metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.7D14, C14.18C4≀C2, (D4×C14).1C4, (Q8×C14).1C4, (C2×C28).231D4, (C2×Q8).1Dic7, (C2×D4).1Dic7, C4.4D4.1D7, (C4×C28).235C22, C2.3(C28.D4), C14.8(C4.D4), C42.D7⋊23C2, C2.6(D4⋊2Dic7), C7⋊2(C42.C22), C22.39(C23.D7), (C2×C4).9(C2×Dic7), (C2×C28).169(C2×C4), (C7×C4.4D4).8C2, (C2×C4).165(C7⋊D4), (C2×C14).98(C22⋊C4), SmallGroup(448,97)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.7D14
G = < a,b,c,d | a4=b4=c14=1, d2=ab-1, ab=ba, cac-1=dad-1=a-1b2, cbc-1=b-1, dbd-1=a2b-1, dcd-1=a2bc-1 >
Subgroups: 236 in 70 conjugacy classes, 27 normal (17 characteristic)
C1, C2, C2, C2, C4, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C14, C14, C14, C42, C22⋊C4, C2×C8, C2×D4, C2×Q8, C28, C2×C14, C2×C14, C8⋊C4, C4.4D4, C7⋊C8, C2×C28, C2×C28, C2×C28, C7×D4, C7×Q8, C22×C14, C42.C22, C2×C7⋊C8, C4×C28, C7×C22⋊C4, D4×C14, Q8×C14, C42.D7, C7×C4.4D4, C42.7D14
Quotients: C1, C2, C4, C22, C2×C4, D4, D7, C22⋊C4, Dic7, D14, C4.D4, C4≀C2, C2×Dic7, C7⋊D4, C42.C22, C23.D7, C28.D4, D4⋊2Dic7, C42.7D14
►On 224 points
Generators in S224
(1 117 26 33)(2 125 27 41)(3 119 28 35)(4 113 22 29)(5 121 23 37)(6 115 24 31)(7 123 25 39)(8 36 16 120)(9 30 17 114)(10 38 18 122)(11 32 19 116)(12 40 20 124)(13 34 21 118)(14 42 15 126)(43 130 157 88)(44 169 158 145)(45 132 159 90)(46 171 160 147)(47 134 161 92)(48 173 162 149)(49 136 163 94)(50 175 164 151)(51 138 165 96)(52 177 166 153)(53 140 167 98)(54 179 168 141)(55 128 155 86)(56 181 156 143)(57 186 64 199)(58 207 65 194)(59 188 66 201)(60 209 67 196)(61 190 68 203)(62 197 69 184)(63 192 70 205)(71 137 217 95)(72 176 218 152)(73 139 219 97)(74 178 220 154)(75 127 221 85)(76 180 222 142)(77 129 223 87)(78 182 224 144)(79 131 211 89)(80 170 212 146)(81 133 213 91)(82 172 214 148)(83 135 215 93)(84 174 216 150)(99 198 106 185)(100 193 107 206)(101 200 108 187)(102 195 109 208)(103 202 110 189)(104 183 111 210)(105 204 112 191)
(1 191 12 184)(2 185 13 192)(3 193 14 186)(4 187 8 194)(5 195 9 188)(6 189 10 196)(7 183 11 190)(15 199 28 206)(16 207 22 200)(17 201 23 208)(18 209 24 202)(19 203 25 210)(20 197 26 204)(21 205 27 198)(29 108 120 65)(30 66 121 109)(31 110 122 67)(32 68 123 111)(33 112 124 69)(34 70 125 99)(35 100 126 57)(36 58 113 101)(37 102 114 59)(38 60 115 103)(39 104 116 61)(40 62 117 105)(41 106 118 63)(42 64 119 107)(43 71 224 164)(44 165 211 72)(45 73 212 166)(46 167 213 74)(47 75 214 168)(48 155 215 76)(49 77 216 156)(50 157 217 78)(51 79 218 158)(52 159 219 80)(53 81 220 160)(54 161 221 82)(55 83 222 162)(56 163 223 84)(85 172 179 92)(86 93 180 173)(87 174 181 94)(88 95 182 175)(89 176 169 96)(90 97 170 177)(91 178 171 98)(127 148 141 134)(128 135 142 149)(129 150 143 136)(130 137 144 151)(131 152 145 138)(132 139 146 153)(133 154 147 140)
(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)
(1 182 62 71 20 130 112 50)(2 174 70 77 21 136 106 56)(3 180 64 83 15 128 100 48)(4 172 58 75 16 134 108 54)(5 178 66 81 17 140 102 46)(6 170 60 73 18 132 110 52)(7 176 68 79 19 138 104 44)(8 92 101 168 22 148 65 221)(9 98 109 160 23 154 59 213)(10 90 103 166 24 146 67 219)(11 96 111 158 25 152 61 211)(12 88 105 164 26 144 69 217)(13 94 99 156 27 150 63 223)(14 86 107 162 28 142 57 215)(29 47 194 141 36 82 200 85)(30 74 208 91 37 53 188 147)(31 45 196 153 38 80 202 97)(32 72 210 89 39 51 190 145)(33 43 184 151 40 78 204 95)(34 84 198 87 41 49 192 143)(35 55 186 149 42 76 206 93)(113 161 207 179 120 214 187 127)(114 220 195 133 121 167 201 171)(115 159 209 177 122 212 189 139)(116 218 183 131 123 165 203 169)(117 157 197 175 124 224 191 137)(118 216 185 129 125 163 205 181)(119 155 199 173 126 222 193 135)
G:=sub<Sym(224)| (1,117,26,33)(2,125,27,41)(3,119,28,35)(4,113,22,29)(5,121,23,37)(6,115,24,31)(7,123,25,39)(8,36,16,120)(9,30,17,114)(10,38,18,122)(11,32,19,116)(12,40,20,124)(13,34,21,118)(14,42,15,126)(43,130,157,88)(44,169,158,145)(45,132,159,90)(46,171,160,147)(47,134,161,92)(48,173,162,149)(49,136,163,94)(50,175,164,151)(51,138,165,96)(52,177,166,153)(53,140,167,98)(54,179,168,141)(55,128,155,86)(56,181,156,143)(57,186,64,199)(58,207,65,194)(59,188,66,201)(60,209,67,196)(61,190,68,203)(62,197,69,184)(63,192,70,205)(71,137,217,95)(72,176,218,152)(73,139,219,97)(74,178,220,154)(75,127,221,85)(76,180,222,142)(77,129,223,87)(78,182,224,144)(79,131,211,89)(80,170,212,146)(81,133,213,91)(82,172,214,148)(83,135,215,93)(84,174,216,150)(99,198,106,185)(100,193,107,206)(101,200,108,187)(102,195,109,208)(103,202,110,189)(104,183,111,210)(105,204,112,191), (1,191,12,184)(2,185,13,192)(3,193,14,186)(4,187,8,194)(5,195,9,188)(6,189,10,196)(7,183,11,190)(15,199,28,206)(16,207,22,200)(17,201,23,208)(18,209,24,202)(19,203,25,210)(20,197,26,204)(21,205,27,198)(29,108,120,65)(30,66,121,109)(31,110,122,67)(32,68,123,111)(33,112,124,69)(34,70,125,99)(35,100,126,57)(36,58,113,101)(37,102,114,59)(38,60,115,103)(39,104,116,61)(40,62,117,105)(41,106,118,63)(42,64,119,107)(43,71,224,164)(44,165,211,72)(45,73,212,166)(46,167,213,74)(47,75,214,168)(48,155,215,76)(49,77,216,156)(50,157,217,78)(51,79,218,158)(52,159,219,80)(53,81,220,160)(54,161,221,82)(55,83,222,162)(56,163,223,84)(85,172,179,92)(86,93,180,173)(87,174,181,94)(88,95,182,175)(89,176,169,96)(90,97,170,177)(91,178,171,98)(127,148,141,134)(128,135,142,149)(129,150,143,136)(130,137,144,151)(131,152,145,138)(132,139,146,153)(133,154,147,140), (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), (1,182,62,71,20,130,112,50)(2,174,70,77,21,136,106,56)(3,180,64,83,15,128,100,48)(4,172,58,75,16,134,108,54)(5,178,66,81,17,140,102,46)(6,170,60,73,18,132,110,52)(7,176,68,79,19,138,104,44)(8,92,101,168,22,148,65,221)(9,98,109,160,23,154,59,213)(10,90,103,166,24,146,67,219)(11,96,111,158,25,152,61,211)(12,88,105,164,26,144,69,217)(13,94,99,156,27,150,63,223)(14,86,107,162,28,142,57,215)(29,47,194,141,36,82,200,85)(30,74,208,91,37,53,188,147)(31,45,196,153,38,80,202,97)(32,72,210,89,39,51,190,145)(33,43,184,151,40,78,204,95)(34,84,198,87,41,49,192,143)(35,55,186,149,42,76,206,93)(113,161,207,179,120,214,187,127)(114,220,195,133,121,167,201,171)(115,159,209,177,122,212,189,139)(116,218,183,131,123,165,203,169)(117,157,197,175,124,224,191,137)(118,216,185,129,125,163,205,181)(119,155,199,173,126,222,193,135)>;
G:=Group( (1,117,26,33)(2,125,27,41)(3,119,28,35)(4,113,22,29)(5,121,23,37)(6,115,24,31)(7,123,25,39)(8,36,16,120)(9,30,17,114)(10,38,18,122)(11,32,19,116)(12,40,20,124)(13,34,21,118)(14,42,15,126)(43,130,157,88)(44,169,158,145)(45,132,159,90)(46,171,160,147)(47,134,161,92)(48,173,162,149)(49,136,163,94)(50,175,164,151)(51,138,165,96)(52,177,166,153)(53,140,167,98)(54,179,168,141)(55,128,155,86)(56,181,156,143)(57,186,64,199)(58,207,65,194)(59,188,66,201)(60,209,67,196)(61,190,68,203)(62,197,69,184)(63,192,70,205)(71,137,217,95)(72,176,218,152)(73,139,219,97)(74,178,220,154)(75,127,221,85)(76,180,222,142)(77,129,223,87)(78,182,224,144)(79,131,211,89)(80,170,212,146)(81,133,213,91)(82,172,214,148)(83,135,215,93)(84,174,216,150)(99,198,106,185)(100,193,107,206)(101,200,108,187)(102,195,109,208)(103,202,110,189)(104,183,111,210)(105,204,112,191), (1,191,12,184)(2,185,13,192)(3,193,14,186)(4,187,8,194)(5,195,9,188)(6,189,10,196)(7,183,11,190)(15,199,28,206)(16,207,22,200)(17,201,23,208)(18,209,24,202)(19,203,25,210)(20,197,26,204)(21,205,27,198)(29,108,120,65)(30,66,121,109)(31,110,122,67)(32,68,123,111)(33,112,124,69)(34,70,125,99)(35,100,126,57)(36,58,113,101)(37,102,114,59)(38,60,115,103)(39,104,116,61)(40,62,117,105)(41,106,118,63)(42,64,119,107)(43,71,224,164)(44,165,211,72)(45,73,212,166)(46,167,213,74)(47,75,214,168)(48,155,215,76)(49,77,216,156)(50,157,217,78)(51,79,218,158)(52,159,219,80)(53,81,220,160)(54,161,221,82)(55,83,222,162)(56,163,223,84)(85,172,179,92)(86,93,180,173)(87,174,181,94)(88,95,182,175)(89,176,169,96)(90,97,170,177)(91,178,171,98)(127,148,141,134)(128,135,142,149)(129,150,143,136)(130,137,144,151)(131,152,145,138)(132,139,146,153)(133,154,147,140), (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), (1,182,62,71,20,130,112,50)(2,174,70,77,21,136,106,56)(3,180,64,83,15,128,100,48)(4,172,58,75,16,134,108,54)(5,178,66,81,17,140,102,46)(6,170,60,73,18,132,110,52)(7,176,68,79,19,138,104,44)(8,92,101,168,22,148,65,221)(9,98,109,160,23,154,59,213)(10,90,103,166,24,146,67,219)(11,96,111,158,25,152,61,211)(12,88,105,164,26,144,69,217)(13,94,99,156,27,150,63,223)(14,86,107,162,28,142,57,215)(29,47,194,141,36,82,200,85)(30,74,208,91,37,53,188,147)(31,45,196,153,38,80,202,97)(32,72,210,89,39,51,190,145)(33,43,184,151,40,78,204,95)(34,84,198,87,41,49,192,143)(35,55,186,149,42,76,206,93)(113,161,207,179,120,214,187,127)(114,220,195,133,121,167,201,171)(115,159,209,177,122,212,189,139)(116,218,183,131,123,165,203,169)(117,157,197,175,124,224,191,137)(118,216,185,129,125,163,205,181)(119,155,199,173,126,222,193,135) );
G=PermutationGroup([[(1,117,26,33),(2,125,27,41),(3,119,28,35),(4,113,22,29),(5,121,23,37),(6,115,24,31),(7,123,25,39),(8,36,16,120),(9,30,17,114),(10,38,18,122),(11,32,19,116),(12,40,20,124),(13,34,21,118),(14,42,15,126),(43,130,157,88),(44,169,158,145),(45,132,159,90),(46,171,160,147),(47,134,161,92),(48,173,162,149),(49,136,163,94),(50,175,164,151),(51,138,165,96),(52,177,166,153),(53,140,167,98),(54,179,168,141),(55,128,155,86),(56,181,156,143),(57,186,64,199),(58,207,65,194),(59,188,66,201),(60,209,67,196),(61,190,68,203),(62,197,69,184),(63,192,70,205),(71,137,217,95),(72,176,218,152),(73,139,219,97),(74,178,220,154),(75,127,221,85),(76,180,222,142),(77,129,223,87),(78,182,224,144),(79,131,211,89),(80,170,212,146),(81,133,213,91),(82,172,214,148),(83,135,215,93),(84,174,216,150),(99,198,106,185),(100,193,107,206),(101,200,108,187),(102,195,109,208),(103,202,110,189),(104,183,111,210),(105,204,112,191)], [(1,191,12,184),(2,185,13,192),(3,193,14,186),(4,187,8,194),(5,195,9,188),(6,189,10,196),(7,183,11,190),(15,199,28,206),(16,207,22,200),(17,201,23,208),(18,209,24,202),(19,203,25,210),(20,197,26,204),(21,205,27,198),(29,108,120,65),(30,66,121,109),(31,110,122,67),(32,68,123,111),(33,112,124,69),(34,70,125,99),(35,100,126,57),(36,58,113,101),(37,102,114,59),(38,60,115,103),(39,104,116,61),(40,62,117,105),(41,106,118,63),(42,64,119,107),(43,71,224,164),(44,165,211,72),(45,73,212,166),(46,167,213,74),(47,75,214,168),(48,155,215,76),(49,77,216,156),(50,157,217,78),(51,79,218,158),(52,159,219,80),(53,81,220,160),(54,161,221,82),(55,83,222,162),(56,163,223,84),(85,172,179,92),(86,93,180,173),(87,174,181,94),(88,95,182,175),(89,176,169,96),(90,97,170,177),(91,178,171,98),(127,148,141,134),(128,135,142,149),(129,150,143,136),(130,137,144,151),(131,152,145,138),(132,139,146,153),(133,154,147,140)], [(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)], [(1,182,62,71,20,130,112,50),(2,174,70,77,21,136,106,56),(3,180,64,83,15,128,100,48),(4,172,58,75,16,134,108,54),(5,178,66,81,17,140,102,46),(6,170,60,73,18,132,110,52),(7,176,68,79,19,138,104,44),(8,92,101,168,22,148,65,221),(9,98,109,160,23,154,59,213),(10,90,103,166,24,146,67,219),(11,96,111,158,25,152,61,211),(12,88,105,164,26,144,69,217),(13,94,99,156,27,150,63,223),(14,86,107,162,28,142,57,215),(29,47,194,141,36,82,200,85),(30,74,208,91,37,53,188,147),(31,45,196,153,38,80,202,97),(32,72,210,89,39,51,190,145),(33,43,184,151,40,78,204,95),(34,84,198,87,41,49,192,143),(35,55,186,149,42,76,206,93),(113,161,207,179,120,214,187,127),(114,220,195,133,121,167,201,171),(115,159,209,177,122,212,189,139),(116,218,183,131,123,165,203,169),(117,157,197,175,124,224,191,137),(118,216,185,129,125,163,205,181),(119,155,199,173,126,222,193,135)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 7A | 7B | 7C | 8A | ··· | 8H | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 8 | 2 | 2 | 2 | 2 | 4 | 8 | 2 | 2 | 2 | 28 | ··· | 28 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | - | - | + | ||||||
| image | C1 | C2 | C2 | C4 | C4 | D4 | D7 | D14 | Dic7 | Dic7 | C4≀C2 | C7⋊D4 | C4.D4 | C28.D4 | D4⋊2Dic7 |
| kernel | C42.7D14 | C42.D7 | C7×C4.4D4 | D4×C14 | Q8×C14 | C2×C28 | C4.4D4 | C42 | C2×D4 | C2×Q8 | C14 | C2×C4 | C14 | C2 | C2 |
| # reps | 1 | 2 | 1 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 8 | 12 | 1 | 6 | 12 |
Matrix representation of C42.7D14 ►in GL6(𝔽113)
| 15 | 0 | 0 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 15 |
| 0 | 0 | 0 | 0 | 98 | 0 |
| 1 | 111 | 0 | 0 | 0 | 0 |
| 1 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 88 | 0 | 0 |
| 0 | 0 | 104 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 0 | 97 | 0 | 0 | 0 | 0 |
| 8 | 97 | 0 | 0 | 0 | 0 |
| 0 | 0 | 56 | 97 | 0 | 0 |
| 0 | 0 | 76 | 57 | 0 | 0 |
| 0 | 0 | 0 | 0 | 105 | 105 |
| 0 | 0 | 0 | 0 | 105 | 8 |
G:=sub<GL(6,GF(113))| [15,0,0,0,0,0,0,15,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,0,98,0,0,0,0,15,0],[1,1,0,0,0,0,111,112,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,112,0,0,0,0,1,0],[1,1,0,0,0,0,0,112,0,0,0,0,0,0,0,104,0,0,0,0,88,9,0,0,0,0,0,0,1,0,0,0,0,0,0,112],[0,8,0,0,0,0,97,97,0,0,0,0,0,0,56,76,0,0,0,0,97,57,0,0,0,0,0,0,105,105,0,0,0,0,105,8] >;
C42.7D14 in GAP, Magma, Sage, TeX
C_4^2._7D_{14} % in TeX
G:=Group("C4^2.7D14"); // GroupNames label
G:=SmallGroup(448,97);
// by ID
G=gap.SmallGroup(448,97);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,28,141,219,268,1571,570,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a*b^-1,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1*b^2,c*b*c^-1=b^-1,d*b*d^-1=a^2*b^-1,d*c*d^-1=a^2*b*c^-1>;
// generators/relations