metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.47D14, C7⋊C8⋊28D4, C7⋊5(C8⋊9D4), (C4×D4).5D7, (D4×C28).6C2, C28⋊C8⋊21C2, C4.215(D4×D7), C14.91(C4×D4), C4⋊C4.7Dic7, C2.8(D4×Dic7), (D4×C14).15C4, C28.374(C2×D4), (C2×C14)⋊3M4(2), (C2×D4).5Dic7, C14.39(C8○D4), (C4×C28).82C22, C42.D7⋊4C2, C22⋊C4.4Dic7, C28.307(C4○D4), C28.55D4⋊25C2, (C2×C28).849C23, (C22×C4).310D14, C14.40(C2×M4(2)), C2.6(Q8.Dic7), C22⋊1(C4.Dic7), C4.134(D4⋊2D7), C23.17(C2×Dic7), (C22×C28).99C22, C22.45(C22×Dic7), (C7×C4⋊C4).11C4, (C22×C7⋊C8)⋊19C2, (C7×C22⋊C4).5C4, (C2×C4.Dic7)⋊4C2, (C2×C28).163(C2×C4), C2.8(C2×C4.Dic7), (C2×C7⋊C8).200C22, (C2×C4).34(C2×Dic7), (C22×C14).60(C2×C4), (C2×C4).791(C22×D7), (C2×C14).186(C22×C4), SmallGroup(448,545)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.47D14
G = < a,b,c,d | a4=b4=c14=1, d2=b, ab=ba, cac-1=a-1, dad-1=a-1b2, bc=cb, bd=db, dcd-1=c-1 >
Subgroups: 340 in 124 conjugacy classes, 61 normal (55 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, D4, C23, C14, C14, C42, C22⋊C4, C4⋊C4, C2×C8, M4(2), C22×C4, C2×D4, C28, C28, C2×C14, C2×C14, C2×C14, C8⋊C4, C22⋊C8, C4⋊C8, C4×D4, C22×C8, C2×M4(2), C7⋊C8, C7⋊C8, C2×C28, C2×C28, C7×D4, C22×C14, C8⋊9D4, C2×C7⋊C8, C2×C7⋊C8, C4.Dic7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C22×C28, D4×C14, C42.D7, C28⋊C8, C28.55D4, C22×C7⋊C8, C2×C4.Dic7, D4×C28, C42.47D14
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, M4(2), C22×C4, C2×D4, C4○D4, Dic7, D14, C4×D4, C2×M4(2), C8○D4, C2×Dic7, C22×D7, C8⋊9D4, C4.Dic7, D4×D7, D4⋊2D7, C22×Dic7, C2×C4.Dic7, D4×Dic7, Q8.Dic7, C42.47D14
►On 224 points
Generators in S224
(1 190 72 183)(2 184 73 191)(3 192 74 185)(4 186 75 193)(5 194 76 187)(6 188 77 195)(7 196 71 189)(8 157 22 164)(9 165 23 158)(10 159 24 166)(11 167 25 160)(12 161 26 168)(13 155 27 162)(14 163 28 156)(15 152 57 145)(16 146 58 153)(17 154 59 147)(18 148 60 141)(19 142 61 149)(20 150 62 143)(21 144 63 151)(29 124 43 117)(30 118 44 125)(31 126 45 119)(32 120 46 113)(33 114 47 121)(34 122 48 115)(35 116 49 123)(36 215 50 222)(37 223 51 216)(38 217 52 224)(39 211 53 218)(40 219 54 212)(41 213 55 220)(42 221 56 214)(64 173 112 180)(65 181 106 174)(66 175 107 182)(67 169 108 176)(68 177 109 170)(69 171 110 178)(70 179 111 172)(78 200 88 207)(79 208 89 201)(80 202 90 209)(81 210 91 203)(82 204 85 197)(83 198 86 205)(84 206 87 199)(92 129 101 136)(93 137 102 130)(94 131 103 138)(95 139 104 132)(96 133 105 140)(97 127 99 134)(98 135 100 128)
(1 105 108 78)(2 99 109 79)(3 100 110 80)(4 101 111 81)(5 102 112 82)(6 103 106 83)(7 104 107 84)(8 29 57 36)(9 30 58 37)(10 31 59 38)(11 32 60 39)(12 33 61 40)(13 34 62 41)(14 35 63 42)(15 50 22 43)(16 51 23 44)(17 52 24 45)(18 53 25 46)(19 54 26 47)(20 55 27 48)(21 56 28 49)(64 85 76 93)(65 86 77 94)(66 87 71 95)(67 88 72 96)(68 89 73 97)(69 90 74 98)(70 91 75 92)(113 148 218 160)(114 149 219 161)(115 150 220 162)(116 151 221 163)(117 152 222 164)(118 153 223 165)(119 154 224 166)(120 141 211 167)(121 142 212 168)(122 143 213 155)(123 144 214 156)(124 145 215 157)(125 146 216 158)(126 147 217 159)(127 177 201 191)(128 178 202 192)(129 179 203 193)(130 180 204 194)(131 181 205 195)(132 182 206 196)(133 169 207 183)(134 170 208 184)(135 171 209 185)(136 172 210 186)(137 173 197 187)(138 174 198 188)(139 175 199 189)(140 176 200 190)
(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 62 105 41 108 13 78 34)(2 61 99 40 109 12 79 33)(3 60 100 39 110 11 80 32)(4 59 101 38 111 10 81 31)(5 58 102 37 112 9 82 30)(6 57 103 36 106 8 83 29)(7 63 104 42 107 14 84 35)(15 94 50 65 22 86 43 77)(16 93 51 64 23 85 44 76)(17 92 52 70 24 91 45 75)(18 98 53 69 25 90 46 74)(19 97 54 68 26 89 47 73)(20 96 55 67 27 88 48 72)(21 95 56 66 28 87 49 71)(113 178 148 202 218 192 160 128)(114 177 149 201 219 191 161 127)(115 176 150 200 220 190 162 140)(116 175 151 199 221 189 163 139)(117 174 152 198 222 188 164 138)(118 173 153 197 223 187 165 137)(119 172 154 210 224 186 166 136)(120 171 141 209 211 185 167 135)(121 170 142 208 212 184 168 134)(122 169 143 207 213 183 155 133)(123 182 144 206 214 196 156 132)(124 181 145 205 215 195 157 131)(125 180 146 204 216 194 158 130)(126 179 147 203 217 193 159 129)
G:=sub<Sym(224)| (1,190,72,183)(2,184,73,191)(3,192,74,185)(4,186,75,193)(5,194,76,187)(6,188,77,195)(7,196,71,189)(8,157,22,164)(9,165,23,158)(10,159,24,166)(11,167,25,160)(12,161,26,168)(13,155,27,162)(14,163,28,156)(15,152,57,145)(16,146,58,153)(17,154,59,147)(18,148,60,141)(19,142,61,149)(20,150,62,143)(21,144,63,151)(29,124,43,117)(30,118,44,125)(31,126,45,119)(32,120,46,113)(33,114,47,121)(34,122,48,115)(35,116,49,123)(36,215,50,222)(37,223,51,216)(38,217,52,224)(39,211,53,218)(40,219,54,212)(41,213,55,220)(42,221,56,214)(64,173,112,180)(65,181,106,174)(66,175,107,182)(67,169,108,176)(68,177,109,170)(69,171,110,178)(70,179,111,172)(78,200,88,207)(79,208,89,201)(80,202,90,209)(81,210,91,203)(82,204,85,197)(83,198,86,205)(84,206,87,199)(92,129,101,136)(93,137,102,130)(94,131,103,138)(95,139,104,132)(96,133,105,140)(97,127,99,134)(98,135,100,128), (1,105,108,78)(2,99,109,79)(3,100,110,80)(4,101,111,81)(5,102,112,82)(6,103,106,83)(7,104,107,84)(8,29,57,36)(9,30,58,37)(10,31,59,38)(11,32,60,39)(12,33,61,40)(13,34,62,41)(14,35,63,42)(15,50,22,43)(16,51,23,44)(17,52,24,45)(18,53,25,46)(19,54,26,47)(20,55,27,48)(21,56,28,49)(64,85,76,93)(65,86,77,94)(66,87,71,95)(67,88,72,96)(68,89,73,97)(69,90,74,98)(70,91,75,92)(113,148,218,160)(114,149,219,161)(115,150,220,162)(116,151,221,163)(117,152,222,164)(118,153,223,165)(119,154,224,166)(120,141,211,167)(121,142,212,168)(122,143,213,155)(123,144,214,156)(124,145,215,157)(125,146,216,158)(126,147,217,159)(127,177,201,191)(128,178,202,192)(129,179,203,193)(130,180,204,194)(131,181,205,195)(132,182,206,196)(133,169,207,183)(134,170,208,184)(135,171,209,185)(136,172,210,186)(137,173,197,187)(138,174,198,188)(139,175,199,189)(140,176,200,190), (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), (1,62,105,41,108,13,78,34)(2,61,99,40,109,12,79,33)(3,60,100,39,110,11,80,32)(4,59,101,38,111,10,81,31)(5,58,102,37,112,9,82,30)(6,57,103,36,106,8,83,29)(7,63,104,42,107,14,84,35)(15,94,50,65,22,86,43,77)(16,93,51,64,23,85,44,76)(17,92,52,70,24,91,45,75)(18,98,53,69,25,90,46,74)(19,97,54,68,26,89,47,73)(20,96,55,67,27,88,48,72)(21,95,56,66,28,87,49,71)(113,178,148,202,218,192,160,128)(114,177,149,201,219,191,161,127)(115,176,150,200,220,190,162,140)(116,175,151,199,221,189,163,139)(117,174,152,198,222,188,164,138)(118,173,153,197,223,187,165,137)(119,172,154,210,224,186,166,136)(120,171,141,209,211,185,167,135)(121,170,142,208,212,184,168,134)(122,169,143,207,213,183,155,133)(123,182,144,206,214,196,156,132)(124,181,145,205,215,195,157,131)(125,180,146,204,216,194,158,130)(126,179,147,203,217,193,159,129)>;
G:=Group( (1,190,72,183)(2,184,73,191)(3,192,74,185)(4,186,75,193)(5,194,76,187)(6,188,77,195)(7,196,71,189)(8,157,22,164)(9,165,23,158)(10,159,24,166)(11,167,25,160)(12,161,26,168)(13,155,27,162)(14,163,28,156)(15,152,57,145)(16,146,58,153)(17,154,59,147)(18,148,60,141)(19,142,61,149)(20,150,62,143)(21,144,63,151)(29,124,43,117)(30,118,44,125)(31,126,45,119)(32,120,46,113)(33,114,47,121)(34,122,48,115)(35,116,49,123)(36,215,50,222)(37,223,51,216)(38,217,52,224)(39,211,53,218)(40,219,54,212)(41,213,55,220)(42,221,56,214)(64,173,112,180)(65,181,106,174)(66,175,107,182)(67,169,108,176)(68,177,109,170)(69,171,110,178)(70,179,111,172)(78,200,88,207)(79,208,89,201)(80,202,90,209)(81,210,91,203)(82,204,85,197)(83,198,86,205)(84,206,87,199)(92,129,101,136)(93,137,102,130)(94,131,103,138)(95,139,104,132)(96,133,105,140)(97,127,99,134)(98,135,100,128), (1,105,108,78)(2,99,109,79)(3,100,110,80)(4,101,111,81)(5,102,112,82)(6,103,106,83)(7,104,107,84)(8,29,57,36)(9,30,58,37)(10,31,59,38)(11,32,60,39)(12,33,61,40)(13,34,62,41)(14,35,63,42)(15,50,22,43)(16,51,23,44)(17,52,24,45)(18,53,25,46)(19,54,26,47)(20,55,27,48)(21,56,28,49)(64,85,76,93)(65,86,77,94)(66,87,71,95)(67,88,72,96)(68,89,73,97)(69,90,74,98)(70,91,75,92)(113,148,218,160)(114,149,219,161)(115,150,220,162)(116,151,221,163)(117,152,222,164)(118,153,223,165)(119,154,224,166)(120,141,211,167)(121,142,212,168)(122,143,213,155)(123,144,214,156)(124,145,215,157)(125,146,216,158)(126,147,217,159)(127,177,201,191)(128,178,202,192)(129,179,203,193)(130,180,204,194)(131,181,205,195)(132,182,206,196)(133,169,207,183)(134,170,208,184)(135,171,209,185)(136,172,210,186)(137,173,197,187)(138,174,198,188)(139,175,199,189)(140,176,200,190), (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), (1,62,105,41,108,13,78,34)(2,61,99,40,109,12,79,33)(3,60,100,39,110,11,80,32)(4,59,101,38,111,10,81,31)(5,58,102,37,112,9,82,30)(6,57,103,36,106,8,83,29)(7,63,104,42,107,14,84,35)(15,94,50,65,22,86,43,77)(16,93,51,64,23,85,44,76)(17,92,52,70,24,91,45,75)(18,98,53,69,25,90,46,74)(19,97,54,68,26,89,47,73)(20,96,55,67,27,88,48,72)(21,95,56,66,28,87,49,71)(113,178,148,202,218,192,160,128)(114,177,149,201,219,191,161,127)(115,176,150,200,220,190,162,140)(116,175,151,199,221,189,163,139)(117,174,152,198,222,188,164,138)(118,173,153,197,223,187,165,137)(119,172,154,210,224,186,166,136)(120,171,141,209,211,185,167,135)(121,170,142,208,212,184,168,134)(122,169,143,207,213,183,155,133)(123,182,144,206,214,196,156,132)(124,181,145,205,215,195,157,131)(125,180,146,204,216,194,158,130)(126,179,147,203,217,193,159,129) );
G=PermutationGroup([[(1,190,72,183),(2,184,73,191),(3,192,74,185),(4,186,75,193),(5,194,76,187),(6,188,77,195),(7,196,71,189),(8,157,22,164),(9,165,23,158),(10,159,24,166),(11,167,25,160),(12,161,26,168),(13,155,27,162),(14,163,28,156),(15,152,57,145),(16,146,58,153),(17,154,59,147),(18,148,60,141),(19,142,61,149),(20,150,62,143),(21,144,63,151),(29,124,43,117),(30,118,44,125),(31,126,45,119),(32,120,46,113),(33,114,47,121),(34,122,48,115),(35,116,49,123),(36,215,50,222),(37,223,51,216),(38,217,52,224),(39,211,53,218),(40,219,54,212),(41,213,55,220),(42,221,56,214),(64,173,112,180),(65,181,106,174),(66,175,107,182),(67,169,108,176),(68,177,109,170),(69,171,110,178),(70,179,111,172),(78,200,88,207),(79,208,89,201),(80,202,90,209),(81,210,91,203),(82,204,85,197),(83,198,86,205),(84,206,87,199),(92,129,101,136),(93,137,102,130),(94,131,103,138),(95,139,104,132),(96,133,105,140),(97,127,99,134),(98,135,100,128)], [(1,105,108,78),(2,99,109,79),(3,100,110,80),(4,101,111,81),(5,102,112,82),(6,103,106,83),(7,104,107,84),(8,29,57,36),(9,30,58,37),(10,31,59,38),(11,32,60,39),(12,33,61,40),(13,34,62,41),(14,35,63,42),(15,50,22,43),(16,51,23,44),(17,52,24,45),(18,53,25,46),(19,54,26,47),(20,55,27,48),(21,56,28,49),(64,85,76,93),(65,86,77,94),(66,87,71,95),(67,88,72,96),(68,89,73,97),(69,90,74,98),(70,91,75,92),(113,148,218,160),(114,149,219,161),(115,150,220,162),(116,151,221,163),(117,152,222,164),(118,153,223,165),(119,154,224,166),(120,141,211,167),(121,142,212,168),(122,143,213,155),(123,144,214,156),(124,145,215,157),(125,146,216,158),(126,147,217,159),(127,177,201,191),(128,178,202,192),(129,179,203,193),(130,180,204,194),(131,181,205,195),(132,182,206,196),(133,169,207,183),(134,170,208,184),(135,171,209,185),(136,172,210,186),(137,173,197,187),(138,174,198,188),(139,175,199,189),(140,176,200,190)], [(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)], [(1,62,105,41,108,13,78,34),(2,61,99,40,109,12,79,33),(3,60,100,39,110,11,80,32),(4,59,101,38,111,10,81,31),(5,58,102,37,112,9,82,30),(6,57,103,36,106,8,83,29),(7,63,104,42,107,14,84,35),(15,94,50,65,22,86,43,77),(16,93,51,64,23,85,44,76),(17,92,52,70,24,91,45,75),(18,98,53,69,25,90,46,74),(19,97,54,68,26,89,47,73),(20,96,55,67,27,88,48,72),(21,95,56,66,28,87,49,71),(113,178,148,202,218,192,160,128),(114,177,149,201,219,191,161,127),(115,176,150,200,220,190,162,140),(116,175,151,199,221,189,163,139),(117,174,152,198,222,188,164,138),(118,173,153,197,223,187,165,137),(119,172,154,210,224,186,166,136),(120,171,141,209,211,185,167,135),(121,170,142,208,212,184,168,134),(122,169,143,207,213,183,155,133),(123,182,144,206,214,196,156,132),(124,181,145,205,215,195,157,131),(125,180,146,204,216,194,158,130),(126,179,147,203,217,193,159,129)]])
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 7A | 7B | 7C | 8A | ··· | 8H | 8I | 8J | 8K | 8L | 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 | 7 | 7 | 7 | 8 | ··· | 8 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 4 | 2 | 2 | 2 | 14 | ··· | 14 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | - | + | - | + | - | ||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | C4 | C4 | D4 | D7 | C4○D4 | M4(2) | D14 | Dic7 | Dic7 | D14 | Dic7 | C8○D4 | C4.Dic7 | D4×D7 | D4⋊2D7 | Q8.Dic7 |
| kernel | C42.47D14 | C42.D7 | C28⋊C8 | C28.55D4 | C22×C7⋊C8 | C2×C4.Dic7 | D4×C28 | C7×C22⋊C4 | C7×C4⋊C4 | D4×C14 | C7⋊C8 | C4×D4 | C28 | C2×C14 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C14 | C22 | C4 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 4 | 2 | 2 | 2 | 3 | 2 | 4 | 3 | 6 | 3 | 6 | 3 | 4 | 24 | 3 | 3 | 6 |
Matrix representation of C42.47D14 ►in GL4(𝔽113) generated by
| 86 | 5 | 0 | 0 |
| 103 | 27 | 0 | 0 |
| 0 | 0 | 112 | 32 |
| 0 | 0 | 7 | 1 |
| 98 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 105 | 33 | 0 | 0 |
| 47 | 32 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 106 | 112 |
| 38 | 10 | 0 | 0 |
| 1 | 75 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 7 | 1 |
G:=sub<GL(4,GF(113))| [86,103,0,0,5,27,0,0,0,0,112,7,0,0,32,1],[98,0,0,0,0,98,0,0,0,0,1,0,0,0,0,1],[105,47,0,0,33,32,0,0,0,0,1,106,0,0,0,112],[38,1,0,0,10,75,0,0,0,0,112,7,0,0,0,1] >;
C42.47D14 in GAP, Magma, Sage, TeX
C_4^2._{47}D_{14} % in TeX
G:=Group("C4^2.47D14"); // GroupNames label
G:=SmallGroup(448,545);
// by ID
G=gap.SmallGroup(448,545);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,56,758,219,136,18822]);
// 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=a^-1,d*a*d^-1=a^-1*b^2,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations