metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.20D14, C8⋊C4⋊11D7, C28⋊2Q8⋊3C2, (C2×C28).38D4, (C2×C4).27D28, (C2×C8).160D14, (C4×C28).5C22, C2.9(C8⋊D14), C14.6(C8⋊C22), C4.D28.2C2, (C2×D28).8C22, C22.99(C2×D28), C2.D56.16C2, C4.109(C4○D28), C28.225(C4○D4), C28.44D4⋊38C2, (C2×C56).314C22, (C2×C28).735C23, C14.9(C4.4D4), C2.8(C8.D14), C14.4(C8.C22), C4⋊Dic7.10C22, C2.14(C4.D28), (C2×Dic14).8C22, C7⋊1(C42.28C22), (C7×C8⋊C4)⋊20C2, (C2×C14).118(C2×D4), (C2×C4).679(C22×D7), SmallGroup(448,248)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.20D14
G = < a,b,c,d | a4=b4=1, c14=a2b, d2=a2, ab=ba, cac-1=ab2, dad-1=a-1, bc=cb, dbd-1=b-1, dcd-1=b-1c13 >
Subgroups: 644 in 100 conjugacy classes, 39 normal (25 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C22⋊C4, C4⋊C4, C2×C8, C2×D4, C2×Q8, Dic7, C28, C28, D14, C2×C14, C8⋊C4, D4⋊C4, Q8⋊C4, C4.4D4, C4⋊Q8, C56, Dic14, D28, C2×Dic7, C2×C28, C22×D7, C42.28C22, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C4×C28, C2×C56, C2×Dic14, C2×Dic14, C2×D28, C28.44D4, C2.D56, C7×C8⋊C4, C28⋊2Q8, C4.D28, C42.20D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4.4D4, C8⋊C22, C8.C22, D28, C22×D7, C42.28C22, C2×D28, C4○D28, C4.D28, C8⋊D14, C8.D14, C42.20D14
►On 224 points
Generators in S224
(1 172 66 119)(2 201 67 148)(3 174 68 121)(4 203 69 150)(5 176 70 123)(6 205 71 152)(7 178 72 125)(8 207 73 154)(9 180 74 127)(10 209 75 156)(11 182 76 129)(12 211 77 158)(13 184 78 131)(14 213 79 160)(15 186 80 133)(16 215 81 162)(17 188 82 135)(18 217 83 164)(19 190 84 137)(20 219 85 166)(21 192 86 139)(22 221 87 168)(23 194 88 141)(24 223 89 114)(25 196 90 143)(26 169 91 116)(27 198 92 145)(28 171 93 118)(29 200 94 147)(30 173 95 120)(31 202 96 149)(32 175 97 122)(33 204 98 151)(34 177 99 124)(35 206 100 153)(36 179 101 126)(37 208 102 155)(38 181 103 128)(39 210 104 157)(40 183 105 130)(41 212 106 159)(42 185 107 132)(43 214 108 161)(44 187 109 134)(45 216 110 163)(46 189 111 136)(47 218 112 165)(48 191 57 138)(49 220 58 167)(50 193 59 140)(51 222 60 113)(52 195 61 142)(53 224 62 115)(54 197 63 144)(55 170 64 117)(56 199 65 146)
(1 80 29 108)(2 81 30 109)(3 82 31 110)(4 83 32 111)(5 84 33 112)(6 85 34 57)(7 86 35 58)(8 87 36 59)(9 88 37 60)(10 89 38 61)(11 90 39 62)(12 91 40 63)(13 92 41 64)(14 93 42 65)(15 94 43 66)(16 95 44 67)(17 96 45 68)(18 97 46 69)(19 98 47 70)(20 99 48 71)(21 100 49 72)(22 101 50 73)(23 102 51 74)(24 103 52 75)(25 104 53 76)(26 105 54 77)(27 106 55 78)(28 107 56 79)(113 180 141 208)(114 181 142 209)(115 182 143 210)(116 183 144 211)(117 184 145 212)(118 185 146 213)(119 186 147 214)(120 187 148 215)(121 188 149 216)(122 189 150 217)(123 190 151 218)(124 191 152 219)(125 192 153 220)(126 193 154 221)(127 194 155 222)(128 195 156 223)(129 196 157 224)(130 197 158 169)(131 198 159 170)(132 199 160 171)(133 200 161 172)(134 201 162 173)(135 202 163 174)(136 203 164 175)(137 204 165 176)(138 205 166 177)(139 206 167 178)(140 207 168 179)
(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 42 66 107)(2 106 67 41)(3 40 68 105)(4 104 69 39)(5 38 70 103)(6 102 71 37)(7 36 72 101)(8 100 73 35)(9 34 74 99)(10 98 75 33)(11 32 76 97)(12 96 77 31)(13 30 78 95)(14 94 79 29)(15 28 80 93)(16 92 81 27)(17 26 82 91)(18 90 83 25)(19 24 84 89)(20 88 85 23)(21 22 86 87)(43 56 108 65)(44 64 109 55)(45 54 110 63)(46 62 111 53)(47 52 112 61)(48 60 57 51)(49 50 58 59)(113 191 222 138)(114 137 223 190)(115 189 224 136)(116 135 169 188)(117 187 170 134)(118 133 171 186)(119 185 172 132)(120 131 173 184)(121 183 174 130)(122 129 175 182)(123 181 176 128)(124 127 177 180)(125 179 178 126)(139 221 192 168)(140 167 193 220)(141 219 194 166)(142 165 195 218)(143 217 196 164)(144 163 197 216)(145 215 198 162)(146 161 199 214)(147 213 200 160)(148 159 201 212)(149 211 202 158)(150 157 203 210)(151 209 204 156)(152 155 205 208)(153 207 206 154)
G:=sub<Sym(224)| (1,172,66,119)(2,201,67,148)(3,174,68,121)(4,203,69,150)(5,176,70,123)(6,205,71,152)(7,178,72,125)(8,207,73,154)(9,180,74,127)(10,209,75,156)(11,182,76,129)(12,211,77,158)(13,184,78,131)(14,213,79,160)(15,186,80,133)(16,215,81,162)(17,188,82,135)(18,217,83,164)(19,190,84,137)(20,219,85,166)(21,192,86,139)(22,221,87,168)(23,194,88,141)(24,223,89,114)(25,196,90,143)(26,169,91,116)(27,198,92,145)(28,171,93,118)(29,200,94,147)(30,173,95,120)(31,202,96,149)(32,175,97,122)(33,204,98,151)(34,177,99,124)(35,206,100,153)(36,179,101,126)(37,208,102,155)(38,181,103,128)(39,210,104,157)(40,183,105,130)(41,212,106,159)(42,185,107,132)(43,214,108,161)(44,187,109,134)(45,216,110,163)(46,189,111,136)(47,218,112,165)(48,191,57,138)(49,220,58,167)(50,193,59,140)(51,222,60,113)(52,195,61,142)(53,224,62,115)(54,197,63,144)(55,170,64,117)(56,199,65,146), (1,80,29,108)(2,81,30,109)(3,82,31,110)(4,83,32,111)(5,84,33,112)(6,85,34,57)(7,86,35,58)(8,87,36,59)(9,88,37,60)(10,89,38,61)(11,90,39,62)(12,91,40,63)(13,92,41,64)(14,93,42,65)(15,94,43,66)(16,95,44,67)(17,96,45,68)(18,97,46,69)(19,98,47,70)(20,99,48,71)(21,100,49,72)(22,101,50,73)(23,102,51,74)(24,103,52,75)(25,104,53,76)(26,105,54,77)(27,106,55,78)(28,107,56,79)(113,180,141,208)(114,181,142,209)(115,182,143,210)(116,183,144,211)(117,184,145,212)(118,185,146,213)(119,186,147,214)(120,187,148,215)(121,188,149,216)(122,189,150,217)(123,190,151,218)(124,191,152,219)(125,192,153,220)(126,193,154,221)(127,194,155,222)(128,195,156,223)(129,196,157,224)(130,197,158,169)(131,198,159,170)(132,199,160,171)(133,200,161,172)(134,201,162,173)(135,202,163,174)(136,203,164,175)(137,204,165,176)(138,205,166,177)(139,206,167,178)(140,207,168,179), (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), (1,42,66,107)(2,106,67,41)(3,40,68,105)(4,104,69,39)(5,38,70,103)(6,102,71,37)(7,36,72,101)(8,100,73,35)(9,34,74,99)(10,98,75,33)(11,32,76,97)(12,96,77,31)(13,30,78,95)(14,94,79,29)(15,28,80,93)(16,92,81,27)(17,26,82,91)(18,90,83,25)(19,24,84,89)(20,88,85,23)(21,22,86,87)(43,56,108,65)(44,64,109,55)(45,54,110,63)(46,62,111,53)(47,52,112,61)(48,60,57,51)(49,50,58,59)(113,191,222,138)(114,137,223,190)(115,189,224,136)(116,135,169,188)(117,187,170,134)(118,133,171,186)(119,185,172,132)(120,131,173,184)(121,183,174,130)(122,129,175,182)(123,181,176,128)(124,127,177,180)(125,179,178,126)(139,221,192,168)(140,167,193,220)(141,219,194,166)(142,165,195,218)(143,217,196,164)(144,163,197,216)(145,215,198,162)(146,161,199,214)(147,213,200,160)(148,159,201,212)(149,211,202,158)(150,157,203,210)(151,209,204,156)(152,155,205,208)(153,207,206,154)>;
G:=Group( (1,172,66,119)(2,201,67,148)(3,174,68,121)(4,203,69,150)(5,176,70,123)(6,205,71,152)(7,178,72,125)(8,207,73,154)(9,180,74,127)(10,209,75,156)(11,182,76,129)(12,211,77,158)(13,184,78,131)(14,213,79,160)(15,186,80,133)(16,215,81,162)(17,188,82,135)(18,217,83,164)(19,190,84,137)(20,219,85,166)(21,192,86,139)(22,221,87,168)(23,194,88,141)(24,223,89,114)(25,196,90,143)(26,169,91,116)(27,198,92,145)(28,171,93,118)(29,200,94,147)(30,173,95,120)(31,202,96,149)(32,175,97,122)(33,204,98,151)(34,177,99,124)(35,206,100,153)(36,179,101,126)(37,208,102,155)(38,181,103,128)(39,210,104,157)(40,183,105,130)(41,212,106,159)(42,185,107,132)(43,214,108,161)(44,187,109,134)(45,216,110,163)(46,189,111,136)(47,218,112,165)(48,191,57,138)(49,220,58,167)(50,193,59,140)(51,222,60,113)(52,195,61,142)(53,224,62,115)(54,197,63,144)(55,170,64,117)(56,199,65,146), (1,80,29,108)(2,81,30,109)(3,82,31,110)(4,83,32,111)(5,84,33,112)(6,85,34,57)(7,86,35,58)(8,87,36,59)(9,88,37,60)(10,89,38,61)(11,90,39,62)(12,91,40,63)(13,92,41,64)(14,93,42,65)(15,94,43,66)(16,95,44,67)(17,96,45,68)(18,97,46,69)(19,98,47,70)(20,99,48,71)(21,100,49,72)(22,101,50,73)(23,102,51,74)(24,103,52,75)(25,104,53,76)(26,105,54,77)(27,106,55,78)(28,107,56,79)(113,180,141,208)(114,181,142,209)(115,182,143,210)(116,183,144,211)(117,184,145,212)(118,185,146,213)(119,186,147,214)(120,187,148,215)(121,188,149,216)(122,189,150,217)(123,190,151,218)(124,191,152,219)(125,192,153,220)(126,193,154,221)(127,194,155,222)(128,195,156,223)(129,196,157,224)(130,197,158,169)(131,198,159,170)(132,199,160,171)(133,200,161,172)(134,201,162,173)(135,202,163,174)(136,203,164,175)(137,204,165,176)(138,205,166,177)(139,206,167,178)(140,207,168,179), (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), (1,42,66,107)(2,106,67,41)(3,40,68,105)(4,104,69,39)(5,38,70,103)(6,102,71,37)(7,36,72,101)(8,100,73,35)(9,34,74,99)(10,98,75,33)(11,32,76,97)(12,96,77,31)(13,30,78,95)(14,94,79,29)(15,28,80,93)(16,92,81,27)(17,26,82,91)(18,90,83,25)(19,24,84,89)(20,88,85,23)(21,22,86,87)(43,56,108,65)(44,64,109,55)(45,54,110,63)(46,62,111,53)(47,52,112,61)(48,60,57,51)(49,50,58,59)(113,191,222,138)(114,137,223,190)(115,189,224,136)(116,135,169,188)(117,187,170,134)(118,133,171,186)(119,185,172,132)(120,131,173,184)(121,183,174,130)(122,129,175,182)(123,181,176,128)(124,127,177,180)(125,179,178,126)(139,221,192,168)(140,167,193,220)(141,219,194,166)(142,165,195,218)(143,217,196,164)(144,163,197,216)(145,215,198,162)(146,161,199,214)(147,213,200,160)(148,159,201,212)(149,211,202,158)(150,157,203,210)(151,209,204,156)(152,155,205,208)(153,207,206,154) );
G=PermutationGroup([[(1,172,66,119),(2,201,67,148),(3,174,68,121),(4,203,69,150),(5,176,70,123),(6,205,71,152),(7,178,72,125),(8,207,73,154),(9,180,74,127),(10,209,75,156),(11,182,76,129),(12,211,77,158),(13,184,78,131),(14,213,79,160),(15,186,80,133),(16,215,81,162),(17,188,82,135),(18,217,83,164),(19,190,84,137),(20,219,85,166),(21,192,86,139),(22,221,87,168),(23,194,88,141),(24,223,89,114),(25,196,90,143),(26,169,91,116),(27,198,92,145),(28,171,93,118),(29,200,94,147),(30,173,95,120),(31,202,96,149),(32,175,97,122),(33,204,98,151),(34,177,99,124),(35,206,100,153),(36,179,101,126),(37,208,102,155),(38,181,103,128),(39,210,104,157),(40,183,105,130),(41,212,106,159),(42,185,107,132),(43,214,108,161),(44,187,109,134),(45,216,110,163),(46,189,111,136),(47,218,112,165),(48,191,57,138),(49,220,58,167),(50,193,59,140),(51,222,60,113),(52,195,61,142),(53,224,62,115),(54,197,63,144),(55,170,64,117),(56,199,65,146)], [(1,80,29,108),(2,81,30,109),(3,82,31,110),(4,83,32,111),(5,84,33,112),(6,85,34,57),(7,86,35,58),(8,87,36,59),(9,88,37,60),(10,89,38,61),(11,90,39,62),(12,91,40,63),(13,92,41,64),(14,93,42,65),(15,94,43,66),(16,95,44,67),(17,96,45,68),(18,97,46,69),(19,98,47,70),(20,99,48,71),(21,100,49,72),(22,101,50,73),(23,102,51,74),(24,103,52,75),(25,104,53,76),(26,105,54,77),(27,106,55,78),(28,107,56,79),(113,180,141,208),(114,181,142,209),(115,182,143,210),(116,183,144,211),(117,184,145,212),(118,185,146,213),(119,186,147,214),(120,187,148,215),(121,188,149,216),(122,189,150,217),(123,190,151,218),(124,191,152,219),(125,192,153,220),(126,193,154,221),(127,194,155,222),(128,195,156,223),(129,196,157,224),(130,197,158,169),(131,198,159,170),(132,199,160,171),(133,200,161,172),(134,201,162,173),(135,202,163,174),(136,203,164,175),(137,204,165,176),(138,205,166,177),(139,206,167,178),(140,207,168,179)], [(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)], [(1,42,66,107),(2,106,67,41),(3,40,68,105),(4,104,69,39),(5,38,70,103),(6,102,71,37),(7,36,72,101),(8,100,73,35),(9,34,74,99),(10,98,75,33),(11,32,76,97),(12,96,77,31),(13,30,78,95),(14,94,79,29),(15,28,80,93),(16,92,81,27),(17,26,82,91),(18,90,83,25),(19,24,84,89),(20,88,85,23),(21,22,86,87),(43,56,108,65),(44,64,109,55),(45,54,110,63),(46,62,111,53),(47,52,112,61),(48,60,57,51),(49,50,58,59),(113,191,222,138),(114,137,223,190),(115,189,224,136),(116,135,169,188),(117,187,170,134),(118,133,171,186),(119,185,172,132),(120,131,173,184),(121,183,174,130),(122,129,175,182),(123,181,176,128),(124,127,177,180),(125,179,178,126),(139,221,192,168),(140,167,193,220),(141,219,194,166),(142,165,195,218),(143,217,196,164),(144,163,197,216),(145,215,198,162),(146,161,199,214),(147,213,200,160),(148,159,201,212),(149,211,202,158),(150,157,203,210),(151,209,204,156),(152,155,205,208),(153,207,206,154)]])
76 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28X | 56A | ··· | 56X |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 56 | 2 | 2 | 4 | 4 | 56 | 56 | 56 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
76 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D28 | C4○D28 | C8⋊C22 | C8.C22 | C8⋊D14 | C8.D14 |
| kernel | C42.20D14 | C28.44D4 | C2.D56 | C7×C8⋊C4 | C28⋊2Q8 | C4.D28 | C2×C28 | C8⋊C4 | C28 | C42 | C2×C8 | C2×C4 | C4 | C14 | C14 | C2 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 2 | 3 | 4 | 3 | 6 | 12 | 24 | 1 | 1 | 6 | 6 |
Matrix representation of C42.20D14 ►in GL6(𝔽113)
| 11 | 111 | 0 | 0 | 0 | 0 |
| 61 | 102 | 0 | 0 | 0 | 0 |
| 0 | 0 | 30 | 35 | 6 | 22 |
| 0 | 0 | 78 | 83 | 91 | 49 |
| 0 | 0 | 49 | 91 | 83 | 78 |
| 0 | 0 | 22 | 6 | 35 | 30 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 67 | 0 | 0 |
| 0 | 0 | 46 | 104 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 67 |
| 0 | 0 | 0 | 0 | 46 | 104 |
| 98 | 0 | 0 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 88 | 88 |
| 0 | 0 | 0 | 0 | 25 | 34 |
| 0 | 0 | 19 | 94 | 0 | 0 |
| 0 | 0 | 19 | 100 | 0 | 0 |
| 98 | 0 | 0 | 0 | 0 | 0 |
| 61 | 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 94 | 19 |
| 0 | 0 | 0 | 0 | 100 | 19 |
| 0 | 0 | 94 | 19 | 0 | 0 |
| 0 | 0 | 100 | 19 | 0 | 0 |
G:=sub<GL(6,GF(113))| [11,61,0,0,0,0,111,102,0,0,0,0,0,0,30,78,49,22,0,0,35,83,91,6,0,0,6,91,83,35,0,0,22,49,78,30],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,9,46,0,0,0,0,67,104,0,0,0,0,0,0,9,46,0,0,0,0,67,104],[98,0,0,0,0,0,0,98,0,0,0,0,0,0,0,0,19,19,0,0,0,0,94,100,0,0,88,25,0,0,0,0,88,34,0,0],[98,61,0,0,0,0,0,15,0,0,0,0,0,0,0,0,94,100,0,0,0,0,19,19,0,0,94,100,0,0,0,0,19,19,0,0] >;
C42.20D14 in GAP, Magma, Sage, TeX
C_4^2._{20}D_{14} % in TeX
G:=Group("C4^2.20D14"); // GroupNames label
G:=SmallGroup(448,248);
// by ID
G=gap.SmallGroup(448,248);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,344,254,387,142,1123,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=a^2*b,d^2=a^2,a*b=b*a,c*a*c^-1=a*b^2,d*a*d^-1=a^-1,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=b^-1*c^13>;
// generators/relations