(61,68,128,135)(62,136,129,69)(63,70,130,137)(113,120,221,214)(114,215,222,121)(115,122,223,216)(116,217,224,123)(117,124,211,218)(118,219,212,125)(119,126,213,220)(141,148,180,173)(142,174,181,149)(143,150,182,175)(144,176,169,151)(145,152,170,177)(146,178,171,153)(147,154,172,179)(155,162,185,192)(156,193,186,163)(157,164,187,194)(158,195,188,165)(159,166,189,196)(160,183,190,167)(161,168,191,184), (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), (1,149,95,142,53,174,88,181)(2,141,89,148,54,180,96,173)(3,147,97,154,55,172,90,179)(4,153,91,146,56,178,98,171)(5,145,85,152,50,170,92,177)(6,151,93,144,51,176,86,169)(7,143,87,150,52,182,94,175)(8,213,205,220,28,119,198,126)(9,219,199,212,22,125,206,118)(10,211,207,218,23,117,200,124)(11,217,201,224,24,123,208,116)(12,223,209,216,25,115,202,122)(13,215,203,222,26,121,210,114)(14,221,197,214,27,113,204,120)(15,161,112,168,44,191,105,184)(16,167,106,160,45,183,99,190)(17,159,100,166,46,189,107,196)(18,165,108,158,47,195,101,188)(19,157,102,164,48,187,109,194)(20,163,110,156,49,193,103,186)(21,155,104,162,43,185,111,192)(29,59,80,66,42,140,73,133)(30,65,74,58,36,132,81,139)(31,57,82,64,37,138,75,131)(32,63,76,70,38,130,83,137)(33,69,84,62,39,136,77,129)(34,61,78,68,40,128,71,135)(35,67,72,60,41,134,79,127) );
G=PermutationGroup([[(1,199,44,73),(2,207,45,81),(3,201,46,75),(4,209,47,83),(5,203,48,77),(6,197,49,71),(7,205,43,79),(8,104,41,94),(9,112,42,88),(10,106,36,96),(11,100,37,90),(12,108,38,98),(13,102,39,92),(14,110,40,86),(15,80,53,206),(16,74,54,200),(17,82,55,208),(18,76,56,202),(19,84,50,210),(20,78,51,204),(21,72,52,198),(22,105,29,95),(23,99,30,89),(24,107,31,97),(25,101,32,91),(26,109,33,85),(27,103,34,93),(28,111,35,87),(57,179,123,166),(58,141,124,183),(59,181,125,168),(60,143,126,185),(61,169,113,156),(62,145,114,187),(63,171,115,158),(64,147,116,189),(65,173,117,160),(66,149,118,191),(67,175,119,162),(68,151,120,193),(69,177,121,164),(70,153,122,195),(127,182,220,155),(128,144,221,186),(129,170,222,157),(130,146,223,188),(131,172,224,159),(132,148,211,190),(133,174,212,161),(134,150,213,192),(135,176,214,163),(136,152,215,194),(137,178,216,165),(138,154,217,196),(139,180,218,167),(140,142,219,184)], [(1,95,53,88),(2,89,54,96),(3,97,55,90),(4,91,56,98),(5,85,50,92),(6,93,51,86),(7,87,52,94),(8,205,28,198),(9,199,22,206),(10,207,23,200),(11,201,24,208),(12,209,25,202),(13,203,26,210),(14,197,27,204),(15,112,44,105),(16,106,45,99),(17,100,46,107),(18,108,47,101),(19,102,48,109),(20,110,49,103),(21,104,43,111),(29,80,42,73),(30,74,36,81),(31,82,37,75),(32,76,38,83),(33,84,39,77),(34,78,40,71),(35,72,41,79),(57,64,138,131),(58,132,139,65),(59,66,140,133),(60,134,127,67),(61,68,128,135),(62,136,129,69),(63,70,130,137),(113,120,221,214),(114,215,222,121),(115,122,223,216),(116,217,224,123),(117,124,211,218),(118,219,212,125),(119,126,213,220),(141,148,180,173),(142,174,181,149),(143,150,182,175),(144,176,169,151),(145,152,170,177),(146,178,171,153),(147,154,172,179),(155,162,185,192),(156,193,186,163),(157,164,187,194),(158,195,188,165),(159,166,189,196),(160,183,190,167),(161,168,191,184)], [(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)], [(1,149,95,142,53,174,88,181),(2,141,89,148,54,180,96,173),(3,147,97,154,55,172,90,179),(4,153,91,146,56,178,98,171),(5,145,85,152,50,170,92,177),(6,151,93,144,51,176,86,169),(7,143,87,150,52,182,94,175),(8,213,205,220,28,119,198,126),(9,219,199,212,22,125,206,118),(10,211,207,218,23,117,200,124),(11,217,201,224,24,123,208,116),(12,223,209,216,25,115,202,122),(13,215,203,222,26,121,210,114),(14,221,197,214,27,113,204,120),(15,161,112,168,44,191,105,184),(16,167,106,160,45,183,99,190),(17,159,100,166,46,189,107,196),(18,165,108,158,47,195,101,188),(19,157,102,164,48,187,109,194),(20,163,110,156,49,193,103,186),(21,155,104,162,43,185,111,192),(29,59,80,66,42,140,73,133),(30,65,74,58,36,132,81,139),(31,57,82,64,37,138,75,131),(32,63,76,70,38,130,83,137),(33,69,84,62,39,136,77,129),(34,61,78,68,40,128,71,135),(35,67,72,60,41,134,79,127)]])
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 2 | ··· | 2 | 4 | 4 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | ||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D7 | C4○D4 | D14 | D14 | D14 | C7⋊D4 | C4×D7 | C4○D28 | C8⋊C22 | C8.C22 | D4.D14 | D4.9D14 |
| kernel | C42.51D14 | C42.D7 | C28.Q8 | C14.Q16 | D4⋊Dic7 | C4×Dic14 | C2×D4.D7 | D4×C28 | D4.D7 | C2×C28 | C4×D4 | C28 | C42 | C4⋊C4 | C2×D4 | C2×C4 | D4 | C4 | C14 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8 | 2 | 3 | 2 | 3 | 3 | 3 | 12 | 12 | 12 | 1 | 1 | 6 | 6 |
Matrix representation of C42.51D14 ►in GL6(𝔽113)
| 98 | 0 | 0 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 | 0 | 0 |
| 0 | 0 | 58 | 75 | 110 | 76 |
| 0 | 0 | 38 | 55 | 37 | 3 |
| 0 | 0 | 58 | 75 | 55 | 38 |
| 0 | 0 | 38 | 55 | 75 | 58 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 111 | 0 |
| 0 | 0 | 0 | 1 | 0 | 111 |
| 0 | 0 | 1 | 0 | 112 | 0 |
| 0 | 0 | 0 | 1 | 0 | 112 |
| 33 | 10 | 0 | 0 | 0 | 0 |
| 71 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 33 | 33 | 0 | 0 |
| 0 | 0 | 80 | 104 | 0 | 0 |
| 0 | 0 | 33 | 33 | 80 | 80 |
| 0 | 0 | 80 | 104 | 33 | 9 |
| 22 | 35 | 0 | 0 | 0 | 0 |
| 54 | 91 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 70 | 33 |
| 0 | 0 | 0 | 0 | 98 | 43 |
| 0 | 0 | 78 | 40 | 70 | 33 |
| 0 | 0 | 64 | 35 | 98 | 43 |
G:=sub<GL(6,GF(113))| [98,0,0,0,0,0,0,98,0,0,0,0,0,0,58,38,58,38,0,0,75,55,75,55,0,0,110,37,55,75,0,0,76,3,38,58],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,111,0,112,0,0,0,0,111,0,112],[33,71,0,0,0,0,10,1,0,0,0,0,0,0,33,80,33,80,0,0,33,104,33,104,0,0,0,0,80,33,0,0,0,0,80,9],[22,54,0,0,0,0,35,91,0,0,0,0,0,0,0,0,78,64,0,0,0,0,40,35,0,0,70,98,70,98,0,0,33,43,33,43] >;
C42.51D14 in GAP, Magma, Sage, TeX
C_4^2._{51}D_{14} % in TeX
G:=Group("C4^2.51D14"); // GroupNames label
G:=SmallGroup(448,552);
// by ID
G=gap.SmallGroup(448,552);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,253,387,58,1684,851,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=b,a*b=b*a,c*a*c^-1=d*a*d^-1=a*b^2,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=b^-1*c^-1>;
// generators/relations