metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.62D14, (C2×C28).81D4, C28⋊2Q8⋊17C2, (C2×D4).45D14, (C2×Q8).35D14, C4.4D4.5D7, C28.66(C4○D4), Q8⋊Dic7⋊20C2, C42.D7⋊8C2, C4.20(D4⋊2D7), (C4×C28).104C22, (C2×C28).373C23, D4⋊Dic7.12C2, (D4×C14).61C22, (Q8×C14).53C22, C2.17(D4⋊D14), C14.118(C8⋊C22), C14.41(C4.4D4), C2.8(C28.17D4), C4⋊Dic7.150C22, C2.18(D4.9D14), C14.119(C8.C22), C7⋊4(C42.28C22), (C2×C14).504(C2×D4), (C2×C4).60(C7⋊D4), (C2×C7⋊C8).120C22, (C7×C4.4D4).3C2, (C2×C4).473(C22×D7), C22.179(C2×C7⋊D4), SmallGroup(448,589)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.62D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2, ab=ba, cac-1=a-1b2, dad-1=a-1, cbc-1=dbd-1=b-1, dcd-1=a2bc-1 >
Subgroups: 428 in 100 conjugacy classes, 39 normal (27 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, C14, C14, C42, C22⋊C4, C4⋊C4, C2×C8, C2×D4, C2×Q8, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C8⋊C4, D4⋊C4, Q8⋊C4, C4.4D4, C4⋊Q8, C7⋊C8, Dic14, C2×Dic7, C2×C28, C2×C28, C7×D4, C7×Q8, C22×C14, C42.28C22, C2×C7⋊C8, C4⋊Dic7, C4⋊Dic7, C4×C28, C7×C22⋊C4, C2×Dic14, D4×C14, Q8×C14, C42.D7, D4⋊Dic7, Q8⋊Dic7, C28⋊2Q8, C7×C4.4D4, C42.62D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4.4D4, C8⋊C22, C8.C22, C7⋊D4, C22×D7, C42.28C22, D4⋊2D7, C2×C7⋊D4, C28.17D4, D4⋊D14, D4.9D14, C42.62D14
►On 224 points
Generators in S224
(1 217 19 78)(2 211 20 72)(3 219 21 80)(4 213 15 74)(5 221 16 82)(6 215 17 76)(7 223 18 84)(8 214 26 75)(9 222 27 83)(10 216 28 77)(11 224 22 71)(12 218 23 79)(13 212 24 73)(14 220 25 81)(29 177 185 166)(30 87 186 107)(31 179 187 168)(32 89 188 109)(33 181 189 156)(34 91 190 111)(35 169 191 158)(36 93 192 99)(37 171 193 160)(38 95 194 101)(39 173 195 162)(40 97 196 103)(41 175 183 164)(42 85 184 105)(43 90 62 110)(44 182 63 157)(45 92 64 112)(46 170 65 159)(47 94 66 100)(48 172 67 161)(49 96 68 102)(50 174 69 163)(51 98 70 104)(52 176 57 165)(53 86 58 106)(54 178 59 167)(55 88 60 108)(56 180 61 155)(113 131 120 198)(114 206 121 139)(115 133 122 200)(116 208 123 127)(117 135 124 202)(118 210 125 129)(119 137 126 204)(128 143 209 150)(130 145 197 152)(132 147 199 154)(134 149 201 142)(136 151 203 144)(138 153 205 146)(140 141 207 148)
(1 135 22 128)(2 129 23 136)(3 137 24 130)(4 131 25 138)(5 139 26 132)(6 133 27 140)(7 127 28 134)(8 199 16 206)(9 207 17 200)(10 201 18 208)(11 209 19 202)(12 203 20 210)(13 197 21 204)(14 205 15 198)(29 36 58 65)(30 66 59 37)(31 38 60 67)(32 68 61 39)(33 40 62 69)(34 70 63 41)(35 42 64 57)(43 50 189 196)(44 183 190 51)(45 52 191 184)(46 185 192 53)(47 54 193 186)(48 187 194 55)(49 56 195 188)(71 143 217 124)(72 125 218 144)(73 145 219 126)(74 113 220 146)(75 147 221 114)(76 115 222 148)(77 149 223 116)(78 117 224 150)(79 151 211 118)(80 119 212 152)(81 153 213 120)(82 121 214 154)(83 141 215 122)(84 123 216 142)(85 112 165 169)(86 170 166 99)(87 100 167 171)(88 172 168 101)(89 102 155 173)(90 174 156 103)(91 104 157 175)(92 176 158 105)(93 106 159 177)(94 178 160 107)(95 108 161 179)(96 180 162 109)(97 110 163 181)(98 182 164 111)
(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)
(1 174 19 163)(2 180 20 155)(3 172 21 161)(4 178 15 167)(5 170 16 159)(6 176 17 165)(7 182 18 157)(8 93 26 99)(9 85 27 105)(10 91 28 111)(11 97 22 103)(12 89 23 109)(13 95 24 101)(14 87 25 107)(29 147 185 154)(30 81 186 220)(31 145 187 152)(32 79 188 218)(33 143 189 150)(34 77 190 216)(35 141 191 148)(36 75 192 214)(37 153 193 146)(38 73 194 212)(39 151 195 144)(40 71 196 224)(41 149 183 142)(42 83 184 222)(43 117 62 124)(44 84 63 223)(45 115 64 122)(46 82 65 221)(47 113 66 120)(48 80 67 219)(49 125 68 118)(50 78 69 217)(51 123 70 116)(52 76 57 215)(53 121 58 114)(54 74 59 213)(55 119 60 126)(56 72 61 211)(86 206 106 139)(88 204 108 137)(90 202 110 135)(92 200 112 133)(94 198 100 131)(96 210 102 129)(98 208 104 127)(128 156 209 181)(130 168 197 179)(132 166 199 177)(134 164 201 175)(136 162 203 173)(138 160 205 171)(140 158 207 169)
G:=sub<Sym(224)| (1,217,19,78)(2,211,20,72)(3,219,21,80)(4,213,15,74)(5,221,16,82)(6,215,17,76)(7,223,18,84)(8,214,26,75)(9,222,27,83)(10,216,28,77)(11,224,22,71)(12,218,23,79)(13,212,24,73)(14,220,25,81)(29,177,185,166)(30,87,186,107)(31,179,187,168)(32,89,188,109)(33,181,189,156)(34,91,190,111)(35,169,191,158)(36,93,192,99)(37,171,193,160)(38,95,194,101)(39,173,195,162)(40,97,196,103)(41,175,183,164)(42,85,184,105)(43,90,62,110)(44,182,63,157)(45,92,64,112)(46,170,65,159)(47,94,66,100)(48,172,67,161)(49,96,68,102)(50,174,69,163)(51,98,70,104)(52,176,57,165)(53,86,58,106)(54,178,59,167)(55,88,60,108)(56,180,61,155)(113,131,120,198)(114,206,121,139)(115,133,122,200)(116,208,123,127)(117,135,124,202)(118,210,125,129)(119,137,126,204)(128,143,209,150)(130,145,197,152)(132,147,199,154)(134,149,201,142)(136,151,203,144)(138,153,205,146)(140,141,207,148), (1,135,22,128)(2,129,23,136)(3,137,24,130)(4,131,25,138)(5,139,26,132)(6,133,27,140)(7,127,28,134)(8,199,16,206)(9,207,17,200)(10,201,18,208)(11,209,19,202)(12,203,20,210)(13,197,21,204)(14,205,15,198)(29,36,58,65)(30,66,59,37)(31,38,60,67)(32,68,61,39)(33,40,62,69)(34,70,63,41)(35,42,64,57)(43,50,189,196)(44,183,190,51)(45,52,191,184)(46,185,192,53)(47,54,193,186)(48,187,194,55)(49,56,195,188)(71,143,217,124)(72,125,218,144)(73,145,219,126)(74,113,220,146)(75,147,221,114)(76,115,222,148)(77,149,223,116)(78,117,224,150)(79,151,211,118)(80,119,212,152)(81,153,213,120)(82,121,214,154)(83,141,215,122)(84,123,216,142)(85,112,165,169)(86,170,166,99)(87,100,167,171)(88,172,168,101)(89,102,155,173)(90,174,156,103)(91,104,157,175)(92,176,158,105)(93,106,159,177)(94,178,160,107)(95,108,161,179)(96,180,162,109)(97,110,163,181)(98,182,164,111), (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), (1,174,19,163)(2,180,20,155)(3,172,21,161)(4,178,15,167)(5,170,16,159)(6,176,17,165)(7,182,18,157)(8,93,26,99)(9,85,27,105)(10,91,28,111)(11,97,22,103)(12,89,23,109)(13,95,24,101)(14,87,25,107)(29,147,185,154)(30,81,186,220)(31,145,187,152)(32,79,188,218)(33,143,189,150)(34,77,190,216)(35,141,191,148)(36,75,192,214)(37,153,193,146)(38,73,194,212)(39,151,195,144)(40,71,196,224)(41,149,183,142)(42,83,184,222)(43,117,62,124)(44,84,63,223)(45,115,64,122)(46,82,65,221)(47,113,66,120)(48,80,67,219)(49,125,68,118)(50,78,69,217)(51,123,70,116)(52,76,57,215)(53,121,58,114)(54,74,59,213)(55,119,60,126)(56,72,61,211)(86,206,106,139)(88,204,108,137)(90,202,110,135)(92,200,112,133)(94,198,100,131)(96,210,102,129)(98,208,104,127)(128,156,209,181)(130,168,197,179)(132,166,199,177)(134,164,201,175)(136,162,203,173)(138,160,205,171)(140,158,207,169)>;
G:=Group( (1,217,19,78)(2,211,20,72)(3,219,21,80)(4,213,15,74)(5,221,16,82)(6,215,17,76)(7,223,18,84)(8,214,26,75)(9,222,27,83)(10,216,28,77)(11,224,22,71)(12,218,23,79)(13,212,24,73)(14,220,25,81)(29,177,185,166)(30,87,186,107)(31,179,187,168)(32,89,188,109)(33,181,189,156)(34,91,190,111)(35,169,191,158)(36,93,192,99)(37,171,193,160)(38,95,194,101)(39,173,195,162)(40,97,196,103)(41,175,183,164)(42,85,184,105)(43,90,62,110)(44,182,63,157)(45,92,64,112)(46,170,65,159)(47,94,66,100)(48,172,67,161)(49,96,68,102)(50,174,69,163)(51,98,70,104)(52,176,57,165)(53,86,58,106)(54,178,59,167)(55,88,60,108)(56,180,61,155)(113,131,120,198)(114,206,121,139)(115,133,122,200)(116,208,123,127)(117,135,124,202)(118,210,125,129)(119,137,126,204)(128,143,209,150)(130,145,197,152)(132,147,199,154)(134,149,201,142)(136,151,203,144)(138,153,205,146)(140,141,207,148), (1,135,22,128)(2,129,23,136)(3,137,24,130)(4,131,25,138)(5,139,26,132)(6,133,27,140)(7,127,28,134)(8,199,16,206)(9,207,17,200)(10,201,18,208)(11,209,19,202)(12,203,20,210)(13,197,21,204)(14,205,15,198)(29,36,58,65)(30,66,59,37)(31,38,60,67)(32,68,61,39)(33,40,62,69)(34,70,63,41)(35,42,64,57)(43,50,189,196)(44,183,190,51)(45,52,191,184)(46,185,192,53)(47,54,193,186)(48,187,194,55)(49,56,195,188)(71,143,217,124)(72,125,218,144)(73,145,219,126)(74,113,220,146)(75,147,221,114)(76,115,222,148)(77,149,223,116)(78,117,224,150)(79,151,211,118)(80,119,212,152)(81,153,213,120)(82,121,214,154)(83,141,215,122)(84,123,216,142)(85,112,165,169)(86,170,166,99)(87,100,167,171)(88,172,168,101)(89,102,155,173)(90,174,156,103)(91,104,157,175)(92,176,158,105)(93,106,159,177)(94,178,160,107)(95,108,161,179)(96,180,162,109)(97,110,163,181)(98,182,164,111), (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), (1,174,19,163)(2,180,20,155)(3,172,21,161)(4,178,15,167)(5,170,16,159)(6,176,17,165)(7,182,18,157)(8,93,26,99)(9,85,27,105)(10,91,28,111)(11,97,22,103)(12,89,23,109)(13,95,24,101)(14,87,25,107)(29,147,185,154)(30,81,186,220)(31,145,187,152)(32,79,188,218)(33,143,189,150)(34,77,190,216)(35,141,191,148)(36,75,192,214)(37,153,193,146)(38,73,194,212)(39,151,195,144)(40,71,196,224)(41,149,183,142)(42,83,184,222)(43,117,62,124)(44,84,63,223)(45,115,64,122)(46,82,65,221)(47,113,66,120)(48,80,67,219)(49,125,68,118)(50,78,69,217)(51,123,70,116)(52,76,57,215)(53,121,58,114)(54,74,59,213)(55,119,60,126)(56,72,61,211)(86,206,106,139)(88,204,108,137)(90,202,110,135)(92,200,112,133)(94,198,100,131)(96,210,102,129)(98,208,104,127)(128,156,209,181)(130,168,197,179)(132,166,199,177)(134,164,201,175)(136,162,203,173)(138,160,205,171)(140,158,207,169) );
G=PermutationGroup([[(1,217,19,78),(2,211,20,72),(3,219,21,80),(4,213,15,74),(5,221,16,82),(6,215,17,76),(7,223,18,84),(8,214,26,75),(9,222,27,83),(10,216,28,77),(11,224,22,71),(12,218,23,79),(13,212,24,73),(14,220,25,81),(29,177,185,166),(30,87,186,107),(31,179,187,168),(32,89,188,109),(33,181,189,156),(34,91,190,111),(35,169,191,158),(36,93,192,99),(37,171,193,160),(38,95,194,101),(39,173,195,162),(40,97,196,103),(41,175,183,164),(42,85,184,105),(43,90,62,110),(44,182,63,157),(45,92,64,112),(46,170,65,159),(47,94,66,100),(48,172,67,161),(49,96,68,102),(50,174,69,163),(51,98,70,104),(52,176,57,165),(53,86,58,106),(54,178,59,167),(55,88,60,108),(56,180,61,155),(113,131,120,198),(114,206,121,139),(115,133,122,200),(116,208,123,127),(117,135,124,202),(118,210,125,129),(119,137,126,204),(128,143,209,150),(130,145,197,152),(132,147,199,154),(134,149,201,142),(136,151,203,144),(138,153,205,146),(140,141,207,148)], [(1,135,22,128),(2,129,23,136),(3,137,24,130),(4,131,25,138),(5,139,26,132),(6,133,27,140),(7,127,28,134),(8,199,16,206),(9,207,17,200),(10,201,18,208),(11,209,19,202),(12,203,20,210),(13,197,21,204),(14,205,15,198),(29,36,58,65),(30,66,59,37),(31,38,60,67),(32,68,61,39),(33,40,62,69),(34,70,63,41),(35,42,64,57),(43,50,189,196),(44,183,190,51),(45,52,191,184),(46,185,192,53),(47,54,193,186),(48,187,194,55),(49,56,195,188),(71,143,217,124),(72,125,218,144),(73,145,219,126),(74,113,220,146),(75,147,221,114),(76,115,222,148),(77,149,223,116),(78,117,224,150),(79,151,211,118),(80,119,212,152),(81,153,213,120),(82,121,214,154),(83,141,215,122),(84,123,216,142),(85,112,165,169),(86,170,166,99),(87,100,167,171),(88,172,168,101),(89,102,155,173),(90,174,156,103),(91,104,157,175),(92,176,158,105),(93,106,159,177),(94,178,160,107),(95,108,161,179),(96,180,162,109),(97,110,163,181),(98,182,164,111)], [(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)], [(1,174,19,163),(2,180,20,155),(3,172,21,161),(4,178,15,167),(5,170,16,159),(6,176,17,165),(7,182,18,157),(8,93,26,99),(9,85,27,105),(10,91,28,111),(11,97,22,103),(12,89,23,109),(13,95,24,101),(14,87,25,107),(29,147,185,154),(30,81,186,220),(31,145,187,152),(32,79,188,218),(33,143,189,150),(34,77,190,216),(35,141,191,148),(36,75,192,214),(37,153,193,146),(38,73,194,212),(39,151,195,144),(40,71,196,224),(41,149,183,142),(42,83,184,222),(43,117,62,124),(44,84,63,223),(45,115,64,122),(46,82,65,221),(47,113,66,120),(48,80,67,219),(49,125,68,118),(50,78,69,217),(51,123,70,116),(52,76,57,215),(53,121,58,114),(54,74,59,213),(55,119,60,126),(56,72,61,211),(86,206,106,139),(88,204,108,137),(90,202,110,135),(92,200,112,133),(94,198,100,131),(96,210,102,129),(98,208,104,127),(128,156,209,181),(130,168,197,179),(132,166,199,177),(134,164,201,175),(136,162,203,173),(138,160,205,171),(140,158,207,169)]])
58 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 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 | 8 | 2 | 2 | 4 | 4 | 8 | 56 | 56 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
58 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | - | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | C7⋊D4 | C8⋊C22 | C8.C22 | D4⋊2D7 | D4⋊D14 | D4.9D14 |
| kernel | C42.62D14 | C42.D7 | D4⋊Dic7 | Q8⋊Dic7 | C28⋊2Q8 | C7×C4.4D4 | C2×C28 | C4.4D4 | C28 | C42 | C2×D4 | C2×Q8 | C2×C4 | C14 | C14 | C4 | C2 | C2 |
| # reps | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 3 | 4 | 3 | 3 | 3 | 12 | 1 | 1 | 6 | 6 | 6 |
Matrix representation of C42.62D14 ►in GL6(𝔽113)
| 112 | 35 | 0 | 0 | 0 | 0 |
| 29 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 30 | 75 | 98 | 92 |
| 0 | 0 | 104 | 83 | 38 | 91 |
| 0 | 0 | 22 | 92 | 55 | 38 |
| 0 | 0 | 38 | 15 | 75 | 58 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 27 | 93 |
| 0 | 0 | 0 | 112 | 12 | 58 |
| 0 | 0 | 58 | 20 | 1 | 0 |
| 0 | 0 | 101 | 27 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 84 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 93 | 33 | 0 | 0 |
| 0 | 0 | 100 | 44 | 0 | 0 |
| 0 | 0 | 64 | 31 | 80 | 80 |
| 0 | 0 | 111 | 112 | 33 | 9 |
| 15 | 40 | 0 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 107 | 90 |
| 0 | 0 | 0 | 0 | 88 | 17 |
| 0 | 0 | 17 | 23 | 0 | 0 |
| 0 | 0 | 25 | 107 | 0 | 0 |
G:=sub<GL(6,GF(113))| [112,29,0,0,0,0,35,1,0,0,0,0,0,0,30,104,22,38,0,0,75,83,92,15,0,0,98,38,55,75,0,0,92,91,38,58],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,112,0,58,101,0,0,0,112,20,27,0,0,27,12,1,0,0,0,93,58,0,1],[1,84,0,0,0,0,0,112,0,0,0,0,0,0,93,100,64,111,0,0,33,44,31,112,0,0,0,0,80,33,0,0,0,0,80,9],[15,0,0,0,0,0,40,98,0,0,0,0,0,0,0,0,17,25,0,0,0,0,23,107,0,0,107,88,0,0,0,0,90,17,0,0] >;
C42.62D14 in GAP, Magma, Sage, TeX
C_4^2._{62}D_{14} % in TeX
G:=Group("C4^2.62D14"); // GroupNames label
G:=SmallGroup(448,589);
// by ID
G=gap.SmallGroup(448,589);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,477,64,590,471,438,102,18822]);
// 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*b^2,d*a*d^-1=a^-1,c*b*c^-1=d*b*d^-1=b^-1,d*c*d^-1=a^2*b*c^-1>;
// generators/relations