metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.182D14, D14.1M4(2), Dic7.3M4(2), C8⋊C4⋊7D7, Dic7⋊C8⋊36C2, D14⋊C8.15C2, (C2×C8).156D14, C2.9(D7×M4(2)), C7⋊1(C42.6C4), (C4×Dic7).15C4, (D7×C42).14C2, C28.245(C4○D4), C4.129(C4○D28), (C4×C28).227C22, (C2×C56).311C22, (C2×C28).811C23, C42.D7⋊18C2, C14.16(C2×M4(2)), C14.9(C42⋊C2), C2.12(C42⋊D7), (C4×Dic7).267C22, (C2×C4×D7).15C4, (C7×C8⋊C4)⋊17C2, C22.98(C2×C4×D7), (C2×C4).127(C4×D7), (C2×C28).146(C2×C4), (C2×C7⋊C8).189C22, (C2×C4×D7).269C22, (C2×C14).66(C22×C4), (C2×Dic7).81(C2×C4), (C22×D7).52(C2×C4), (C2×C4).753(C22×D7), SmallGroup(448,239)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.182D14
G = < a,b,c,d | a4=b4=1, c14=b-1, d2=a2b, ab=ba, cac-1=dad-1=ab2, bc=cb, bd=db, dcd-1=a2b2c13 >
Subgroups: 452 in 110 conjugacy classes, 51 normal (33 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, C23, D7, C14, C42, C42, C2×C8, C2×C8, C22×C4, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C8⋊C4, C8⋊C4, C22⋊C8, C4⋊C8, C2×C42, C7⋊C8, C56, C4×D7, C2×Dic7, C2×C28, C22×D7, C42.6C4, C2×C7⋊C8, C4×Dic7, C4×C28, C2×C56, C2×C4×D7, C42.D7, Dic7⋊C8, D14⋊C8, C7×C8⋊C4, D7×C42, C42.182D14
Quotients: C1, C2, C4, C22, C2×C4, C23, D7, M4(2), C22×C4, C4○D4, D14, C42⋊C2, C2×M4(2), C4×D7, C22×D7, C42.6C4, C2×C4×D7, C4○D28, C42⋊D7, D7×M4(2), C42.182D14
►On 224 points
Generators in S224
(1 174 75 114)(2 203 76 143)(3 176 77 116)(4 205 78 145)(5 178 79 118)(6 207 80 147)(7 180 81 120)(8 209 82 149)(9 182 83 122)(10 211 84 151)(11 184 85 124)(12 213 86 153)(13 186 87 126)(14 215 88 155)(15 188 89 128)(16 217 90 157)(17 190 91 130)(18 219 92 159)(19 192 93 132)(20 221 94 161)(21 194 95 134)(22 223 96 163)(23 196 97 136)(24 169 98 165)(25 198 99 138)(26 171 100 167)(27 200 101 140)(28 173 102 113)(29 202 103 142)(30 175 104 115)(31 204 105 144)(32 177 106 117)(33 206 107 146)(34 179 108 119)(35 208 109 148)(36 181 110 121)(37 210 111 150)(38 183 112 123)(39 212 57 152)(40 185 58 125)(41 214 59 154)(42 187 60 127)(43 216 61 156)(44 189 62 129)(45 218 63 158)(46 191 64 131)(47 220 65 160)(48 193 66 133)(49 222 67 162)(50 195 68 135)(51 224 69 164)(52 197 70 137)(53 170 71 166)(54 199 72 139)(55 172 73 168)(56 201 74 141)
(1 43 29 15)(2 44 30 16)(3 45 31 17)(4 46 32 18)(5 47 33 19)(6 48 34 20)(7 49 35 21)(8 50 36 22)(9 51 37 23)(10 52 38 24)(11 53 39 25)(12 54 40 26)(13 55 41 27)(14 56 42 28)(57 99 85 71)(58 100 86 72)(59 101 87 73)(60 102 88 74)(61 103 89 75)(62 104 90 76)(63 105 91 77)(64 106 92 78)(65 107 93 79)(66 108 94 80)(67 109 95 81)(68 110 96 82)(69 111 97 83)(70 112 98 84)(113 155 141 127)(114 156 142 128)(115 157 143 129)(116 158 144 130)(117 159 145 131)(118 160 146 132)(119 161 147 133)(120 162 148 134)(121 163 149 135)(122 164 150 136)(123 165 151 137)(124 166 152 138)(125 167 153 139)(126 168 154 140)(169 211 197 183)(170 212 198 184)(171 213 199 185)(172 214 200 186)(173 215 201 187)(174 216 202 188)(175 217 203 189)(176 218 204 190)(177 219 205 191)(178 220 206 192)(179 221 207 193)(180 222 208 194)(181 223 209 195)(182 224 210 196)
(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 14 61 74 29 42 89 102)(2 73 62 41 30 101 90 13)(3 40 63 100 31 12 91 72)(4 99 64 11 32 71 92 39)(5 10 65 70 33 38 93 98)(6 69 66 37 34 97 94 9)(7 36 67 96 35 8 95 68)(15 28 75 88 43 56 103 60)(16 87 76 55 44 59 104 27)(17 54 77 58 45 26 105 86)(18 57 78 25 46 85 106 53)(19 24 79 84 47 52 107 112)(20 83 80 51 48 111 108 23)(21 50 81 110 49 22 109 82)(113 202 215 128 141 174 187 156)(114 127 216 173 142 155 188 201)(115 172 217 154 143 200 189 126)(116 153 218 199 144 125 190 171)(117 198 219 124 145 170 191 152)(118 123 220 169 146 151 192 197)(119 224 221 150 147 196 193 122)(120 149 222 195 148 121 194 223)(129 186 175 168 157 214 203 140)(130 167 176 213 158 139 204 185)(131 212 177 138 159 184 205 166)(132 137 178 183 160 165 206 211)(133 182 179 164 161 210 207 136)(134 163 180 209 162 135 208 181)
G:=sub<Sym(224)| (1,174,75,114)(2,203,76,143)(3,176,77,116)(4,205,78,145)(5,178,79,118)(6,207,80,147)(7,180,81,120)(8,209,82,149)(9,182,83,122)(10,211,84,151)(11,184,85,124)(12,213,86,153)(13,186,87,126)(14,215,88,155)(15,188,89,128)(16,217,90,157)(17,190,91,130)(18,219,92,159)(19,192,93,132)(20,221,94,161)(21,194,95,134)(22,223,96,163)(23,196,97,136)(24,169,98,165)(25,198,99,138)(26,171,100,167)(27,200,101,140)(28,173,102,113)(29,202,103,142)(30,175,104,115)(31,204,105,144)(32,177,106,117)(33,206,107,146)(34,179,108,119)(35,208,109,148)(36,181,110,121)(37,210,111,150)(38,183,112,123)(39,212,57,152)(40,185,58,125)(41,214,59,154)(42,187,60,127)(43,216,61,156)(44,189,62,129)(45,218,63,158)(46,191,64,131)(47,220,65,160)(48,193,66,133)(49,222,67,162)(50,195,68,135)(51,224,69,164)(52,197,70,137)(53,170,71,166)(54,199,72,139)(55,172,73,168)(56,201,74,141), (1,43,29,15)(2,44,30,16)(3,45,31,17)(4,46,32,18)(5,47,33,19)(6,48,34,20)(7,49,35,21)(8,50,36,22)(9,51,37,23)(10,52,38,24)(11,53,39,25)(12,54,40,26)(13,55,41,27)(14,56,42,28)(57,99,85,71)(58,100,86,72)(59,101,87,73)(60,102,88,74)(61,103,89,75)(62,104,90,76)(63,105,91,77)(64,106,92,78)(65,107,93,79)(66,108,94,80)(67,109,95,81)(68,110,96,82)(69,111,97,83)(70,112,98,84)(113,155,141,127)(114,156,142,128)(115,157,143,129)(116,158,144,130)(117,159,145,131)(118,160,146,132)(119,161,147,133)(120,162,148,134)(121,163,149,135)(122,164,150,136)(123,165,151,137)(124,166,152,138)(125,167,153,139)(126,168,154,140)(169,211,197,183)(170,212,198,184)(171,213,199,185)(172,214,200,186)(173,215,201,187)(174,216,202,188)(175,217,203,189)(176,218,204,190)(177,219,205,191)(178,220,206,192)(179,221,207,193)(180,222,208,194)(181,223,209,195)(182,224,210,196), (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), (1,14,61,74,29,42,89,102)(2,73,62,41,30,101,90,13)(3,40,63,100,31,12,91,72)(4,99,64,11,32,71,92,39)(5,10,65,70,33,38,93,98)(6,69,66,37,34,97,94,9)(7,36,67,96,35,8,95,68)(15,28,75,88,43,56,103,60)(16,87,76,55,44,59,104,27)(17,54,77,58,45,26,105,86)(18,57,78,25,46,85,106,53)(19,24,79,84,47,52,107,112)(20,83,80,51,48,111,108,23)(21,50,81,110,49,22,109,82)(113,202,215,128,141,174,187,156)(114,127,216,173,142,155,188,201)(115,172,217,154,143,200,189,126)(116,153,218,199,144,125,190,171)(117,198,219,124,145,170,191,152)(118,123,220,169,146,151,192,197)(119,224,221,150,147,196,193,122)(120,149,222,195,148,121,194,223)(129,186,175,168,157,214,203,140)(130,167,176,213,158,139,204,185)(131,212,177,138,159,184,205,166)(132,137,178,183,160,165,206,211)(133,182,179,164,161,210,207,136)(134,163,180,209,162,135,208,181)>;
G:=Group( (1,174,75,114)(2,203,76,143)(3,176,77,116)(4,205,78,145)(5,178,79,118)(6,207,80,147)(7,180,81,120)(8,209,82,149)(9,182,83,122)(10,211,84,151)(11,184,85,124)(12,213,86,153)(13,186,87,126)(14,215,88,155)(15,188,89,128)(16,217,90,157)(17,190,91,130)(18,219,92,159)(19,192,93,132)(20,221,94,161)(21,194,95,134)(22,223,96,163)(23,196,97,136)(24,169,98,165)(25,198,99,138)(26,171,100,167)(27,200,101,140)(28,173,102,113)(29,202,103,142)(30,175,104,115)(31,204,105,144)(32,177,106,117)(33,206,107,146)(34,179,108,119)(35,208,109,148)(36,181,110,121)(37,210,111,150)(38,183,112,123)(39,212,57,152)(40,185,58,125)(41,214,59,154)(42,187,60,127)(43,216,61,156)(44,189,62,129)(45,218,63,158)(46,191,64,131)(47,220,65,160)(48,193,66,133)(49,222,67,162)(50,195,68,135)(51,224,69,164)(52,197,70,137)(53,170,71,166)(54,199,72,139)(55,172,73,168)(56,201,74,141), (1,43,29,15)(2,44,30,16)(3,45,31,17)(4,46,32,18)(5,47,33,19)(6,48,34,20)(7,49,35,21)(8,50,36,22)(9,51,37,23)(10,52,38,24)(11,53,39,25)(12,54,40,26)(13,55,41,27)(14,56,42,28)(57,99,85,71)(58,100,86,72)(59,101,87,73)(60,102,88,74)(61,103,89,75)(62,104,90,76)(63,105,91,77)(64,106,92,78)(65,107,93,79)(66,108,94,80)(67,109,95,81)(68,110,96,82)(69,111,97,83)(70,112,98,84)(113,155,141,127)(114,156,142,128)(115,157,143,129)(116,158,144,130)(117,159,145,131)(118,160,146,132)(119,161,147,133)(120,162,148,134)(121,163,149,135)(122,164,150,136)(123,165,151,137)(124,166,152,138)(125,167,153,139)(126,168,154,140)(169,211,197,183)(170,212,198,184)(171,213,199,185)(172,214,200,186)(173,215,201,187)(174,216,202,188)(175,217,203,189)(176,218,204,190)(177,219,205,191)(178,220,206,192)(179,221,207,193)(180,222,208,194)(181,223,209,195)(182,224,210,196), (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), (1,14,61,74,29,42,89,102)(2,73,62,41,30,101,90,13)(3,40,63,100,31,12,91,72)(4,99,64,11,32,71,92,39)(5,10,65,70,33,38,93,98)(6,69,66,37,34,97,94,9)(7,36,67,96,35,8,95,68)(15,28,75,88,43,56,103,60)(16,87,76,55,44,59,104,27)(17,54,77,58,45,26,105,86)(18,57,78,25,46,85,106,53)(19,24,79,84,47,52,107,112)(20,83,80,51,48,111,108,23)(21,50,81,110,49,22,109,82)(113,202,215,128,141,174,187,156)(114,127,216,173,142,155,188,201)(115,172,217,154,143,200,189,126)(116,153,218,199,144,125,190,171)(117,198,219,124,145,170,191,152)(118,123,220,169,146,151,192,197)(119,224,221,150,147,196,193,122)(120,149,222,195,148,121,194,223)(129,186,175,168,157,214,203,140)(130,167,176,213,158,139,204,185)(131,212,177,138,159,184,205,166)(132,137,178,183,160,165,206,211)(133,182,179,164,161,210,207,136)(134,163,180,209,162,135,208,181) );
G=PermutationGroup([[(1,174,75,114),(2,203,76,143),(3,176,77,116),(4,205,78,145),(5,178,79,118),(6,207,80,147),(7,180,81,120),(8,209,82,149),(9,182,83,122),(10,211,84,151),(11,184,85,124),(12,213,86,153),(13,186,87,126),(14,215,88,155),(15,188,89,128),(16,217,90,157),(17,190,91,130),(18,219,92,159),(19,192,93,132),(20,221,94,161),(21,194,95,134),(22,223,96,163),(23,196,97,136),(24,169,98,165),(25,198,99,138),(26,171,100,167),(27,200,101,140),(28,173,102,113),(29,202,103,142),(30,175,104,115),(31,204,105,144),(32,177,106,117),(33,206,107,146),(34,179,108,119),(35,208,109,148),(36,181,110,121),(37,210,111,150),(38,183,112,123),(39,212,57,152),(40,185,58,125),(41,214,59,154),(42,187,60,127),(43,216,61,156),(44,189,62,129),(45,218,63,158),(46,191,64,131),(47,220,65,160),(48,193,66,133),(49,222,67,162),(50,195,68,135),(51,224,69,164),(52,197,70,137),(53,170,71,166),(54,199,72,139),(55,172,73,168),(56,201,74,141)], [(1,43,29,15),(2,44,30,16),(3,45,31,17),(4,46,32,18),(5,47,33,19),(6,48,34,20),(7,49,35,21),(8,50,36,22),(9,51,37,23),(10,52,38,24),(11,53,39,25),(12,54,40,26),(13,55,41,27),(14,56,42,28),(57,99,85,71),(58,100,86,72),(59,101,87,73),(60,102,88,74),(61,103,89,75),(62,104,90,76),(63,105,91,77),(64,106,92,78),(65,107,93,79),(66,108,94,80),(67,109,95,81),(68,110,96,82),(69,111,97,83),(70,112,98,84),(113,155,141,127),(114,156,142,128),(115,157,143,129),(116,158,144,130),(117,159,145,131),(118,160,146,132),(119,161,147,133),(120,162,148,134),(121,163,149,135),(122,164,150,136),(123,165,151,137),(124,166,152,138),(125,167,153,139),(126,168,154,140),(169,211,197,183),(170,212,198,184),(171,213,199,185),(172,214,200,186),(173,215,201,187),(174,216,202,188),(175,217,203,189),(176,218,204,190),(177,219,205,191),(178,220,206,192),(179,221,207,193),(180,222,208,194),(181,223,209,195),(182,224,210,196)], [(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)], [(1,14,61,74,29,42,89,102),(2,73,62,41,30,101,90,13),(3,40,63,100,31,12,91,72),(4,99,64,11,32,71,92,39),(5,10,65,70,33,38,93,98),(6,69,66,37,34,97,94,9),(7,36,67,96,35,8,95,68),(15,28,75,88,43,56,103,60),(16,87,76,55,44,59,104,27),(17,54,77,58,45,26,105,86),(18,57,78,25,46,85,106,53),(19,24,79,84,47,52,107,112),(20,83,80,51,48,111,108,23),(21,50,81,110,49,22,109,82),(113,202,215,128,141,174,187,156),(114,127,216,173,142,155,188,201),(115,172,217,154,143,200,189,126),(116,153,218,199,144,125,190,171),(117,198,219,124,145,170,191,152),(118,123,220,169,146,151,192,197),(119,224,221,150,147,196,193,122),(120,149,222,195,148,121,194,223),(129,186,175,168,157,214,203,140),(130,167,176,213,158,139,204,185),(131,212,177,138,159,184,205,166),(132,137,178,183,160,165,206,211),(133,182,179,164,161,210,207,136),(134,163,180,209,162,135,208,181)]])
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4N | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28X | 56A | ··· | 56X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 14 | ··· | 14 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | ||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | C4 | D7 | M4(2) | C4○D4 | M4(2) | D14 | D14 | C4×D7 | C4○D28 | D7×M4(2) |
| kernel | C42.182D14 | C42.D7 | Dic7⋊C8 | D14⋊C8 | C7×C8⋊C4 | D7×C42 | C4×Dic7 | C2×C4×D7 | C8⋊C4 | Dic7 | C28 | D14 | C42 | C2×C8 | C2×C4 | C4 | C2 |
| # reps | 1 | 1 | 2 | 2 | 1 | 1 | 4 | 4 | 3 | 4 | 4 | 4 | 3 | 6 | 12 | 24 | 12 |
Matrix representation of C42.182D14 ►in GL4(𝔽113) generated by
| 15 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 |
| 0 | 0 | 98 | 43 |
| 0 | 0 | 0 | 15 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 98 | 0 |
| 0 | 0 | 0 | 98 |
| 59 | 54 | 0 | 0 |
| 59 | 31 | 0 | 0 |
| 0 | 0 | 43 | 81 |
| 0 | 0 | 30 | 70 |
| 54 | 59 | 0 | 0 |
| 31 | 59 | 0 | 0 |
| 0 | 0 | 70 | 31 |
| 0 | 0 | 83 | 43 |
G:=sub<GL(4,GF(113))| [15,0,0,0,0,15,0,0,0,0,98,0,0,0,43,15],[1,0,0,0,0,1,0,0,0,0,98,0,0,0,0,98],[59,59,0,0,54,31,0,0,0,0,43,30,0,0,81,70],[54,31,0,0,59,59,0,0,0,0,70,83,0,0,31,43] >;
C42.182D14 in GAP, Magma, Sage, TeX
C_4^2._{182}D_{14} % in TeX
G:=Group("C4^2.182D14"); // GroupNames label
G:=SmallGroup(448,239);
// by ID
G=gap.SmallGroup(448,239);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,422,387,58,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=b^-1,d^2=a^2*b,a*b=b*a,c*a*c^-1=d*a*d^-1=a*b^2,b*c=c*b,b*d=d*b,d*c*d^-1=a^2*b^2*c^13>;
// generators/relations