metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.19D14, C8⋊C4⋊10D7, (C2×C4).26D28, (C2×C28).37D4, C28⋊4D4.3C2, (C2×C8).159D14, (C4×C28).4C22, C28.6Q8⋊2C2, C2.D56⋊38C2, C2.8(C8⋊D14), C14.5(C8⋊C22), (C2×D28).7C22, C22.98(C2×D28), C4⋊Dic7.9C22, C4.108(C4○D28), C28.224(C4○D4), (C2×C56).313C22, (C2×C28).734C23, C14.8(C4.4D4), C2.13(C4.D28), C7⋊1(C42.29C22), (C7×C8⋊C4)⋊19C2, (C2×C14).117(C2×D4), (C2×C4).678(C22×D7), SmallGroup(448,247)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.19D14
G = < a,b,c,d | a4=b4=1, c14=a2b-1, d2=a2b2, ab=ba, cac-1=ab2, dad-1=a-1b2, bc=cb, dbd-1=b-1, dcd-1=b-1c13 >
Subgroups: 836 in 110 conjugacy classes, 39 normal (15 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, D4, C23, D7, C14, C14, C42, C4⋊C4, C2×C8, C2×D4, Dic7, C28, C28, D14, C2×C14, C8⋊C4, D4⋊C4, C42.C2, C4⋊1D4, C56, D28, C2×Dic7, C2×C28, C2×C28, C22×D7, C42.29C22, Dic7⋊C4, C4⋊Dic7, C4×C28, C2×C56, C2×D28, C2×D28, C2.D56, C7×C8⋊C4, C28.6Q8, C28⋊4D4, C42.19D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4.4D4, C8⋊C22, D28, C22×D7, C42.29C22, C2×D28, C4○D28, C4.D28, C8⋊D14, C42.19D14
►On 224 points
Generators in S224
(1 179 108 125)(2 208 109 154)(3 181 110 127)(4 210 111 156)(5 183 112 129)(6 212 57 158)(7 185 58 131)(8 214 59 160)(9 187 60 133)(10 216 61 162)(11 189 62 135)(12 218 63 164)(13 191 64 137)(14 220 65 166)(15 193 66 139)(16 222 67 168)(17 195 68 141)(18 224 69 114)(19 197 70 143)(20 170 71 116)(21 199 72 145)(22 172 73 118)(23 201 74 147)(24 174 75 120)(25 203 76 149)(26 176 77 122)(27 205 78 151)(28 178 79 124)(29 207 80 153)(30 180 81 126)(31 209 82 155)(32 182 83 128)(33 211 84 157)(34 184 85 130)(35 213 86 159)(36 186 87 132)(37 215 88 161)(38 188 89 134)(39 217 90 163)(40 190 91 136)(41 219 92 165)(42 192 93 138)(43 221 94 167)(44 194 95 140)(45 223 96 113)(46 196 97 142)(47 169 98 115)(48 198 99 144)(49 171 100 117)(50 200 101 146)(51 173 102 119)(52 202 103 148)(53 175 104 121)(54 204 105 150)(55 177 106 123)(56 206 107 152)
(1 94 29 66)(2 95 30 67)(3 96 31 68)(4 97 32 69)(5 98 33 70)(6 99 34 71)(7 100 35 72)(8 101 36 73)(9 102 37 74)(10 103 38 75)(11 104 39 76)(12 105 40 77)(13 106 41 78)(14 107 42 79)(15 108 43 80)(16 109 44 81)(17 110 45 82)(18 111 46 83)(19 112 47 84)(20 57 48 85)(21 58 49 86)(22 59 50 87)(23 60 51 88)(24 61 52 89)(25 62 53 90)(26 63 54 91)(27 64 55 92)(28 65 56 93)(113 209 141 181)(114 210 142 182)(115 211 143 183)(116 212 144 184)(117 213 145 185)(118 214 146 186)(119 215 147 187)(120 216 148 188)(121 217 149 189)(122 218 150 190)(123 219 151 191)(124 220 152 192)(125 221 153 193)(126 222 154 194)(127 223 155 195)(128 224 156 196)(129 169 157 197)(130 170 158 198)(131 171 159 199)(132 172 160 200)(133 173 161 201)(134 174 162 202)(135 175 163 203)(136 176 164 204)(137 177 165 205)(138 178 166 206)(139 179 167 207)(140 180 168 208)
(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 80 65)(2 64 81 41)(3 40 82 63)(4 62 83 39)(5 38 84 61)(6 60 85 37)(7 36 86 59)(8 58 87 35)(9 34 88 57)(10 112 89 33)(11 32 90 111)(12 110 91 31)(13 30 92 109)(14 108 93 29)(15 28 94 107)(16 106 95 27)(17 26 96 105)(18 104 97 25)(19 24 98 103)(20 102 99 23)(21 22 100 101)(43 56 66 79)(44 78 67 55)(45 54 68 77)(46 76 69 53)(47 52 70 75)(48 74 71 51)(49 50 72 73)(113 176 195 150)(114 149 196 175)(115 174 197 148)(116 147 198 173)(117 172 199 146)(118 145 200 171)(119 170 201 144)(120 143 202 169)(121 224 203 142)(122 141 204 223)(123 222 205 140)(124 139 206 221)(125 220 207 138)(126 137 208 219)(127 218 209 136)(128 135 210 217)(129 216 211 134)(130 133 212 215)(131 214 213 132)(151 194 177 168)(152 167 178 193)(153 192 179 166)(154 165 180 191)(155 190 181 164)(156 163 182 189)(157 188 183 162)(158 161 184 187)(159 186 185 160)
G:=sub<Sym(224)| (1,179,108,125)(2,208,109,154)(3,181,110,127)(4,210,111,156)(5,183,112,129)(6,212,57,158)(7,185,58,131)(8,214,59,160)(9,187,60,133)(10,216,61,162)(11,189,62,135)(12,218,63,164)(13,191,64,137)(14,220,65,166)(15,193,66,139)(16,222,67,168)(17,195,68,141)(18,224,69,114)(19,197,70,143)(20,170,71,116)(21,199,72,145)(22,172,73,118)(23,201,74,147)(24,174,75,120)(25,203,76,149)(26,176,77,122)(27,205,78,151)(28,178,79,124)(29,207,80,153)(30,180,81,126)(31,209,82,155)(32,182,83,128)(33,211,84,157)(34,184,85,130)(35,213,86,159)(36,186,87,132)(37,215,88,161)(38,188,89,134)(39,217,90,163)(40,190,91,136)(41,219,92,165)(42,192,93,138)(43,221,94,167)(44,194,95,140)(45,223,96,113)(46,196,97,142)(47,169,98,115)(48,198,99,144)(49,171,100,117)(50,200,101,146)(51,173,102,119)(52,202,103,148)(53,175,104,121)(54,204,105,150)(55,177,106,123)(56,206,107,152), (1,94,29,66)(2,95,30,67)(3,96,31,68)(4,97,32,69)(5,98,33,70)(6,99,34,71)(7,100,35,72)(8,101,36,73)(9,102,37,74)(10,103,38,75)(11,104,39,76)(12,105,40,77)(13,106,41,78)(14,107,42,79)(15,108,43,80)(16,109,44,81)(17,110,45,82)(18,111,46,83)(19,112,47,84)(20,57,48,85)(21,58,49,86)(22,59,50,87)(23,60,51,88)(24,61,52,89)(25,62,53,90)(26,63,54,91)(27,64,55,92)(28,65,56,93)(113,209,141,181)(114,210,142,182)(115,211,143,183)(116,212,144,184)(117,213,145,185)(118,214,146,186)(119,215,147,187)(120,216,148,188)(121,217,149,189)(122,218,150,190)(123,219,151,191)(124,220,152,192)(125,221,153,193)(126,222,154,194)(127,223,155,195)(128,224,156,196)(129,169,157,197)(130,170,158,198)(131,171,159,199)(132,172,160,200)(133,173,161,201)(134,174,162,202)(135,175,163,203)(136,176,164,204)(137,177,165,205)(138,178,166,206)(139,179,167,207)(140,180,168,208), (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), (1,42,80,65)(2,64,81,41)(3,40,82,63)(4,62,83,39)(5,38,84,61)(6,60,85,37)(7,36,86,59)(8,58,87,35)(9,34,88,57)(10,112,89,33)(11,32,90,111)(12,110,91,31)(13,30,92,109)(14,108,93,29)(15,28,94,107)(16,106,95,27)(17,26,96,105)(18,104,97,25)(19,24,98,103)(20,102,99,23)(21,22,100,101)(43,56,66,79)(44,78,67,55)(45,54,68,77)(46,76,69,53)(47,52,70,75)(48,74,71,51)(49,50,72,73)(113,176,195,150)(114,149,196,175)(115,174,197,148)(116,147,198,173)(117,172,199,146)(118,145,200,171)(119,170,201,144)(120,143,202,169)(121,224,203,142)(122,141,204,223)(123,222,205,140)(124,139,206,221)(125,220,207,138)(126,137,208,219)(127,218,209,136)(128,135,210,217)(129,216,211,134)(130,133,212,215)(131,214,213,132)(151,194,177,168)(152,167,178,193)(153,192,179,166)(154,165,180,191)(155,190,181,164)(156,163,182,189)(157,188,183,162)(158,161,184,187)(159,186,185,160)>;
G:=Group( (1,179,108,125)(2,208,109,154)(3,181,110,127)(4,210,111,156)(5,183,112,129)(6,212,57,158)(7,185,58,131)(8,214,59,160)(9,187,60,133)(10,216,61,162)(11,189,62,135)(12,218,63,164)(13,191,64,137)(14,220,65,166)(15,193,66,139)(16,222,67,168)(17,195,68,141)(18,224,69,114)(19,197,70,143)(20,170,71,116)(21,199,72,145)(22,172,73,118)(23,201,74,147)(24,174,75,120)(25,203,76,149)(26,176,77,122)(27,205,78,151)(28,178,79,124)(29,207,80,153)(30,180,81,126)(31,209,82,155)(32,182,83,128)(33,211,84,157)(34,184,85,130)(35,213,86,159)(36,186,87,132)(37,215,88,161)(38,188,89,134)(39,217,90,163)(40,190,91,136)(41,219,92,165)(42,192,93,138)(43,221,94,167)(44,194,95,140)(45,223,96,113)(46,196,97,142)(47,169,98,115)(48,198,99,144)(49,171,100,117)(50,200,101,146)(51,173,102,119)(52,202,103,148)(53,175,104,121)(54,204,105,150)(55,177,106,123)(56,206,107,152), (1,94,29,66)(2,95,30,67)(3,96,31,68)(4,97,32,69)(5,98,33,70)(6,99,34,71)(7,100,35,72)(8,101,36,73)(9,102,37,74)(10,103,38,75)(11,104,39,76)(12,105,40,77)(13,106,41,78)(14,107,42,79)(15,108,43,80)(16,109,44,81)(17,110,45,82)(18,111,46,83)(19,112,47,84)(20,57,48,85)(21,58,49,86)(22,59,50,87)(23,60,51,88)(24,61,52,89)(25,62,53,90)(26,63,54,91)(27,64,55,92)(28,65,56,93)(113,209,141,181)(114,210,142,182)(115,211,143,183)(116,212,144,184)(117,213,145,185)(118,214,146,186)(119,215,147,187)(120,216,148,188)(121,217,149,189)(122,218,150,190)(123,219,151,191)(124,220,152,192)(125,221,153,193)(126,222,154,194)(127,223,155,195)(128,224,156,196)(129,169,157,197)(130,170,158,198)(131,171,159,199)(132,172,160,200)(133,173,161,201)(134,174,162,202)(135,175,163,203)(136,176,164,204)(137,177,165,205)(138,178,166,206)(139,179,167,207)(140,180,168,208), (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), (1,42,80,65)(2,64,81,41)(3,40,82,63)(4,62,83,39)(5,38,84,61)(6,60,85,37)(7,36,86,59)(8,58,87,35)(9,34,88,57)(10,112,89,33)(11,32,90,111)(12,110,91,31)(13,30,92,109)(14,108,93,29)(15,28,94,107)(16,106,95,27)(17,26,96,105)(18,104,97,25)(19,24,98,103)(20,102,99,23)(21,22,100,101)(43,56,66,79)(44,78,67,55)(45,54,68,77)(46,76,69,53)(47,52,70,75)(48,74,71,51)(49,50,72,73)(113,176,195,150)(114,149,196,175)(115,174,197,148)(116,147,198,173)(117,172,199,146)(118,145,200,171)(119,170,201,144)(120,143,202,169)(121,224,203,142)(122,141,204,223)(123,222,205,140)(124,139,206,221)(125,220,207,138)(126,137,208,219)(127,218,209,136)(128,135,210,217)(129,216,211,134)(130,133,212,215)(131,214,213,132)(151,194,177,168)(152,167,178,193)(153,192,179,166)(154,165,180,191)(155,190,181,164)(156,163,182,189)(157,188,183,162)(158,161,184,187)(159,186,185,160) );
G=PermutationGroup([[(1,179,108,125),(2,208,109,154),(3,181,110,127),(4,210,111,156),(5,183,112,129),(6,212,57,158),(7,185,58,131),(8,214,59,160),(9,187,60,133),(10,216,61,162),(11,189,62,135),(12,218,63,164),(13,191,64,137),(14,220,65,166),(15,193,66,139),(16,222,67,168),(17,195,68,141),(18,224,69,114),(19,197,70,143),(20,170,71,116),(21,199,72,145),(22,172,73,118),(23,201,74,147),(24,174,75,120),(25,203,76,149),(26,176,77,122),(27,205,78,151),(28,178,79,124),(29,207,80,153),(30,180,81,126),(31,209,82,155),(32,182,83,128),(33,211,84,157),(34,184,85,130),(35,213,86,159),(36,186,87,132),(37,215,88,161),(38,188,89,134),(39,217,90,163),(40,190,91,136),(41,219,92,165),(42,192,93,138),(43,221,94,167),(44,194,95,140),(45,223,96,113),(46,196,97,142),(47,169,98,115),(48,198,99,144),(49,171,100,117),(50,200,101,146),(51,173,102,119),(52,202,103,148),(53,175,104,121),(54,204,105,150),(55,177,106,123),(56,206,107,152)], [(1,94,29,66),(2,95,30,67),(3,96,31,68),(4,97,32,69),(5,98,33,70),(6,99,34,71),(7,100,35,72),(8,101,36,73),(9,102,37,74),(10,103,38,75),(11,104,39,76),(12,105,40,77),(13,106,41,78),(14,107,42,79),(15,108,43,80),(16,109,44,81),(17,110,45,82),(18,111,46,83),(19,112,47,84),(20,57,48,85),(21,58,49,86),(22,59,50,87),(23,60,51,88),(24,61,52,89),(25,62,53,90),(26,63,54,91),(27,64,55,92),(28,65,56,93),(113,209,141,181),(114,210,142,182),(115,211,143,183),(116,212,144,184),(117,213,145,185),(118,214,146,186),(119,215,147,187),(120,216,148,188),(121,217,149,189),(122,218,150,190),(123,219,151,191),(124,220,152,192),(125,221,153,193),(126,222,154,194),(127,223,155,195),(128,224,156,196),(129,169,157,197),(130,170,158,198),(131,171,159,199),(132,172,160,200),(133,173,161,201),(134,174,162,202),(135,175,163,203),(136,176,164,204),(137,177,165,205),(138,178,166,206),(139,179,167,207),(140,180,168,208)], [(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)], [(1,42,80,65),(2,64,81,41),(3,40,82,63),(4,62,83,39),(5,38,84,61),(6,60,85,37),(7,36,86,59),(8,58,87,35),(9,34,88,57),(10,112,89,33),(11,32,90,111),(12,110,91,31),(13,30,92,109),(14,108,93,29),(15,28,94,107),(16,106,95,27),(17,26,96,105),(18,104,97,25),(19,24,98,103),(20,102,99,23),(21,22,100,101),(43,56,66,79),(44,78,67,55),(45,54,68,77),(46,76,69,53),(47,52,70,75),(48,74,71,51),(49,50,72,73),(113,176,195,150),(114,149,196,175),(115,174,197,148),(116,147,198,173),(117,172,199,146),(118,145,200,171),(119,170,201,144),(120,143,202,169),(121,224,203,142),(122,141,204,223),(123,222,205,140),(124,139,206,221),(125,220,207,138),(126,137,208,219),(127,218,209,136),(128,135,210,217),(129,216,211,134),(130,133,212,215),(131,214,213,132),(151,194,177,168),(152,167,178,193),(153,192,179,166),(154,165,180,191),(155,190,181,164),(156,163,182,189),(157,188,183,162),(158,161,184,187),(159,186,185,160)]])
76 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28X | 56A | ··· | 56X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 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 | 56 | 2 | 2 | 4 | 4 | 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 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D28 | C4○D28 | C8⋊C22 | C8⋊D14 |
| kernel | C42.19D14 | C2.D56 | C7×C8⋊C4 | C28.6Q8 | C28⋊4D4 | C2×C28 | C8⋊C4 | C28 | C42 | C2×C8 | C2×C4 | C4 | C14 | C2 |
| # reps | 1 | 4 | 1 | 1 | 1 | 2 | 3 | 4 | 3 | 6 | 12 | 24 | 2 | 12 |
Matrix representation of C42.19D14 ►in GL6(𝔽113)
| 0 | 15 | 0 | 0 | 0 | 0 |
| 15 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 34 | 2 | 45 |
| 0 | 0 | 79 | 94 | 68 | 54 |
| 0 | 0 | 81 | 97 | 106 | 79 |
| 0 | 0 | 16 | 60 | 34 | 19 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 104 | 46 | 0 | 0 |
| 0 | 0 | 67 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 104 | 46 |
| 0 | 0 | 0 | 0 | 67 | 9 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 94 | 50 | 50 |
| 0 | 0 | 19 | 100 | 63 | 45 |
| 0 | 0 | 3 | 22 | 94 | 19 |
| 0 | 0 | 91 | 46 | 94 | 13 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 25 | 75 | 38 |
| 0 | 0 | 79 | 88 | 87 | 38 |
| 0 | 0 | 19 | 94 | 25 | 25 |
| 0 | 0 | 13 | 94 | 79 | 88 |
G:=sub<GL(6,GF(113))| [0,15,0,0,0,0,15,0,0,0,0,0,0,0,7,79,81,16,0,0,34,94,97,60,0,0,2,68,106,34,0,0,45,54,79,19],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,104,67,0,0,0,0,46,9,0,0,0,0,0,0,104,67,0,0,0,0,46,9],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,19,19,3,91,0,0,94,100,22,46,0,0,50,63,94,94,0,0,50,45,19,13],[0,1,0,0,0,0,112,0,0,0,0,0,0,0,25,79,19,13,0,0,25,88,94,94,0,0,75,87,25,79,0,0,38,38,25,88] >;
C42.19D14 in GAP, Magma, Sage, TeX
C_4^2._{19}D_{14} % in TeX
G:=Group("C4^2.19D14"); // GroupNames label
G:=SmallGroup(448,247);
// by ID
G=gap.SmallGroup(448,247);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,120,254,387,142,1123,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=a^2*b^-1,d^2=a^2*b^2,a*b=b*a,c*a*c^-1=a*b^2,d*a*d^-1=a^-1*b^2,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=b^-1*c^13>;
// generators/relations