metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.274D14, (C2×C28)⋊13Q8, C28.89(C2×Q8), C28⋊2Q8⋊37C2, (C4×Dic14)⋊3C2, (C2×C4)⋊10Dic14, (C2×C42).21D7, C14.4(C22×Q8), (C2×C14).14C24, C28.6Q8⋊31C2, C4.54(C2×Dic14), C28.233(C4○D4), C4.117(C4○D28), (C2×C28).692C23, (C4×C28).314C22, (C22×C4).436D14, (C2×Dic7).3C23, C2.6(C22×Dic14), C22.61(C23×D7), C28.48D4.20C2, Dic7⋊C4.95C22, C4⋊Dic7.288C22, C22.10(C2×Dic14), C23.216(C22×D7), C23.D7.80C22, (C22×C28).522C22, (C22×C14).376C23, C7⋊1(C23.37C23), (C4×Dic7).190C22, C23.21D14.6C2, (C2×Dic14).223C22, (C2×C4×C28).23C2, C2.8(C2×C4○D28), C14.3(C2×C4○D4), (C2×C14).48(C2×Q8), (C2×C4).728(C22×D7), SmallGroup(448,923)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.274D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2b2, ab=ba, ac=ca, dad-1=a-1, bc=cb, bd=db, dcd-1=b2c-1 >
Subgroups: 772 in 222 conjugacy classes, 119 normal (21 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, Q8, C23, C14, C14, C14, C42, C42, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C2×C14, C2×C42, C42⋊C2, C4×Q8, C22⋊Q8, C42.C2, C4⋊Q8, Dic14, C2×Dic7, C2×C28, C2×C28, C2×C28, C22×C14, C23.37C23, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C23.D7, C4×C28, C4×C28, C2×Dic14, C22×C28, C22×C28, C4×Dic14, C28⋊2Q8, C28.6Q8, C28.48D4, C23.21D14, C2×C4×C28, C42.274D14
Quotients: C1, C2, C22, Q8, C23, D7, C2×Q8, C4○D4, C24, D14, C22×Q8, C2×C4○D4, Dic14, C22×D7, C23.37C23, C2×Dic14, C4○D28, C23×D7, C22×Dic14, C2×C4○D28, C42.274D14
►On 224 points
Generators in S224
(1 182 8 175)(2 169 9 176)(3 170 10 177)(4 171 11 178)(5 172 12 179)(6 173 13 180)(7 174 14 181)(15 32 50 187)(16 33 51 188)(17 34 52 189)(18 35 53 190)(19 36 54 191)(20 37 55 192)(21 38 56 193)(22 39 43 194)(23 40 44 195)(24 41 45 196)(25 42 46 183)(26 29 47 184)(27 30 48 185)(28 31 49 186)(57 206 117 167)(58 207 118 168)(59 208 119 155)(60 209 120 156)(61 210 121 157)(62 197 122 158)(63 198 123 159)(64 199 124 160)(65 200 125 161)(66 201 126 162)(67 202 113 163)(68 203 114 164)(69 204 115 165)(70 205 116 166)(71 128 78 135)(72 129 79 136)(73 130 80 137)(74 131 81 138)(75 132 82 139)(76 133 83 140)(77 134 84 127)(85 221 92 214)(86 222 93 215)(87 223 94 216)(88 224 95 217)(89 211 96 218)(90 212 97 219)(91 213 98 220)(99 143 106 150)(100 144 107 151)(101 145 108 152)(102 146 109 153)(103 147 110 154)(104 148 111 141)(105 149 112 142)
(1 146 131 221)(2 147 132 222)(3 148 133 223)(4 149 134 224)(5 150 135 211)(6 151 136 212)(7 152 137 213)(8 153 138 214)(9 154 139 215)(10 141 140 216)(11 142 127 217)(12 143 128 218)(13 144 129 219)(14 145 130 220)(15 165 43 197)(16 166 44 198)(17 167 45 199)(18 168 46 200)(19 155 47 201)(20 156 48 202)(21 157 49 203)(22 158 50 204)(23 159 51 205)(24 160 52 206)(25 161 53 207)(26 162 54 208)(27 163 55 209)(28 164 56 210)(29 66 191 119)(30 67 192 120)(31 68 193 121)(32 69 194 122)(33 70 195 123)(34 57 196 124)(35 58 183 125)(36 59 184 126)(37 60 185 113)(38 61 186 114)(39 62 187 115)(40 63 188 116)(41 64 189 117)(42 65 190 118)(71 96 172 99)(72 97 173 100)(73 98 174 101)(74 85 175 102)(75 86 176 103)(76 87 177 104)(77 88 178 105)(78 89 179 106)(79 90 180 107)(80 91 181 108)(81 92 182 109)(82 93 169 110)(83 94 170 111)(84 95 171 112)
(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 62 138 69)(2 114 139 121)(3 60 140 67)(4 126 127 119)(5 58 128 65)(6 124 129 117)(7 70 130 63)(8 122 131 115)(9 68 132 61)(10 120 133 113)(11 66 134 59)(12 118 135 125)(13 64 136 57)(14 116 137 123)(15 92 22 102)(16 108 23 98)(17 90 24 100)(18 106 25 96)(19 88 26 112)(20 104 27 94)(21 86 28 110)(29 149 36 217)(30 223 37 141)(31 147 38 215)(32 221 39 153)(33 145 40 213)(34 219 41 151)(35 143 42 211)(43 109 50 85)(44 91 51 101)(45 107 52 97)(46 89 53 99)(47 105 54 95)(48 87 55 111)(49 103 56 93)(71 200 179 207)(72 167 180 160)(73 198 181 205)(74 165 182 158)(75 210 169 203)(76 163 170 156)(77 208 171 201)(78 161 172 168)(79 206 173 199)(80 159 174 166)(81 204 175 197)(82 157 176 164)(83 202 177 209)(84 155 178 162)(142 191 224 184)(144 189 212 196)(146 187 214 194)(148 185 216 192)(150 183 218 190)(152 195 220 188)(154 193 222 186)
G:=sub<Sym(224)| (1,182,8,175)(2,169,9,176)(3,170,10,177)(4,171,11,178)(5,172,12,179)(6,173,13,180)(7,174,14,181)(15,32,50,187)(16,33,51,188)(17,34,52,189)(18,35,53,190)(19,36,54,191)(20,37,55,192)(21,38,56,193)(22,39,43,194)(23,40,44,195)(24,41,45,196)(25,42,46,183)(26,29,47,184)(27,30,48,185)(28,31,49,186)(57,206,117,167)(58,207,118,168)(59,208,119,155)(60,209,120,156)(61,210,121,157)(62,197,122,158)(63,198,123,159)(64,199,124,160)(65,200,125,161)(66,201,126,162)(67,202,113,163)(68,203,114,164)(69,204,115,165)(70,205,116,166)(71,128,78,135)(72,129,79,136)(73,130,80,137)(74,131,81,138)(75,132,82,139)(76,133,83,140)(77,134,84,127)(85,221,92,214)(86,222,93,215)(87,223,94,216)(88,224,95,217)(89,211,96,218)(90,212,97,219)(91,213,98,220)(99,143,106,150)(100,144,107,151)(101,145,108,152)(102,146,109,153)(103,147,110,154)(104,148,111,141)(105,149,112,142), (1,146,131,221)(2,147,132,222)(3,148,133,223)(4,149,134,224)(5,150,135,211)(6,151,136,212)(7,152,137,213)(8,153,138,214)(9,154,139,215)(10,141,140,216)(11,142,127,217)(12,143,128,218)(13,144,129,219)(14,145,130,220)(15,165,43,197)(16,166,44,198)(17,167,45,199)(18,168,46,200)(19,155,47,201)(20,156,48,202)(21,157,49,203)(22,158,50,204)(23,159,51,205)(24,160,52,206)(25,161,53,207)(26,162,54,208)(27,163,55,209)(28,164,56,210)(29,66,191,119)(30,67,192,120)(31,68,193,121)(32,69,194,122)(33,70,195,123)(34,57,196,124)(35,58,183,125)(36,59,184,126)(37,60,185,113)(38,61,186,114)(39,62,187,115)(40,63,188,116)(41,64,189,117)(42,65,190,118)(71,96,172,99)(72,97,173,100)(73,98,174,101)(74,85,175,102)(75,86,176,103)(76,87,177,104)(77,88,178,105)(78,89,179,106)(79,90,180,107)(80,91,181,108)(81,92,182,109)(82,93,169,110)(83,94,170,111)(84,95,171,112), (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), (1,62,138,69)(2,114,139,121)(3,60,140,67)(4,126,127,119)(5,58,128,65)(6,124,129,117)(7,70,130,63)(8,122,131,115)(9,68,132,61)(10,120,133,113)(11,66,134,59)(12,118,135,125)(13,64,136,57)(14,116,137,123)(15,92,22,102)(16,108,23,98)(17,90,24,100)(18,106,25,96)(19,88,26,112)(20,104,27,94)(21,86,28,110)(29,149,36,217)(30,223,37,141)(31,147,38,215)(32,221,39,153)(33,145,40,213)(34,219,41,151)(35,143,42,211)(43,109,50,85)(44,91,51,101)(45,107,52,97)(46,89,53,99)(47,105,54,95)(48,87,55,111)(49,103,56,93)(71,200,179,207)(72,167,180,160)(73,198,181,205)(74,165,182,158)(75,210,169,203)(76,163,170,156)(77,208,171,201)(78,161,172,168)(79,206,173,199)(80,159,174,166)(81,204,175,197)(82,157,176,164)(83,202,177,209)(84,155,178,162)(142,191,224,184)(144,189,212,196)(146,187,214,194)(148,185,216,192)(150,183,218,190)(152,195,220,188)(154,193,222,186)>;
G:=Group( (1,182,8,175)(2,169,9,176)(3,170,10,177)(4,171,11,178)(5,172,12,179)(6,173,13,180)(7,174,14,181)(15,32,50,187)(16,33,51,188)(17,34,52,189)(18,35,53,190)(19,36,54,191)(20,37,55,192)(21,38,56,193)(22,39,43,194)(23,40,44,195)(24,41,45,196)(25,42,46,183)(26,29,47,184)(27,30,48,185)(28,31,49,186)(57,206,117,167)(58,207,118,168)(59,208,119,155)(60,209,120,156)(61,210,121,157)(62,197,122,158)(63,198,123,159)(64,199,124,160)(65,200,125,161)(66,201,126,162)(67,202,113,163)(68,203,114,164)(69,204,115,165)(70,205,116,166)(71,128,78,135)(72,129,79,136)(73,130,80,137)(74,131,81,138)(75,132,82,139)(76,133,83,140)(77,134,84,127)(85,221,92,214)(86,222,93,215)(87,223,94,216)(88,224,95,217)(89,211,96,218)(90,212,97,219)(91,213,98,220)(99,143,106,150)(100,144,107,151)(101,145,108,152)(102,146,109,153)(103,147,110,154)(104,148,111,141)(105,149,112,142), (1,146,131,221)(2,147,132,222)(3,148,133,223)(4,149,134,224)(5,150,135,211)(6,151,136,212)(7,152,137,213)(8,153,138,214)(9,154,139,215)(10,141,140,216)(11,142,127,217)(12,143,128,218)(13,144,129,219)(14,145,130,220)(15,165,43,197)(16,166,44,198)(17,167,45,199)(18,168,46,200)(19,155,47,201)(20,156,48,202)(21,157,49,203)(22,158,50,204)(23,159,51,205)(24,160,52,206)(25,161,53,207)(26,162,54,208)(27,163,55,209)(28,164,56,210)(29,66,191,119)(30,67,192,120)(31,68,193,121)(32,69,194,122)(33,70,195,123)(34,57,196,124)(35,58,183,125)(36,59,184,126)(37,60,185,113)(38,61,186,114)(39,62,187,115)(40,63,188,116)(41,64,189,117)(42,65,190,118)(71,96,172,99)(72,97,173,100)(73,98,174,101)(74,85,175,102)(75,86,176,103)(76,87,177,104)(77,88,178,105)(78,89,179,106)(79,90,180,107)(80,91,181,108)(81,92,182,109)(82,93,169,110)(83,94,170,111)(84,95,171,112), (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), (1,62,138,69)(2,114,139,121)(3,60,140,67)(4,126,127,119)(5,58,128,65)(6,124,129,117)(7,70,130,63)(8,122,131,115)(9,68,132,61)(10,120,133,113)(11,66,134,59)(12,118,135,125)(13,64,136,57)(14,116,137,123)(15,92,22,102)(16,108,23,98)(17,90,24,100)(18,106,25,96)(19,88,26,112)(20,104,27,94)(21,86,28,110)(29,149,36,217)(30,223,37,141)(31,147,38,215)(32,221,39,153)(33,145,40,213)(34,219,41,151)(35,143,42,211)(43,109,50,85)(44,91,51,101)(45,107,52,97)(46,89,53,99)(47,105,54,95)(48,87,55,111)(49,103,56,93)(71,200,179,207)(72,167,180,160)(73,198,181,205)(74,165,182,158)(75,210,169,203)(76,163,170,156)(77,208,171,201)(78,161,172,168)(79,206,173,199)(80,159,174,166)(81,204,175,197)(82,157,176,164)(83,202,177,209)(84,155,178,162)(142,191,224,184)(144,189,212,196)(146,187,214,194)(148,185,216,192)(150,183,218,190)(152,195,220,188)(154,193,222,186) );
G=PermutationGroup([[(1,182,8,175),(2,169,9,176),(3,170,10,177),(4,171,11,178),(5,172,12,179),(6,173,13,180),(7,174,14,181),(15,32,50,187),(16,33,51,188),(17,34,52,189),(18,35,53,190),(19,36,54,191),(20,37,55,192),(21,38,56,193),(22,39,43,194),(23,40,44,195),(24,41,45,196),(25,42,46,183),(26,29,47,184),(27,30,48,185),(28,31,49,186),(57,206,117,167),(58,207,118,168),(59,208,119,155),(60,209,120,156),(61,210,121,157),(62,197,122,158),(63,198,123,159),(64,199,124,160),(65,200,125,161),(66,201,126,162),(67,202,113,163),(68,203,114,164),(69,204,115,165),(70,205,116,166),(71,128,78,135),(72,129,79,136),(73,130,80,137),(74,131,81,138),(75,132,82,139),(76,133,83,140),(77,134,84,127),(85,221,92,214),(86,222,93,215),(87,223,94,216),(88,224,95,217),(89,211,96,218),(90,212,97,219),(91,213,98,220),(99,143,106,150),(100,144,107,151),(101,145,108,152),(102,146,109,153),(103,147,110,154),(104,148,111,141),(105,149,112,142)], [(1,146,131,221),(2,147,132,222),(3,148,133,223),(4,149,134,224),(5,150,135,211),(6,151,136,212),(7,152,137,213),(8,153,138,214),(9,154,139,215),(10,141,140,216),(11,142,127,217),(12,143,128,218),(13,144,129,219),(14,145,130,220),(15,165,43,197),(16,166,44,198),(17,167,45,199),(18,168,46,200),(19,155,47,201),(20,156,48,202),(21,157,49,203),(22,158,50,204),(23,159,51,205),(24,160,52,206),(25,161,53,207),(26,162,54,208),(27,163,55,209),(28,164,56,210),(29,66,191,119),(30,67,192,120),(31,68,193,121),(32,69,194,122),(33,70,195,123),(34,57,196,124),(35,58,183,125),(36,59,184,126),(37,60,185,113),(38,61,186,114),(39,62,187,115),(40,63,188,116),(41,64,189,117),(42,65,190,118),(71,96,172,99),(72,97,173,100),(73,98,174,101),(74,85,175,102),(75,86,176,103),(76,87,177,104),(77,88,178,105),(78,89,179,106),(79,90,180,107),(80,91,181,108),(81,92,182,109),(82,93,169,110),(83,94,170,111),(84,95,171,112)], [(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)], [(1,62,138,69),(2,114,139,121),(3,60,140,67),(4,126,127,119),(5,58,128,65),(6,124,129,117),(7,70,130,63),(8,122,131,115),(9,68,132,61),(10,120,133,113),(11,66,134,59),(12,118,135,125),(13,64,136,57),(14,116,137,123),(15,92,22,102),(16,108,23,98),(17,90,24,100),(18,106,25,96),(19,88,26,112),(20,104,27,94),(21,86,28,110),(29,149,36,217),(30,223,37,141),(31,147,38,215),(32,221,39,153),(33,145,40,213),(34,219,41,151),(35,143,42,211),(43,109,50,85),(44,91,51,101),(45,107,52,97),(46,89,53,99),(47,105,54,95),(48,87,55,111),(49,103,56,93),(71,200,179,207),(72,167,180,160),(73,198,181,205),(74,165,182,158),(75,210,169,203),(76,163,170,156),(77,208,171,201),(78,161,172,168),(79,206,173,199),(80,159,174,166),(81,204,175,197),(82,157,176,164),(83,202,177,209),(84,155,178,162),(142,191,224,184),(144,189,212,196),(146,187,214,194),(148,185,216,192),(150,183,218,190),(152,195,220,188),(154,193,222,186)]])
124 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | ··· | 4N | 4O | ··· | 4V | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28BT |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
124 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | - | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | Q8 | D7 | C4○D4 | D14 | D14 | Dic14 | C4○D28 |
| kernel | C42.274D14 | C4×Dic14 | C28⋊2Q8 | C28.6Q8 | C28.48D4 | C23.21D14 | C2×C4×C28 | C2×C28 | C2×C42 | C28 | C42 | C22×C4 | C2×C4 | C4 |
| # reps | 1 | 4 | 2 | 2 | 4 | 2 | 1 | 4 | 3 | 8 | 12 | 9 | 24 | 48 |
Matrix representation of C42.274D14 ►in GL4(𝔽29) generated by
| 17 | 0 | 0 | 0 |
| 15 | 12 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 17 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 |
| 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 17 |
| 4 | 0 | 0 | 0 |
| 20 | 7 | 0 | 0 |
| 0 | 0 | 23 | 0 |
| 0 | 0 | 0 | 5 |
| 10 | 16 | 0 | 0 |
| 21 | 19 | 0 | 0 |
| 0 | 0 | 0 | 24 |
| 0 | 0 | 6 | 0 |
G:=sub<GL(4,GF(29))| [17,15,0,0,0,12,0,0,0,0,1,0,0,0,0,1],[17,0,0,0,0,17,0,0,0,0,17,0,0,0,0,17],[4,20,0,0,0,7,0,0,0,0,23,0,0,0,0,5],[10,21,0,0,16,19,0,0,0,0,0,6,0,0,24,0] >;
C42.274D14 in GAP, Magma, Sage, TeX
C_4^2._{274}D_{14} % in TeX
G:=Group("C4^2.274D14"); // GroupNames label
G:=SmallGroup(448,923);
// by ID
G=gap.SmallGroup(448,923);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,477,232,100,675,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2*b^2,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,b*c=c*b,b*d=d*b,d*c*d^-1=b^2*c^-1>;
// generators/relations