metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.187D14, C28⋊C8⋊7C2, C4⋊C4.6Dic7, C14.37(C8○D4), (C4×C28).19C22, C42⋊C2.8D7, C22⋊C4.3Dic7, C4.134(C4○D28), C28.250(C4○D4), C23.8(C2×Dic7), (C2×C28).847C23, C42.D7⋊22C2, (C22×C4).109D14, C2.5(Q8.Dic7), C28.55D4.17C2, C7⋊5(C42.7C22), C14.46(C42⋊C2), (C22×C28).373C22, C22.44(C22×Dic7), C2.10(C23.21D14), (C4×C7⋊C8)⋊26C2, (C7×C4⋊C4).9C4, (C7×C22⋊C4).4C4, (C2×C28).161(C2×C4), (C2×C7⋊C8).314C22, (C2×C4).19(C2×Dic7), (C7×C42⋊C2).9C2, (C22×C14).58(C2×C4), (C2×C4).789(C22×D7), (C2×C14).184(C22×C4), SmallGroup(448,534)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.187D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2b, ab=ba, cac-1=dad-1=ab2, bc=cb, bd=db, dcd-1=a2c-1 >
Subgroups: 244 in 96 conjugacy classes, 55 normal (23 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, C23, C14, C14, C14, C42, C22⋊C4, C4⋊C4, C2×C8, C22×C4, C28, C28, C2×C14, C2×C14, C4×C8, C8⋊C4, C22⋊C8, C4⋊C8, C42⋊C2, C7⋊C8, C2×C28, C2×C28, C2×C28, C22×C14, C42.7C22, C2×C7⋊C8, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C22×C28, C4×C7⋊C8, C42.D7, C28⋊C8, C28.55D4, C7×C42⋊C2, C42.187D14
Quotients: C1, C2, C4, C22, C2×C4, C23, D7, C22×C4, C4○D4, Dic7, D14, C42⋊C2, C8○D4, C2×Dic7, C22×D7, C42.7C22, C4○D28, C22×Dic7, C23.21D14, Q8.Dic7, C42.187D14
►On 224 points
Generators in S224
(1 87 15 109)(2 95 16 103)(3 89 17 111)(4 97 18 105)(5 91 19 99)(6 85 20 107)(7 93 21 101)(8 94 22 102)(9 88 23 110)(10 96 24 104)(11 90 25 112)(12 98 26 106)(13 92 27 100)(14 86 28 108)(29 135 43 160)(30 129 44 168)(31 137 45 162)(32 131 46 156)(33 139 47 164)(34 133 48 158)(35 127 49 166)(36 128 50 167)(37 136 51 161)(38 130 52 155)(39 138 53 163)(40 132 54 157)(41 140 55 165)(42 134 56 159)(57 119 64 189)(58 183 65 113)(59 121 66 191)(60 185 67 115)(61 123 68 193)(62 187 69 117)(63 125 70 195)(71 181 211 174)(72 210 212 203)(73 169 213 176)(74 198 214 205)(75 171 215 178)(76 200 216 207)(77 173 217 180)(78 202 218 209)(79 175 219 182)(80 204 220 197)(81 177 221 170)(82 206 222 199)(83 179 223 172)(84 208 224 201)(114 141 184 148)(116 143 186 150)(118 145 188 152)(120 147 190 154)(122 149 192 142)(124 151 194 144)(126 153 196 146)
(1 36 8 29)(2 37 9 30)(3 38 10 31)(4 39 11 32)(5 40 12 33)(6 41 13 34)(7 42 14 35)(15 50 22 43)(16 51 23 44)(17 52 24 45)(18 53 25 46)(19 54 26 47)(20 55 27 48)(21 56 28 49)(57 208 153 180)(58 209 154 181)(59 210 141 182)(60 197 142 169)(61 198 143 170)(62 199 144 171)(63 200 145 172)(64 201 146 173)(65 202 147 174)(66 203 148 175)(67 204 149 176)(68 205 150 177)(69 206 151 178)(70 207 152 179)(71 113 218 190)(72 114 219 191)(73 115 220 192)(74 116 221 193)(75 117 222 194)(76 118 223 195)(77 119 224 196)(78 120 211 183)(79 121 212 184)(80 122 213 185)(81 123 214 186)(82 124 215 187)(83 125 216 188)(84 126 217 189)(85 140 92 133)(86 127 93 134)(87 128 94 135)(88 129 95 136)(89 130 96 137)(90 131 97 138)(91 132 98 139)(99 157 106 164)(100 158 107 165)(101 159 108 166)(102 160 109 167)(103 161 110 168)(104 162 111 155)(105 163 112 156)
(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 66 50 210 8 148 43 182)(2 58 51 202 9 154 44 174)(3 64 52 208 10 146 45 180)(4 70 53 200 11 152 46 172)(5 62 54 206 12 144 47 178)(6 68 55 198 13 150 48 170)(7 60 56 204 14 142 49 176)(15 59 36 203 22 141 29 175)(16 65 37 209 23 147 30 181)(17 57 38 201 24 153 31 173)(18 63 39 207 25 145 32 179)(19 69 40 199 26 151 33 171)(20 61 41 205 27 143 34 177)(21 67 42 197 28 149 35 169)(71 88 183 168 218 95 120 161)(72 109 184 128 219 102 121 135)(73 86 185 166 220 93 122 159)(74 107 186 140 221 100 123 133)(75 98 187 164 222 91 124 157)(76 105 188 138 223 112 125 131)(77 96 189 162 224 89 126 155)(78 103 190 136 211 110 113 129)(79 94 191 160 212 87 114 167)(80 101 192 134 213 108 115 127)(81 92 193 158 214 85 116 165)(82 99 194 132 215 106 117 139)(83 90 195 156 216 97 118 163)(84 111 196 130 217 104 119 137)
G:=sub<Sym(224)| (1,87,15,109)(2,95,16,103)(3,89,17,111)(4,97,18,105)(5,91,19,99)(6,85,20,107)(7,93,21,101)(8,94,22,102)(9,88,23,110)(10,96,24,104)(11,90,25,112)(12,98,26,106)(13,92,27,100)(14,86,28,108)(29,135,43,160)(30,129,44,168)(31,137,45,162)(32,131,46,156)(33,139,47,164)(34,133,48,158)(35,127,49,166)(36,128,50,167)(37,136,51,161)(38,130,52,155)(39,138,53,163)(40,132,54,157)(41,140,55,165)(42,134,56,159)(57,119,64,189)(58,183,65,113)(59,121,66,191)(60,185,67,115)(61,123,68,193)(62,187,69,117)(63,125,70,195)(71,181,211,174)(72,210,212,203)(73,169,213,176)(74,198,214,205)(75,171,215,178)(76,200,216,207)(77,173,217,180)(78,202,218,209)(79,175,219,182)(80,204,220,197)(81,177,221,170)(82,206,222,199)(83,179,223,172)(84,208,224,201)(114,141,184,148)(116,143,186,150)(118,145,188,152)(120,147,190,154)(122,149,192,142)(124,151,194,144)(126,153,196,146), (1,36,8,29)(2,37,9,30)(3,38,10,31)(4,39,11,32)(5,40,12,33)(6,41,13,34)(7,42,14,35)(15,50,22,43)(16,51,23,44)(17,52,24,45)(18,53,25,46)(19,54,26,47)(20,55,27,48)(21,56,28,49)(57,208,153,180)(58,209,154,181)(59,210,141,182)(60,197,142,169)(61,198,143,170)(62,199,144,171)(63,200,145,172)(64,201,146,173)(65,202,147,174)(66,203,148,175)(67,204,149,176)(68,205,150,177)(69,206,151,178)(70,207,152,179)(71,113,218,190)(72,114,219,191)(73,115,220,192)(74,116,221,193)(75,117,222,194)(76,118,223,195)(77,119,224,196)(78,120,211,183)(79,121,212,184)(80,122,213,185)(81,123,214,186)(82,124,215,187)(83,125,216,188)(84,126,217,189)(85,140,92,133)(86,127,93,134)(87,128,94,135)(88,129,95,136)(89,130,96,137)(90,131,97,138)(91,132,98,139)(99,157,106,164)(100,158,107,165)(101,159,108,166)(102,160,109,167)(103,161,110,168)(104,162,111,155)(105,163,112,156), (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), (1,66,50,210,8,148,43,182)(2,58,51,202,9,154,44,174)(3,64,52,208,10,146,45,180)(4,70,53,200,11,152,46,172)(5,62,54,206,12,144,47,178)(6,68,55,198,13,150,48,170)(7,60,56,204,14,142,49,176)(15,59,36,203,22,141,29,175)(16,65,37,209,23,147,30,181)(17,57,38,201,24,153,31,173)(18,63,39,207,25,145,32,179)(19,69,40,199,26,151,33,171)(20,61,41,205,27,143,34,177)(21,67,42,197,28,149,35,169)(71,88,183,168,218,95,120,161)(72,109,184,128,219,102,121,135)(73,86,185,166,220,93,122,159)(74,107,186,140,221,100,123,133)(75,98,187,164,222,91,124,157)(76,105,188,138,223,112,125,131)(77,96,189,162,224,89,126,155)(78,103,190,136,211,110,113,129)(79,94,191,160,212,87,114,167)(80,101,192,134,213,108,115,127)(81,92,193,158,214,85,116,165)(82,99,194,132,215,106,117,139)(83,90,195,156,216,97,118,163)(84,111,196,130,217,104,119,137)>;
G:=Group( (1,87,15,109)(2,95,16,103)(3,89,17,111)(4,97,18,105)(5,91,19,99)(6,85,20,107)(7,93,21,101)(8,94,22,102)(9,88,23,110)(10,96,24,104)(11,90,25,112)(12,98,26,106)(13,92,27,100)(14,86,28,108)(29,135,43,160)(30,129,44,168)(31,137,45,162)(32,131,46,156)(33,139,47,164)(34,133,48,158)(35,127,49,166)(36,128,50,167)(37,136,51,161)(38,130,52,155)(39,138,53,163)(40,132,54,157)(41,140,55,165)(42,134,56,159)(57,119,64,189)(58,183,65,113)(59,121,66,191)(60,185,67,115)(61,123,68,193)(62,187,69,117)(63,125,70,195)(71,181,211,174)(72,210,212,203)(73,169,213,176)(74,198,214,205)(75,171,215,178)(76,200,216,207)(77,173,217,180)(78,202,218,209)(79,175,219,182)(80,204,220,197)(81,177,221,170)(82,206,222,199)(83,179,223,172)(84,208,224,201)(114,141,184,148)(116,143,186,150)(118,145,188,152)(120,147,190,154)(122,149,192,142)(124,151,194,144)(126,153,196,146), (1,36,8,29)(2,37,9,30)(3,38,10,31)(4,39,11,32)(5,40,12,33)(6,41,13,34)(7,42,14,35)(15,50,22,43)(16,51,23,44)(17,52,24,45)(18,53,25,46)(19,54,26,47)(20,55,27,48)(21,56,28,49)(57,208,153,180)(58,209,154,181)(59,210,141,182)(60,197,142,169)(61,198,143,170)(62,199,144,171)(63,200,145,172)(64,201,146,173)(65,202,147,174)(66,203,148,175)(67,204,149,176)(68,205,150,177)(69,206,151,178)(70,207,152,179)(71,113,218,190)(72,114,219,191)(73,115,220,192)(74,116,221,193)(75,117,222,194)(76,118,223,195)(77,119,224,196)(78,120,211,183)(79,121,212,184)(80,122,213,185)(81,123,214,186)(82,124,215,187)(83,125,216,188)(84,126,217,189)(85,140,92,133)(86,127,93,134)(87,128,94,135)(88,129,95,136)(89,130,96,137)(90,131,97,138)(91,132,98,139)(99,157,106,164)(100,158,107,165)(101,159,108,166)(102,160,109,167)(103,161,110,168)(104,162,111,155)(105,163,112,156), (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), (1,66,50,210,8,148,43,182)(2,58,51,202,9,154,44,174)(3,64,52,208,10,146,45,180)(4,70,53,200,11,152,46,172)(5,62,54,206,12,144,47,178)(6,68,55,198,13,150,48,170)(7,60,56,204,14,142,49,176)(15,59,36,203,22,141,29,175)(16,65,37,209,23,147,30,181)(17,57,38,201,24,153,31,173)(18,63,39,207,25,145,32,179)(19,69,40,199,26,151,33,171)(20,61,41,205,27,143,34,177)(21,67,42,197,28,149,35,169)(71,88,183,168,218,95,120,161)(72,109,184,128,219,102,121,135)(73,86,185,166,220,93,122,159)(74,107,186,140,221,100,123,133)(75,98,187,164,222,91,124,157)(76,105,188,138,223,112,125,131)(77,96,189,162,224,89,126,155)(78,103,190,136,211,110,113,129)(79,94,191,160,212,87,114,167)(80,101,192,134,213,108,115,127)(81,92,193,158,214,85,116,165)(82,99,194,132,215,106,117,139)(83,90,195,156,216,97,118,163)(84,111,196,130,217,104,119,137) );
G=PermutationGroup([[(1,87,15,109),(2,95,16,103),(3,89,17,111),(4,97,18,105),(5,91,19,99),(6,85,20,107),(7,93,21,101),(8,94,22,102),(9,88,23,110),(10,96,24,104),(11,90,25,112),(12,98,26,106),(13,92,27,100),(14,86,28,108),(29,135,43,160),(30,129,44,168),(31,137,45,162),(32,131,46,156),(33,139,47,164),(34,133,48,158),(35,127,49,166),(36,128,50,167),(37,136,51,161),(38,130,52,155),(39,138,53,163),(40,132,54,157),(41,140,55,165),(42,134,56,159),(57,119,64,189),(58,183,65,113),(59,121,66,191),(60,185,67,115),(61,123,68,193),(62,187,69,117),(63,125,70,195),(71,181,211,174),(72,210,212,203),(73,169,213,176),(74,198,214,205),(75,171,215,178),(76,200,216,207),(77,173,217,180),(78,202,218,209),(79,175,219,182),(80,204,220,197),(81,177,221,170),(82,206,222,199),(83,179,223,172),(84,208,224,201),(114,141,184,148),(116,143,186,150),(118,145,188,152),(120,147,190,154),(122,149,192,142),(124,151,194,144),(126,153,196,146)], [(1,36,8,29),(2,37,9,30),(3,38,10,31),(4,39,11,32),(5,40,12,33),(6,41,13,34),(7,42,14,35),(15,50,22,43),(16,51,23,44),(17,52,24,45),(18,53,25,46),(19,54,26,47),(20,55,27,48),(21,56,28,49),(57,208,153,180),(58,209,154,181),(59,210,141,182),(60,197,142,169),(61,198,143,170),(62,199,144,171),(63,200,145,172),(64,201,146,173),(65,202,147,174),(66,203,148,175),(67,204,149,176),(68,205,150,177),(69,206,151,178),(70,207,152,179),(71,113,218,190),(72,114,219,191),(73,115,220,192),(74,116,221,193),(75,117,222,194),(76,118,223,195),(77,119,224,196),(78,120,211,183),(79,121,212,184),(80,122,213,185),(81,123,214,186),(82,124,215,187),(83,125,216,188),(84,126,217,189),(85,140,92,133),(86,127,93,134),(87,128,94,135),(88,129,95,136),(89,130,96,137),(90,131,97,138),(91,132,98,139),(99,157,106,164),(100,158,107,165),(101,159,108,166),(102,160,109,167),(103,161,110,168),(104,162,111,155),(105,163,112,156)], [(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)], [(1,66,50,210,8,148,43,182),(2,58,51,202,9,154,44,174),(3,64,52,208,10,146,45,180),(4,70,53,200,11,152,46,172),(5,62,54,206,12,144,47,178),(6,68,55,198,13,150,48,170),(7,60,56,204,14,142,49,176),(15,59,36,203,22,141,29,175),(16,65,37,209,23,147,30,181),(17,57,38,201,24,153,31,173),(18,63,39,207,25,145,32,179),(19,69,40,199,26,151,33,171),(20,61,41,205,27,143,34,177),(21,67,42,197,28,149,35,169),(71,88,183,168,218,95,120,161),(72,109,184,128,219,102,121,135),(73,86,185,166,220,93,122,159),(74,107,186,140,221,100,123,133),(75,98,187,164,222,91,124,157),(76,105,188,138,223,112,125,131),(77,96,189,162,224,89,126,155),(78,103,190,136,211,110,113,129),(79,94,191,160,212,87,114,167),(80,101,192,134,213,108,115,127),(81,92,193,158,214,85,116,165),(82,99,194,132,215,106,117,139),(83,90,195,156,216,97,118,163),(84,111,196,130,217,104,119,137)]])
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 7A | 7B | 7C | 8A | ··· | 8H | 8I | 8J | 8K | 8L | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 2 | 2 | 2 | 14 | ··· | 14 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 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 | C4○D4 | D14 | Dic7 | Dic7 | D14 | C8○D4 | C4○D28 | Q8.Dic7 |
| kernel | C42.187D14 | C4×C7⋊C8 | C42.D7 | C28⋊C8 | C28.55D4 | C7×C42⋊C2 | C7×C22⋊C4 | C7×C4⋊C4 | C42⋊C2 | C28 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 4 | 4 | 3 | 4 | 6 | 6 | 6 | 3 | 8 | 24 | 12 |
Matrix representation of C42.187D14 ►in GL4(𝔽113) generated by
| 98 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 15 | 0 |
| 0 | 0 | 44 | 98 |
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 98 | 0 |
| 0 | 0 | 0 | 98 |
| 30 | 78 | 0 | 0 |
| 0 | 64 | 0 | 0 |
| 0 | 0 | 1 | 25 |
| 0 | 0 | 0 | 112 |
| 39 | 110 | 0 | 0 |
| 17 | 74 | 0 | 0 |
| 0 | 0 | 95 | 2 |
| 0 | 0 | 15 | 18 |
G:=sub<GL(4,GF(113))| [98,0,0,0,0,98,0,0,0,0,15,44,0,0,0,98],[112,0,0,0,0,112,0,0,0,0,98,0,0,0,0,98],[30,0,0,0,78,64,0,0,0,0,1,0,0,0,25,112],[39,17,0,0,110,74,0,0,0,0,95,15,0,0,2,18] >;
C42.187D14 in GAP, Magma, Sage, TeX
C_4^2._{187}D_{14} % in TeX
G:=Group("C4^2.187D14"); // GroupNames label
G:=SmallGroup(448,534);
// by ID
G=gap.SmallGroup(448,534);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,56,120,422,387,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=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*c^-1>;
// generators/relations