metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.48D14, D4⋊D7⋊5C4, (C4×D4)⋊2D7, D4⋊4(C4×D7), (D4×C28)⋊2C2, (C4×D28)⋊20C2, D28⋊11(C2×C4), C7⋊4(D8⋊C4), C14.70(C4×D4), C4⋊C4.242D14, (C2×C28).254D4, C14.D8⋊29C2, (C2×D4).189D14, C28.49(C4○D4), C4.37(C4○D28), D4⋊Dic7⋊11C2, (C4×C28).85C22, C28.22(C22×C4), C4.Dic14⋊32C2, C42.D7⋊5C2, C2.3(D4⋊D14), (C2×C28).336C23, C14.108(C8⋊C22), C2.3(D4.D14), (C2×D28).237C22, (D4×C14).231C22, C4⋊Dic7.327C22, C7⋊C8⋊8(C2×C4), C4.22(C2×C4×D7), (C7×D4)⋊9(C2×C4), (C2×D4⋊D7).4C2, C2.16(C4×C7⋊D4), (C2×C7⋊C8).92C22, (C2×C14).467(C2×D4), C22.76(C2×C7⋊D4), (C2×C4).217(C7⋊D4), (C7×C4⋊C4).273C22, (C2×C4).436(C22×D7), SmallGroup(448,548)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.48D14
G = < a,b,c,d | a4=b4=c14=1, d2=cbc-1=b-1, ab=ba, cac-1=dad-1=ab2, bd=db, dcd-1=b-1c-1 >
Subgroups: 628 in 132 conjugacy classes, 51 normal (39 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, D4, C23, D7, C14, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, D8, C22×C4, C2×D4, C2×D4, Dic7, C28, C28, D14, C2×C14, C2×C14, C8⋊C4, D4⋊C4, C4.Q8, C4×D4, C4×D4, C2×D8, C7⋊C8, C7⋊C8, C4×D7, D28, D28, C2×Dic7, C2×C28, C2×C28, C7×D4, C7×D4, C22×D7, C22×C14, D8⋊C4, C2×C7⋊C8, C4⋊Dic7, D14⋊C4, D4⋊D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×C4×D7, C2×D28, C22×C28, D4×C14, C42.D7, C4.Dic14, C14.D8, D4⋊Dic7, C4×D28, C2×D4⋊D7, D4×C28, C42.48D14
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22×C4, C2×D4, C4○D4, D14, C4×D4, C8⋊C22, C4×D7, C7⋊D4, C22×D7, D8⋊C4, C2×C4×D7, C4○D28, C2×C7⋊D4, C4×C7⋊D4, D4.D14, D4⋊D14, C42.48D14
►On 224 points
Generators in S224
(1 72 33 63)(2 80 34 57)(3 74 35 65)(4 82 29 59)(5 76 30 67)(6 84 31 61)(7 78 32 69)(8 75 36 66)(9 83 37 60)(10 77 38 68)(11 71 39 62)(12 79 40 70)(13 73 41 64)(14 81 42 58)(15 211 55 191)(16 219 56 185)(17 213 50 193)(18 221 51 187)(19 215 52 195)(20 223 53 189)(21 217 54 183)(22 188 47 222)(23 196 48 216)(24 190 49 224)(25 184 43 218)(26 192 44 212)(27 186 45 220)(28 194 46 214)(85 210 150 155)(86 99 151 181)(87 198 152 157)(88 101 153 169)(89 200 154 159)(90 103 141 171)(91 202 142 161)(92 105 143 173)(93 204 144 163)(94 107 145 175)(95 206 146 165)(96 109 147 177)(97 208 148 167)(98 111 149 179)(100 138 182 119)(102 140 170 121)(104 128 172 123)(106 130 174 125)(108 132 176 113)(110 134 178 115)(112 136 180 117)(114 207 133 166)(116 209 135 168)(118 197 137 156)(120 199 139 158)(122 201 127 160)(124 203 129 162)(126 205 131 164)
(1 194 12 187)(2 188 13 195)(3 196 14 189)(4 190 8 183)(5 184 9 191)(6 192 10 185)(7 186 11 193)(15 76 43 83)(16 84 44 77)(17 78 45 71)(18 72 46 79)(19 80 47 73)(20 74 48 81)(21 82 49 75)(22 64 52 57)(23 58 53 65)(24 66 54 59)(25 60 55 67)(26 68 56 61)(27 62 50 69)(28 70 51 63)(29 224 36 217)(30 218 37 211)(31 212 38 219)(32 220 39 213)(33 214 40 221)(34 222 41 215)(35 216 42 223)(85 92 117 124)(86 125 118 93)(87 94 119 126)(88 113 120 95)(89 96 121 114)(90 115 122 97)(91 98 123 116)(99 106 197 204)(100 205 198 107)(101 108 199 206)(102 207 200 109)(103 110 201 208)(104 209 202 111)(105 112 203 210)(127 148 141 134)(128 135 142 149)(129 150 143 136)(130 137 144 151)(131 152 145 138)(132 139 146 153)(133 154 147 140)(155 173 180 162)(156 163 181 174)(157 175 182 164)(158 165 169 176)(159 177 170 166)(160 167 171 178)(161 179 172 168)
(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 87 187 126 12 119 194 94)(2 93 195 118 13 125 188 86)(3 85 189 124 14 117 196 92)(4 91 183 116 8 123 190 98)(5 97 191 122 9 115 184 90)(6 89 185 114 10 121 192 96)(7 95 193 120 11 113 186 88)(15 103 83 208 43 201 76 110)(16 109 77 200 44 207 84 102)(17 101 71 206 45 199 78 108)(18 107 79 198 46 205 72 100)(19 99 73 204 47 197 80 106)(20 105 81 210 48 203 74 112)(21 111 75 202 49 209 82 104)(22 156 57 174 52 181 64 163)(23 162 65 180 53 173 58 155)(24 168 59 172 54 179 66 161)(25 160 67 178 55 171 60 167)(26 166 61 170 56 177 68 159)(27 158 69 176 50 169 62 165)(28 164 63 182 51 175 70 157)(29 142 217 135 36 128 224 149)(30 148 211 127 37 134 218 141)(31 154 219 133 38 140 212 147)(32 146 213 139 39 132 220 153)(33 152 221 131 40 138 214 145)(34 144 215 137 41 130 222 151)(35 150 223 129 42 136 216 143)
G:=sub<Sym(224)| (1,72,33,63)(2,80,34,57)(3,74,35,65)(4,82,29,59)(5,76,30,67)(6,84,31,61)(7,78,32,69)(8,75,36,66)(9,83,37,60)(10,77,38,68)(11,71,39,62)(12,79,40,70)(13,73,41,64)(14,81,42,58)(15,211,55,191)(16,219,56,185)(17,213,50,193)(18,221,51,187)(19,215,52,195)(20,223,53,189)(21,217,54,183)(22,188,47,222)(23,196,48,216)(24,190,49,224)(25,184,43,218)(26,192,44,212)(27,186,45,220)(28,194,46,214)(85,210,150,155)(86,99,151,181)(87,198,152,157)(88,101,153,169)(89,200,154,159)(90,103,141,171)(91,202,142,161)(92,105,143,173)(93,204,144,163)(94,107,145,175)(95,206,146,165)(96,109,147,177)(97,208,148,167)(98,111,149,179)(100,138,182,119)(102,140,170,121)(104,128,172,123)(106,130,174,125)(108,132,176,113)(110,134,178,115)(112,136,180,117)(114,207,133,166)(116,209,135,168)(118,197,137,156)(120,199,139,158)(122,201,127,160)(124,203,129,162)(126,205,131,164), (1,194,12,187)(2,188,13,195)(3,196,14,189)(4,190,8,183)(5,184,9,191)(6,192,10,185)(7,186,11,193)(15,76,43,83)(16,84,44,77)(17,78,45,71)(18,72,46,79)(19,80,47,73)(20,74,48,81)(21,82,49,75)(22,64,52,57)(23,58,53,65)(24,66,54,59)(25,60,55,67)(26,68,56,61)(27,62,50,69)(28,70,51,63)(29,224,36,217)(30,218,37,211)(31,212,38,219)(32,220,39,213)(33,214,40,221)(34,222,41,215)(35,216,42,223)(85,92,117,124)(86,125,118,93)(87,94,119,126)(88,113,120,95)(89,96,121,114)(90,115,122,97)(91,98,123,116)(99,106,197,204)(100,205,198,107)(101,108,199,206)(102,207,200,109)(103,110,201,208)(104,209,202,111)(105,112,203,210)(127,148,141,134)(128,135,142,149)(129,150,143,136)(130,137,144,151)(131,152,145,138)(132,139,146,153)(133,154,147,140)(155,173,180,162)(156,163,181,174)(157,175,182,164)(158,165,169,176)(159,177,170,166)(160,167,171,178)(161,179,172,168), (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), (1,87,187,126,12,119,194,94)(2,93,195,118,13,125,188,86)(3,85,189,124,14,117,196,92)(4,91,183,116,8,123,190,98)(5,97,191,122,9,115,184,90)(6,89,185,114,10,121,192,96)(7,95,193,120,11,113,186,88)(15,103,83,208,43,201,76,110)(16,109,77,200,44,207,84,102)(17,101,71,206,45,199,78,108)(18,107,79,198,46,205,72,100)(19,99,73,204,47,197,80,106)(20,105,81,210,48,203,74,112)(21,111,75,202,49,209,82,104)(22,156,57,174,52,181,64,163)(23,162,65,180,53,173,58,155)(24,168,59,172,54,179,66,161)(25,160,67,178,55,171,60,167)(26,166,61,170,56,177,68,159)(27,158,69,176,50,169,62,165)(28,164,63,182,51,175,70,157)(29,142,217,135,36,128,224,149)(30,148,211,127,37,134,218,141)(31,154,219,133,38,140,212,147)(32,146,213,139,39,132,220,153)(33,152,221,131,40,138,214,145)(34,144,215,137,41,130,222,151)(35,150,223,129,42,136,216,143)>;
G:=Group( (1,72,33,63)(2,80,34,57)(3,74,35,65)(4,82,29,59)(5,76,30,67)(6,84,31,61)(7,78,32,69)(8,75,36,66)(9,83,37,60)(10,77,38,68)(11,71,39,62)(12,79,40,70)(13,73,41,64)(14,81,42,58)(15,211,55,191)(16,219,56,185)(17,213,50,193)(18,221,51,187)(19,215,52,195)(20,223,53,189)(21,217,54,183)(22,188,47,222)(23,196,48,216)(24,190,49,224)(25,184,43,218)(26,192,44,212)(27,186,45,220)(28,194,46,214)(85,210,150,155)(86,99,151,181)(87,198,152,157)(88,101,153,169)(89,200,154,159)(90,103,141,171)(91,202,142,161)(92,105,143,173)(93,204,144,163)(94,107,145,175)(95,206,146,165)(96,109,147,177)(97,208,148,167)(98,111,149,179)(100,138,182,119)(102,140,170,121)(104,128,172,123)(106,130,174,125)(108,132,176,113)(110,134,178,115)(112,136,180,117)(114,207,133,166)(116,209,135,168)(118,197,137,156)(120,199,139,158)(122,201,127,160)(124,203,129,162)(126,205,131,164), (1,194,12,187)(2,188,13,195)(3,196,14,189)(4,190,8,183)(5,184,9,191)(6,192,10,185)(7,186,11,193)(15,76,43,83)(16,84,44,77)(17,78,45,71)(18,72,46,79)(19,80,47,73)(20,74,48,81)(21,82,49,75)(22,64,52,57)(23,58,53,65)(24,66,54,59)(25,60,55,67)(26,68,56,61)(27,62,50,69)(28,70,51,63)(29,224,36,217)(30,218,37,211)(31,212,38,219)(32,220,39,213)(33,214,40,221)(34,222,41,215)(35,216,42,223)(85,92,117,124)(86,125,118,93)(87,94,119,126)(88,113,120,95)(89,96,121,114)(90,115,122,97)(91,98,123,116)(99,106,197,204)(100,205,198,107)(101,108,199,206)(102,207,200,109)(103,110,201,208)(104,209,202,111)(105,112,203,210)(127,148,141,134)(128,135,142,149)(129,150,143,136)(130,137,144,151)(131,152,145,138)(132,139,146,153)(133,154,147,140)(155,173,180,162)(156,163,181,174)(157,175,182,164)(158,165,169,176)(159,177,170,166)(160,167,171,178)(161,179,172,168), (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), (1,87,187,126,12,119,194,94)(2,93,195,118,13,125,188,86)(3,85,189,124,14,117,196,92)(4,91,183,116,8,123,190,98)(5,97,191,122,9,115,184,90)(6,89,185,114,10,121,192,96)(7,95,193,120,11,113,186,88)(15,103,83,208,43,201,76,110)(16,109,77,200,44,207,84,102)(17,101,71,206,45,199,78,108)(18,107,79,198,46,205,72,100)(19,99,73,204,47,197,80,106)(20,105,81,210,48,203,74,112)(21,111,75,202,49,209,82,104)(22,156,57,174,52,181,64,163)(23,162,65,180,53,173,58,155)(24,168,59,172,54,179,66,161)(25,160,67,178,55,171,60,167)(26,166,61,170,56,177,68,159)(27,158,69,176,50,169,62,165)(28,164,63,182,51,175,70,157)(29,142,217,135,36,128,224,149)(30,148,211,127,37,134,218,141)(31,154,219,133,38,140,212,147)(32,146,213,139,39,132,220,153)(33,152,221,131,40,138,214,145)(34,144,215,137,41,130,222,151)(35,150,223,129,42,136,216,143) );
G=PermutationGroup([[(1,72,33,63),(2,80,34,57),(3,74,35,65),(4,82,29,59),(5,76,30,67),(6,84,31,61),(7,78,32,69),(8,75,36,66),(9,83,37,60),(10,77,38,68),(11,71,39,62),(12,79,40,70),(13,73,41,64),(14,81,42,58),(15,211,55,191),(16,219,56,185),(17,213,50,193),(18,221,51,187),(19,215,52,195),(20,223,53,189),(21,217,54,183),(22,188,47,222),(23,196,48,216),(24,190,49,224),(25,184,43,218),(26,192,44,212),(27,186,45,220),(28,194,46,214),(85,210,150,155),(86,99,151,181),(87,198,152,157),(88,101,153,169),(89,200,154,159),(90,103,141,171),(91,202,142,161),(92,105,143,173),(93,204,144,163),(94,107,145,175),(95,206,146,165),(96,109,147,177),(97,208,148,167),(98,111,149,179),(100,138,182,119),(102,140,170,121),(104,128,172,123),(106,130,174,125),(108,132,176,113),(110,134,178,115),(112,136,180,117),(114,207,133,166),(116,209,135,168),(118,197,137,156),(120,199,139,158),(122,201,127,160),(124,203,129,162),(126,205,131,164)], [(1,194,12,187),(2,188,13,195),(3,196,14,189),(4,190,8,183),(5,184,9,191),(6,192,10,185),(7,186,11,193),(15,76,43,83),(16,84,44,77),(17,78,45,71),(18,72,46,79),(19,80,47,73),(20,74,48,81),(21,82,49,75),(22,64,52,57),(23,58,53,65),(24,66,54,59),(25,60,55,67),(26,68,56,61),(27,62,50,69),(28,70,51,63),(29,224,36,217),(30,218,37,211),(31,212,38,219),(32,220,39,213),(33,214,40,221),(34,222,41,215),(35,216,42,223),(85,92,117,124),(86,125,118,93),(87,94,119,126),(88,113,120,95),(89,96,121,114),(90,115,122,97),(91,98,123,116),(99,106,197,204),(100,205,198,107),(101,108,199,206),(102,207,200,109),(103,110,201,208),(104,209,202,111),(105,112,203,210),(127,148,141,134),(128,135,142,149),(129,150,143,136),(130,137,144,151),(131,152,145,138),(132,139,146,153),(133,154,147,140),(155,173,180,162),(156,163,181,174),(157,175,182,164),(158,165,169,176),(159,177,170,166),(160,167,171,178),(161,179,172,168)], [(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)], [(1,87,187,126,12,119,194,94),(2,93,195,118,13,125,188,86),(3,85,189,124,14,117,196,92),(4,91,183,116,8,123,190,98),(5,97,191,122,9,115,184,90),(6,89,185,114,10,121,192,96),(7,95,193,120,11,113,186,88),(15,103,83,208,43,201,76,110),(16,109,77,200,44,207,84,102),(17,101,71,206,45,199,78,108),(18,107,79,198,46,205,72,100),(19,99,73,204,47,197,80,106),(20,105,81,210,48,203,74,112),(21,111,75,202,49,209,82,104),(22,156,57,174,52,181,64,163),(23,162,65,180,53,173,58,155),(24,168,59,172,54,179,66,161),(25,160,67,178,55,171,60,167),(26,166,61,170,56,177,68,159),(27,158,69,176,50,169,62,165),(28,164,63,182,51,175,70,157),(29,142,217,135,36,128,224,149),(30,148,211,127,37,134,218,141),(31,154,219,133,38,140,212,147),(32,146,213,139,39,132,220,153),(33,152,221,131,40,138,214,145),(34,144,215,137,41,130,222,151),(35,150,223,129,42,136,216,143)]])
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 28 | 28 | 2 | ··· | 2 | 4 | 4 | 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 |
| 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 | D4.D14 | D4⋊D14 |
| kernel | C42.48D14 | C42.D7 | C4.Dic14 | C14.D8 | D4⋊Dic7 | C4×D28 | C2×D4⋊D7 | D4×C28 | D4⋊D7 | C2×C28 | C4×D4 | C28 | C42 | C4⋊C4 | C2×D4 | C2×C4 | D4 | C4 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8 | 2 | 3 | 2 | 3 | 3 | 3 | 12 | 12 | 12 | 2 | 6 | 6 |
Matrix representation of C42.48D14 ►in GL6(𝔽113)
| 98 | 0 | 0 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 8 | 79 | 97 |
| 0 | 0 | 105 | 96 | 16 | 34 |
| 0 | 0 | 17 | 8 | 96 | 105 |
| 0 | 0 | 105 | 96 | 8 | 17 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 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 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 103 | 103 | 0 | 0 |
| 0 | 0 | 10 | 89 | 0 | 0 |
| 0 | 0 | 103 | 103 | 10 | 10 |
| 0 | 0 | 10 | 89 | 103 | 24 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 33 | 100 |
| 0 | 0 | 0 | 0 | 101 | 80 |
| 0 | 0 | 40 | 63 | 33 | 100 |
| 0 | 0 | 6 | 73 | 101 | 80 |
G:=sub<GL(6,GF(113))| [98,0,0,0,0,0,0,98,0,0,0,0,0,0,17,105,17,105,0,0,8,96,8,96,0,0,79,16,96,8,0,0,97,34,105,17],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,111,0,112,0,0,0,0,111,0,112],[1,0,0,0,0,0,0,112,0,0,0,0,0,0,103,10,103,10,0,0,103,89,103,89,0,0,0,0,10,103,0,0,0,0,10,24],[0,112,0,0,0,0,1,0,0,0,0,0,0,0,0,0,40,6,0,0,0,0,63,73,0,0,33,101,33,101,0,0,100,80,100,80] >;
C42.48D14 in GAP, Magma, Sage, TeX
C_4^2._{48}D_{14} % in TeX
G:=Group("C4^2.48D14"); // GroupNames label
G:=SmallGroup(448,548);
// by ID
G=gap.SmallGroup(448,548);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,387,58,1684,851,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=c*b*c^-1=b^-1,a*b=b*a,c*a*c^-1=d*a*d^-1=a*b^2,b*d=d*b,d*c*d^-1=b^-1*c^-1>;
// generators/relations