metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.202D14, D14.2M4(2), C28.10M4(2), C4⋊C8⋊11D7, D14⋊C8.8C2, C56⋊C4⋊21C2, C28⋊C8⋊13C2, (C2×C8).181D14, (D7×C42).3C2, C4.11(C8⋊D7), (C4×C28).61C22, C7⋊3(C42.6C4), (C4×Dic7).19C4, C2.16(D7×M4(2)), C28.305(C4○D4), (C2×C28).832C23, (C2×C56).211C22, C4.54(Q8⋊2D7), C14.27(C2×M4(2)), C4.131(D4⋊2D7), C14.32(C42⋊C2), (C4×Dic7).276C22, (C7×C4⋊C8)⋊16C2, (C2×C4×D7).19C4, (C2×C28).70(C2×C4), (C2×C4).146(C4×D7), C2.12(C2×C8⋊D7), C22.110(C2×C4×D7), C2.9(C4⋊C4⋊7D7), (C2×C7⋊C8).194C22, (C2×C4×D7).278C22, (C2×C14).87(C22×C4), (C2×Dic7).89(C2×C4), (C22×D7).58(C2×C4), (C2×C4).774(C22×D7), SmallGroup(448,369)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.202D14
G = < a,b,c,d | a4=b4=1, c14=b-1, d2=a2b-1, ab=ba, cac-1=dad-1=a-1, bc=cb, bd=db, dcd-1=a2c13 >
Subgroups: 452 in 110 conjugacy classes, 53 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, C28, C28, C28, D14, D14, C2×C14, C8⋊C4, C22⋊C8, C4⋊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, C28⋊C8, C56⋊C4, D14⋊C8, C7×C4⋊C8, D7×C42, C42.202D14
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, C8⋊D7, C2×C4×D7, D4⋊2D7, Q8⋊2D7, C4⋊C4⋊7D7, C2×C8⋊D7, D7×M4(2), C42.202D14
►On 224 points
Generators in S224
(1 108 175 157)(2 158 176 109)(3 110 177 159)(4 160 178 111)(5 112 179 161)(6 162 180 57)(7 58 181 163)(8 164 182 59)(9 60 183 165)(10 166 184 61)(11 62 185 167)(12 168 186 63)(13 64 187 113)(14 114 188 65)(15 66 189 115)(16 116 190 67)(17 68 191 117)(18 118 192 69)(19 70 193 119)(20 120 194 71)(21 72 195 121)(22 122 196 73)(23 74 197 123)(24 124 198 75)(25 76 199 125)(26 126 200 77)(27 78 201 127)(28 128 202 79)(29 80 203 129)(30 130 204 81)(31 82 205 131)(32 132 206 83)(33 84 207 133)(34 134 208 85)(35 86 209 135)(36 136 210 87)(37 88 211 137)(38 138 212 89)(39 90 213 139)(40 140 214 91)(41 92 215 141)(42 142 216 93)(43 94 217 143)(44 144 218 95)(45 96 219 145)(46 146 220 97)(47 98 221 147)(48 148 222 99)(49 100 223 149)(50 150 224 101)(51 102 169 151)(52 152 170 103)(53 104 171 153)(54 154 172 105)(55 106 173 155)(56 156 174 107)
(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 14 189 202 29 42 217 174)(2 201 190 41 30 173 218 13)(3 40 191 172 31 12 219 200)(4 171 192 11 32 199 220 39)(5 10 193 198 33 38 221 170)(6 197 194 37 34 169 222 9)(7 36 195 224 35 8 223 196)(15 28 203 216 43 56 175 188)(16 215 204 55 44 187 176 27)(17 54 205 186 45 26 177 214)(18 185 206 25 46 213 178 53)(19 24 207 212 47 52 179 184)(20 211 208 51 48 183 180 23)(21 50 209 182 49 22 181 210)(57 123 120 88 85 151 148 60)(58 87 121 150 86 59 149 122)(61 119 124 84 89 147 152 112)(62 83 125 146 90 111 153 118)(63 145 126 110 91 117 154 82)(64 109 127 116 92 81 155 144)(65 115 128 80 93 143 156 108)(66 79 129 142 94 107 157 114)(67 141 130 106 95 113 158 78)(68 105 131 168 96 77 159 140)(69 167 132 76 97 139 160 104)(70 75 133 138 98 103 161 166)(71 137 134 102 99 165 162 74)(72 101 135 164 100 73 163 136)
G:=sub<Sym(224)| (1,108,175,157)(2,158,176,109)(3,110,177,159)(4,160,178,111)(5,112,179,161)(6,162,180,57)(7,58,181,163)(8,164,182,59)(9,60,183,165)(10,166,184,61)(11,62,185,167)(12,168,186,63)(13,64,187,113)(14,114,188,65)(15,66,189,115)(16,116,190,67)(17,68,191,117)(18,118,192,69)(19,70,193,119)(20,120,194,71)(21,72,195,121)(22,122,196,73)(23,74,197,123)(24,124,198,75)(25,76,199,125)(26,126,200,77)(27,78,201,127)(28,128,202,79)(29,80,203,129)(30,130,204,81)(31,82,205,131)(32,132,206,83)(33,84,207,133)(34,134,208,85)(35,86,209,135)(36,136,210,87)(37,88,211,137)(38,138,212,89)(39,90,213,139)(40,140,214,91)(41,92,215,141)(42,142,216,93)(43,94,217,143)(44,144,218,95)(45,96,219,145)(46,146,220,97)(47,98,221,147)(48,148,222,99)(49,100,223,149)(50,150,224,101)(51,102,169,151)(52,152,170,103)(53,104,171,153)(54,154,172,105)(55,106,173,155)(56,156,174,107), (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), (1,14,189,202,29,42,217,174)(2,201,190,41,30,173,218,13)(3,40,191,172,31,12,219,200)(4,171,192,11,32,199,220,39)(5,10,193,198,33,38,221,170)(6,197,194,37,34,169,222,9)(7,36,195,224,35,8,223,196)(15,28,203,216,43,56,175,188)(16,215,204,55,44,187,176,27)(17,54,205,186,45,26,177,214)(18,185,206,25,46,213,178,53)(19,24,207,212,47,52,179,184)(20,211,208,51,48,183,180,23)(21,50,209,182,49,22,181,210)(57,123,120,88,85,151,148,60)(58,87,121,150,86,59,149,122)(61,119,124,84,89,147,152,112)(62,83,125,146,90,111,153,118)(63,145,126,110,91,117,154,82)(64,109,127,116,92,81,155,144)(65,115,128,80,93,143,156,108)(66,79,129,142,94,107,157,114)(67,141,130,106,95,113,158,78)(68,105,131,168,96,77,159,140)(69,167,132,76,97,139,160,104)(70,75,133,138,98,103,161,166)(71,137,134,102,99,165,162,74)(72,101,135,164,100,73,163,136)>;
G:=Group( (1,108,175,157)(2,158,176,109)(3,110,177,159)(4,160,178,111)(5,112,179,161)(6,162,180,57)(7,58,181,163)(8,164,182,59)(9,60,183,165)(10,166,184,61)(11,62,185,167)(12,168,186,63)(13,64,187,113)(14,114,188,65)(15,66,189,115)(16,116,190,67)(17,68,191,117)(18,118,192,69)(19,70,193,119)(20,120,194,71)(21,72,195,121)(22,122,196,73)(23,74,197,123)(24,124,198,75)(25,76,199,125)(26,126,200,77)(27,78,201,127)(28,128,202,79)(29,80,203,129)(30,130,204,81)(31,82,205,131)(32,132,206,83)(33,84,207,133)(34,134,208,85)(35,86,209,135)(36,136,210,87)(37,88,211,137)(38,138,212,89)(39,90,213,139)(40,140,214,91)(41,92,215,141)(42,142,216,93)(43,94,217,143)(44,144,218,95)(45,96,219,145)(46,146,220,97)(47,98,221,147)(48,148,222,99)(49,100,223,149)(50,150,224,101)(51,102,169,151)(52,152,170,103)(53,104,171,153)(54,154,172,105)(55,106,173,155)(56,156,174,107), (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), (1,14,189,202,29,42,217,174)(2,201,190,41,30,173,218,13)(3,40,191,172,31,12,219,200)(4,171,192,11,32,199,220,39)(5,10,193,198,33,38,221,170)(6,197,194,37,34,169,222,9)(7,36,195,224,35,8,223,196)(15,28,203,216,43,56,175,188)(16,215,204,55,44,187,176,27)(17,54,205,186,45,26,177,214)(18,185,206,25,46,213,178,53)(19,24,207,212,47,52,179,184)(20,211,208,51,48,183,180,23)(21,50,209,182,49,22,181,210)(57,123,120,88,85,151,148,60)(58,87,121,150,86,59,149,122)(61,119,124,84,89,147,152,112)(62,83,125,146,90,111,153,118)(63,145,126,110,91,117,154,82)(64,109,127,116,92,81,155,144)(65,115,128,80,93,143,156,108)(66,79,129,142,94,107,157,114)(67,141,130,106,95,113,158,78)(68,105,131,168,96,77,159,140)(69,167,132,76,97,139,160,104)(70,75,133,138,98,103,161,166)(71,137,134,102,99,165,162,74)(72,101,135,164,100,73,163,136) );
G=PermutationGroup([[(1,108,175,157),(2,158,176,109),(3,110,177,159),(4,160,178,111),(5,112,179,161),(6,162,180,57),(7,58,181,163),(8,164,182,59),(9,60,183,165),(10,166,184,61),(11,62,185,167),(12,168,186,63),(13,64,187,113),(14,114,188,65),(15,66,189,115),(16,116,190,67),(17,68,191,117),(18,118,192,69),(19,70,193,119),(20,120,194,71),(21,72,195,121),(22,122,196,73),(23,74,197,123),(24,124,198,75),(25,76,199,125),(26,126,200,77),(27,78,201,127),(28,128,202,79),(29,80,203,129),(30,130,204,81),(31,82,205,131),(32,132,206,83),(33,84,207,133),(34,134,208,85),(35,86,209,135),(36,136,210,87),(37,88,211,137),(38,138,212,89),(39,90,213,139),(40,140,214,91),(41,92,215,141),(42,142,216,93),(43,94,217,143),(44,144,218,95),(45,96,219,145),(46,146,220,97),(47,98,221,147),(48,148,222,99),(49,100,223,149),(50,150,224,101),(51,102,169,151),(52,152,170,103),(53,104,171,153),(54,154,172,105),(55,106,173,155),(56,156,174,107)], [(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)], [(1,14,189,202,29,42,217,174),(2,201,190,41,30,173,218,13),(3,40,191,172,31,12,219,200),(4,171,192,11,32,199,220,39),(5,10,193,198,33,38,221,170),(6,197,194,37,34,169,222,9),(7,36,195,224,35,8,223,196),(15,28,203,216,43,56,175,188),(16,215,204,55,44,187,176,27),(17,54,205,186,45,26,177,214),(18,185,206,25,46,213,178,53),(19,24,207,212,47,52,179,184),(20,211,208,51,48,183,180,23),(21,50,209,182,49,22,181,210),(57,123,120,88,85,151,148,60),(58,87,121,150,86,59,149,122),(61,119,124,84,89,147,152,112),(62,83,125,146,90,111,153,118),(63,145,126,110,91,117,154,82),(64,109,127,116,92,81,155,144),(65,115,128,80,93,143,156,108),(66,79,129,142,94,107,157,114),(67,141,130,106,95,113,158,78),(68,105,131,168,96,77,159,140),(69,167,132,76,97,139,160,104),(70,75,133,138,98,103,161,166),(71,137,134,102,99,165,162,74),(72,101,135,164,100,73,163,136)]])
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 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | + | ||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | C4 | D7 | M4(2) | C4○D4 | M4(2) | D14 | D14 | C4×D7 | C8⋊D7 | D4⋊2D7 | Q8⋊2D7 | D7×M4(2) |
| kernel | C42.202D14 | C28⋊C8 | C56⋊C4 | D14⋊C8 | C7×C4⋊C8 | D7×C42 | C4×Dic7 | C2×C4×D7 | C4⋊C8 | C28 | C28 | D14 | C42 | C2×C8 | C2×C4 | C4 | C4 | C4 | C2 |
| # reps | 1 | 1 | 2 | 2 | 1 | 1 | 4 | 4 | 3 | 4 | 4 | 4 | 3 | 6 | 12 | 24 | 3 | 3 | 6 |
Matrix representation of C42.202D14 ►in GL4(𝔽113) generated by
| 15 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 15 | 0 |
| 0 | 0 | 0 | 15 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 72 | 41 |
| 0 | 0 | 72 | 102 |
| 0 | 112 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 72 | 41 |
| 0 | 0 | 11 | 41 |
G:=sub<GL(4,GF(113))| [15,0,0,0,0,98,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,15,0,0,0,0,15],[0,1,0,0,1,0,0,0,0,0,72,72,0,0,41,102],[0,1,0,0,112,0,0,0,0,0,72,11,0,0,41,41] >;
C42.202D14 in GAP, Magma, Sage, TeX
C_4^2._{202}D_{14} % in TeX
G:=Group("C4^2.202D14"); // GroupNames label
G:=SmallGroup(448,369);
// by ID
G=gap.SmallGroup(448,369);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,1094,219,58,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=b^-1,d^2=a^2*b^-1,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*c^13>;
// generators/relations