metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.200D14, Dic7.6M4(2), C4⋊C8⋊17D7, (C4×D7)⋊2C8, C4.14(C8×D7), C28.11(C2×C8), D14⋊C8.7C2, C28⋊C8⋊12C2, D14.4(C2×C8), (C8×Dic7)⋊23C2, (C2×C8).215D14, (C4×Dic7).6C4, Dic7.9(C2×C8), (D7×C42).2C2, C2.6(D7×M4(2)), C14.10(C22×C8), (C4×C28).59C22, C28.304(C4○D4), (C2×C56).209C22, (C2×C28).830C23, C7⋊3(C42.12C4), C4.52(Q8⋊2D7), C14.26(C2×M4(2)), C4.130(D4⋊2D7), C14.31(C42⋊C2), (C4×Dic7).301C22, (C7×C4⋊C8)⋊14C2, (C2×C4×D7).6C4, C2.12(D7×C2×C8), C22.47(C2×C4×D7), (C2×C28).69(C2×C4), (C2×C4).145(C4×D7), C2.3(C4⋊C4⋊7D7), (C2×C7⋊C8).305C22, (C2×C4×D7).276C22, (C2×C14).85(C22×C4), (C2×Dic7).88(C2×C4), (C22×D7).57(C2×C4), (C2×C4).772(C22×D7), SmallGroup(448,367)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.200D14
G = < a,b,c,d | a4=b4=1, c14=b-1, d2=a2b, ab=ba, cac-1=dad-1=a-1, bc=cb, bd=db, dcd-1=a2b2c13 >
Subgroups: 452 in 118 conjugacy classes, 61 normal (37 characteristic)
C1, C2, C2, C4, 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, C28, D14, D14, C2×C14, C4×C8, C22⋊C8, C4⋊C8, C4⋊C8, C2×C42, C7⋊C8, C56, C4×D7, C4×D7, C2×Dic7, C2×C28, C22×D7, C42.12C4, C2×C7⋊C8, C4×Dic7, C4×C28, C2×C56, C2×C4×D7, C28⋊C8, C8×Dic7, D14⋊C8, C7×C4⋊C8, D7×C42, C42.200D14
Quotients: C1, C2, C4, C22, C8, C2×C4, C23, D7, C2×C8, M4(2), C22×C4, C4○D4, D14, C42⋊C2, C22×C8, C2×M4(2), C4×D7, C22×D7, C42.12C4, C8×D7, C2×C4×D7, D4⋊2D7, Q8⋊2D7, C4⋊C4⋊7D7, D7×C2×C8, D7×M4(2), C42.200D14
►On 224 points
Generators in S224
(1 186 104 156)(2 157 105 187)(3 188 106 158)(4 159 107 189)(5 190 108 160)(6 161 109 191)(7 192 110 162)(8 163 111 193)(9 194 112 164)(10 165 57 195)(11 196 58 166)(12 167 59 197)(13 198 60 168)(14 113 61 199)(15 200 62 114)(16 115 63 201)(17 202 64 116)(18 117 65 203)(19 204 66 118)(20 119 67 205)(21 206 68 120)(22 121 69 207)(23 208 70 122)(24 123 71 209)(25 210 72 124)(26 125 73 211)(27 212 74 126)(28 127 75 213)(29 214 76 128)(30 129 77 215)(31 216 78 130)(32 131 79 217)(33 218 80 132)(34 133 81 219)(35 220 82 134)(36 135 83 221)(37 222 84 136)(38 137 85 223)(39 224 86 138)(40 139 87 169)(41 170 88 140)(42 141 89 171)(43 172 90 142)(44 143 91 173)(45 174 92 144)(46 145 93 175)(47 176 94 146)(48 147 95 177)(49 178 96 148)(50 149 97 179)(51 180 98 150)(52 151 99 181)(53 182 100 152)(54 153 101 183)(55 184 102 154)(56 155 103 185)
(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 90 103 29 42 62 75)(2 102 91 41 30 74 63 13)(3 40 92 73 31 12 64 101)(4 72 93 11 32 100 65 39)(5 10 94 99 33 38 66 71)(6 98 95 37 34 70 67 9)(7 36 96 69 35 8 68 97)(15 28 104 61 43 56 76 89)(16 60 105 55 44 88 77 27)(17 54 106 87 45 26 78 59)(18 86 107 25 46 58 79 53)(19 24 108 57 47 52 80 85)(20 112 109 51 48 84 81 23)(21 50 110 83 49 22 82 111)(113 172 185 128 141 200 213 156)(114 127 186 199 142 155 214 171)(115 198 187 154 143 170 215 126)(116 153 188 169 144 125 216 197)(117 224 189 124 145 196 217 152)(118 123 190 195 146 151 218 223)(119 194 191 150 147 222 219 122)(120 149 192 221 148 121 220 193)(129 212 201 168 157 184 173 140)(130 167 202 183 158 139 174 211)(131 182 203 138 159 210 175 166)(132 137 204 209 160 165 176 181)(133 208 205 164 161 180 177 136)(134 163 206 179 162 135 178 207)
G:=sub<Sym(224)| (1,186,104,156)(2,157,105,187)(3,188,106,158)(4,159,107,189)(5,190,108,160)(6,161,109,191)(7,192,110,162)(8,163,111,193)(9,194,112,164)(10,165,57,195)(11,196,58,166)(12,167,59,197)(13,198,60,168)(14,113,61,199)(15,200,62,114)(16,115,63,201)(17,202,64,116)(18,117,65,203)(19,204,66,118)(20,119,67,205)(21,206,68,120)(22,121,69,207)(23,208,70,122)(24,123,71,209)(25,210,72,124)(26,125,73,211)(27,212,74,126)(28,127,75,213)(29,214,76,128)(30,129,77,215)(31,216,78,130)(32,131,79,217)(33,218,80,132)(34,133,81,219)(35,220,82,134)(36,135,83,221)(37,222,84,136)(38,137,85,223)(39,224,86,138)(40,139,87,169)(41,170,88,140)(42,141,89,171)(43,172,90,142)(44,143,91,173)(45,174,92,144)(46,145,93,175)(47,176,94,146)(48,147,95,177)(49,178,96,148)(50,149,97,179)(51,180,98,150)(52,151,99,181)(53,182,100,152)(54,153,101,183)(55,184,102,154)(56,155,103,185), (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), (1,14,90,103,29,42,62,75)(2,102,91,41,30,74,63,13)(3,40,92,73,31,12,64,101)(4,72,93,11,32,100,65,39)(5,10,94,99,33,38,66,71)(6,98,95,37,34,70,67,9)(7,36,96,69,35,8,68,97)(15,28,104,61,43,56,76,89)(16,60,105,55,44,88,77,27)(17,54,106,87,45,26,78,59)(18,86,107,25,46,58,79,53)(19,24,108,57,47,52,80,85)(20,112,109,51,48,84,81,23)(21,50,110,83,49,22,82,111)(113,172,185,128,141,200,213,156)(114,127,186,199,142,155,214,171)(115,198,187,154,143,170,215,126)(116,153,188,169,144,125,216,197)(117,224,189,124,145,196,217,152)(118,123,190,195,146,151,218,223)(119,194,191,150,147,222,219,122)(120,149,192,221,148,121,220,193)(129,212,201,168,157,184,173,140)(130,167,202,183,158,139,174,211)(131,182,203,138,159,210,175,166)(132,137,204,209,160,165,176,181)(133,208,205,164,161,180,177,136)(134,163,206,179,162,135,178,207)>;
G:=Group( (1,186,104,156)(2,157,105,187)(3,188,106,158)(4,159,107,189)(5,190,108,160)(6,161,109,191)(7,192,110,162)(8,163,111,193)(9,194,112,164)(10,165,57,195)(11,196,58,166)(12,167,59,197)(13,198,60,168)(14,113,61,199)(15,200,62,114)(16,115,63,201)(17,202,64,116)(18,117,65,203)(19,204,66,118)(20,119,67,205)(21,206,68,120)(22,121,69,207)(23,208,70,122)(24,123,71,209)(25,210,72,124)(26,125,73,211)(27,212,74,126)(28,127,75,213)(29,214,76,128)(30,129,77,215)(31,216,78,130)(32,131,79,217)(33,218,80,132)(34,133,81,219)(35,220,82,134)(36,135,83,221)(37,222,84,136)(38,137,85,223)(39,224,86,138)(40,139,87,169)(41,170,88,140)(42,141,89,171)(43,172,90,142)(44,143,91,173)(45,174,92,144)(46,145,93,175)(47,176,94,146)(48,147,95,177)(49,178,96,148)(50,149,97,179)(51,180,98,150)(52,151,99,181)(53,182,100,152)(54,153,101,183)(55,184,102,154)(56,155,103,185), (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), (1,14,90,103,29,42,62,75)(2,102,91,41,30,74,63,13)(3,40,92,73,31,12,64,101)(4,72,93,11,32,100,65,39)(5,10,94,99,33,38,66,71)(6,98,95,37,34,70,67,9)(7,36,96,69,35,8,68,97)(15,28,104,61,43,56,76,89)(16,60,105,55,44,88,77,27)(17,54,106,87,45,26,78,59)(18,86,107,25,46,58,79,53)(19,24,108,57,47,52,80,85)(20,112,109,51,48,84,81,23)(21,50,110,83,49,22,82,111)(113,172,185,128,141,200,213,156)(114,127,186,199,142,155,214,171)(115,198,187,154,143,170,215,126)(116,153,188,169,144,125,216,197)(117,224,189,124,145,196,217,152)(118,123,190,195,146,151,218,223)(119,194,191,150,147,222,219,122)(120,149,192,221,148,121,220,193)(129,212,201,168,157,184,173,140)(130,167,202,183,158,139,174,211)(131,182,203,138,159,210,175,166)(132,137,204,209,160,165,176,181)(133,208,205,164,161,180,177,136)(134,163,206,179,162,135,178,207) );
G=PermutationGroup([[(1,186,104,156),(2,157,105,187),(3,188,106,158),(4,159,107,189),(5,190,108,160),(6,161,109,191),(7,192,110,162),(8,163,111,193),(9,194,112,164),(10,165,57,195),(11,196,58,166),(12,167,59,197),(13,198,60,168),(14,113,61,199),(15,200,62,114),(16,115,63,201),(17,202,64,116),(18,117,65,203),(19,204,66,118),(20,119,67,205),(21,206,68,120),(22,121,69,207),(23,208,70,122),(24,123,71,209),(25,210,72,124),(26,125,73,211),(27,212,74,126),(28,127,75,213),(29,214,76,128),(30,129,77,215),(31,216,78,130),(32,131,79,217),(33,218,80,132),(34,133,81,219),(35,220,82,134),(36,135,83,221),(37,222,84,136),(38,137,85,223),(39,224,86,138),(40,139,87,169),(41,170,88,140),(42,141,89,171),(43,172,90,142),(44,143,91,173),(45,174,92,144),(46,145,93,175),(47,176,94,146),(48,147,95,177),(49,178,96,148),(50,149,97,179),(51,180,98,150),(52,151,99,181),(53,182,100,152),(54,153,101,183),(55,184,102,154),(56,155,103,185)], [(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)], [(1,14,90,103,29,42,62,75),(2,102,91,41,30,74,63,13),(3,40,92,73,31,12,64,101),(4,72,93,11,32,100,65,39),(5,10,94,99,33,38,66,71),(6,98,95,37,34,70,67,9),(7,36,96,69,35,8,68,97),(15,28,104,61,43,56,76,89),(16,60,105,55,44,88,77,27),(17,54,106,87,45,26,78,59),(18,86,107,25,46,58,79,53),(19,24,108,57,47,52,80,85),(20,112,109,51,48,84,81,23),(21,50,110,83,49,22,82,111),(113,172,185,128,141,200,213,156),(114,127,186,199,142,155,214,171),(115,198,187,154,143,170,215,126),(116,153,188,169,144,125,216,197),(117,224,189,124,145,196,217,152),(118,123,190,195,146,151,218,223),(119,194,191,150,147,222,219,122),(120,149,192,221,148,121,220,193),(129,212,201,168,157,184,173,140),(130,167,202,183,158,139,174,211),(131,182,203,138,159,210,175,166),(132,137,204,209,160,165,176,181),(133,208,205,164,161,180,177,136),(134,163,206,179,162,135,178,207)]])
100 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4P | 4Q | 4R | 7A | 7B | 7C | 8A | ··· | 8H | 8I | ··· | 8P | 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 | 4 | 4 | 7 | 7 | 7 | 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 | 7 | ··· | 7 | 14 | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 14 | ··· | 14 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
100 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | + | ||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | C4 | C8 | D7 | M4(2) | C4○D4 | D14 | D14 | C4×D7 | C8×D7 | D4⋊2D7 | Q8⋊2D7 | D7×M4(2) |
| kernel | C42.200D14 | C28⋊C8 | C8×Dic7 | D14⋊C8 | C7×C4⋊C8 | D7×C42 | C4×Dic7 | C2×C4×D7 | C4×D7 | C4⋊C8 | Dic7 | C28 | C42 | C2×C8 | C2×C4 | C4 | C4 | C4 | C2 |
| # reps | 1 | 1 | 2 | 2 | 1 | 1 | 4 | 4 | 16 | 3 | 4 | 4 | 3 | 6 | 12 | 24 | 3 | 3 | 6 |
Matrix representation of C42.200D14 ►in GL4(𝔽113) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 15 | 0 |
| 0 | 0 | 0 | 98 |
| 15 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 30 | 30 | 0 | 0 |
| 83 | 27 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 112 | 0 |
| 83 | 83 | 0 | 0 |
| 86 | 30 | 0 | 0 |
| 0 | 0 | 0 | 112 |
| 0 | 0 | 112 | 0 |
G:=sub<GL(4,GF(113))| [1,0,0,0,0,1,0,0,0,0,15,0,0,0,0,98],[15,0,0,0,0,15,0,0,0,0,112,0,0,0,0,112],[30,83,0,0,30,27,0,0,0,0,0,112,0,0,1,0],[83,86,0,0,83,30,0,0,0,0,0,112,0,0,112,0] >;
C42.200D14 in GAP, Magma, Sage, TeX
C_4^2._{200}D_{14} % in TeX
G:=Group("C4^2.200D14"); // GroupNames label
G:=SmallGroup(448,367);
// by ID
G=gap.SmallGroup(448,367);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,422,219,58,136,18822]);
// 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^-1,b*c=c*b,b*d=d*b,d*c*d^-1=a^2*b^2*c^13>;
// generators/relations