metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.163D14, C14.1402+ 1+4, (C4×D28)⋊16C2, C4⋊D28⋊37C2, C4⋊C4.214D14, C42⋊2C2⋊6D7, C42⋊D7⋊8C2, D28⋊C4⋊42C2, D14⋊D4⋊45C2, Dic7.Q8⋊39C2, (C2×C28).96C23, (C4×C28).35C22, C22⋊C4.81D14, Dic7⋊4D4⋊37C2, D14.33(C4○D4), D14.5D4⋊42C2, (C2×C14).253C24, D14⋊C4.46C22, C2.65(D4⋊8D14), C23.59(C22×D7), Dic7.33(C4○D4), (C2×D28).169C22, C22.D28⋊30C2, C4⋊Dic7.318C22, (C22×C14).67C23, C22.274(C23×D7), Dic7⋊C4.147C22, (C2×Dic7).266C23, (C4×Dic7).152C22, (C22×D7).112C23, C7⋊11(C22.47C24), (C22×Dic7).153C22, (D7×C4⋊C4)⋊43C2, C4⋊C4⋊D7⋊43C2, C2.100(D7×C4○D4), (C7×C42⋊2C2)⋊8C2, C14.211(C2×C4○D4), (C2×C4×D7).135C22, (C2×C4).89(C22×D7), (C7×C4⋊C4).205C22, (C2×C7⋊D4).73C22, (C7×C22⋊C4).78C22, SmallGroup(448,1162)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.163D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2, ab=ba, cac-1=dad-1=a-1b2, cbc-1=a2b, dbd-1=a2b-1, dcd-1=c13 >
Subgroups: 1196 in 238 conjugacy classes, 95 normal (91 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, Dic7, Dic7, C28, D14, D14, C2×C14, C2×C14, C2×C4⋊C4, C42⋊C2, C4×D4, C4⋊D4, C22.D4, C42.C2, C42⋊2C2, C42⋊2C2, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C22×D7, C22×C14, C22.47C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×C4×D7, C2×D28, C22×Dic7, C2×C7⋊D4, C42⋊D7, C4×D28, Dic7⋊4D4, D14⋊D4, C22.D28, Dic7.Q8, D7×C4⋊C4, D28⋊C4, D14.5D4, C4⋊D28, C4⋊C4⋊D7, C7×C42⋊2C2, C42.163D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.47C24, C23×D7, D7×C4○D4, D4⋊8D14, C42.163D14
►On 224 points
Generators in S224
(1 168 15 154)(2 105 16 91)(3 142 17 156)(4 107 18 93)(5 144 19 158)(6 109 20 95)(7 146 21 160)(8 111 22 97)(9 148 23 162)(10 85 24 99)(11 150 25 164)(12 87 26 101)(13 152 27 166)(14 89 28 103)(29 129 43 115)(30 195 44 181)(31 131 45 117)(32 169 46 183)(33 133 47 119)(34 171 48 185)(35 135 49 121)(36 173 50 187)(37 137 51 123)(38 175 52 189)(39 139 53 125)(40 177 54 191)(41 113 55 127)(42 179 56 193)(57 120 71 134)(58 186 72 172)(59 122 73 136)(60 188 74 174)(61 124 75 138)(62 190 76 176)(63 126 77 140)(64 192 78 178)(65 128 79 114)(66 194 80 180)(67 130 81 116)(68 196 82 182)(69 132 83 118)(70 170 84 184)(86 213 100 199)(88 215 102 201)(90 217 104 203)(92 219 106 205)(94 221 108 207)(96 223 110 209)(98 197 112 211)(141 204 155 218)(143 206 157 220)(145 208 159 222)(147 210 161 224)(149 212 163 198)(151 214 165 200)(153 216 167 202)
(1 186 203 135)(2 173 204 122)(3 188 205 137)(4 175 206 124)(5 190 207 139)(6 177 208 126)(7 192 209 113)(8 179 210 128)(9 194 211 115)(10 181 212 130)(11 196 213 117)(12 183 214 132)(13 170 215 119)(14 185 216 134)(15 172 217 121)(16 187 218 136)(17 174 219 123)(18 189 220 138)(19 176 221 125)(20 191 222 140)(21 178 223 127)(22 193 224 114)(23 180 197 129)(24 195 198 116)(25 182 199 131)(26 169 200 118)(27 184 201 133)(28 171 202 120)(29 148 80 98)(30 163 81 85)(31 150 82 100)(32 165 83 87)(33 152 84 102)(34 167 57 89)(35 154 58 104)(36 141 59 91)(37 156 60 106)(38 143 61 93)(39 158 62 108)(40 145 63 95)(41 160 64 110)(42 147 65 97)(43 162 66 112)(44 149 67 99)(45 164 68 86)(46 151 69 101)(47 166 70 88)(48 153 71 103)(49 168 72 90)(50 155 73 105)(51 142 74 92)(52 157 75 107)(53 144 76 94)(54 159 77 109)(55 146 78 96)(56 161 79 111)
(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 28 15 14)(2 13 16 27)(3 26 17 12)(4 11 18 25)(5 24 19 10)(6 9 20 23)(7 22 21 8)(29 63 43 77)(30 76 44 62)(31 61 45 75)(32 74 46 60)(33 59 47 73)(34 72 48 58)(35 57 49 71)(36 70 50 84)(37 83 51 69)(38 68 52 82)(39 81 53 67)(40 66 54 80)(41 79 55 65)(42 64 56 78)(85 108 99 94)(86 93 100 107)(87 106 101 92)(88 91 102 105)(89 104 103 90)(95 98 109 112)(96 111 110 97)(113 179 127 193)(114 192 128 178)(115 177 129 191)(116 190 130 176)(117 175 131 189)(118 188 132 174)(119 173 133 187)(120 186 134 172)(121 171 135 185)(122 184 136 170)(123 169 137 183)(124 182 138 196)(125 195 139 181)(126 180 140 194)(141 152 155 166)(142 165 156 151)(143 150 157 164)(144 163 158 149)(145 148 159 162)(146 161 160 147)(153 168 167 154)(197 208 211 222)(198 221 212 207)(199 206 213 220)(200 219 214 205)(201 204 215 218)(202 217 216 203)(209 224 223 210)
G:=sub<Sym(224)| (1,168,15,154)(2,105,16,91)(3,142,17,156)(4,107,18,93)(5,144,19,158)(6,109,20,95)(7,146,21,160)(8,111,22,97)(9,148,23,162)(10,85,24,99)(11,150,25,164)(12,87,26,101)(13,152,27,166)(14,89,28,103)(29,129,43,115)(30,195,44,181)(31,131,45,117)(32,169,46,183)(33,133,47,119)(34,171,48,185)(35,135,49,121)(36,173,50,187)(37,137,51,123)(38,175,52,189)(39,139,53,125)(40,177,54,191)(41,113,55,127)(42,179,56,193)(57,120,71,134)(58,186,72,172)(59,122,73,136)(60,188,74,174)(61,124,75,138)(62,190,76,176)(63,126,77,140)(64,192,78,178)(65,128,79,114)(66,194,80,180)(67,130,81,116)(68,196,82,182)(69,132,83,118)(70,170,84,184)(86,213,100,199)(88,215,102,201)(90,217,104,203)(92,219,106,205)(94,221,108,207)(96,223,110,209)(98,197,112,211)(141,204,155,218)(143,206,157,220)(145,208,159,222)(147,210,161,224)(149,212,163,198)(151,214,165,200)(153,216,167,202), (1,186,203,135)(2,173,204,122)(3,188,205,137)(4,175,206,124)(5,190,207,139)(6,177,208,126)(7,192,209,113)(8,179,210,128)(9,194,211,115)(10,181,212,130)(11,196,213,117)(12,183,214,132)(13,170,215,119)(14,185,216,134)(15,172,217,121)(16,187,218,136)(17,174,219,123)(18,189,220,138)(19,176,221,125)(20,191,222,140)(21,178,223,127)(22,193,224,114)(23,180,197,129)(24,195,198,116)(25,182,199,131)(26,169,200,118)(27,184,201,133)(28,171,202,120)(29,148,80,98)(30,163,81,85)(31,150,82,100)(32,165,83,87)(33,152,84,102)(34,167,57,89)(35,154,58,104)(36,141,59,91)(37,156,60,106)(38,143,61,93)(39,158,62,108)(40,145,63,95)(41,160,64,110)(42,147,65,97)(43,162,66,112)(44,149,67,99)(45,164,68,86)(46,151,69,101)(47,166,70,88)(48,153,71,103)(49,168,72,90)(50,155,73,105)(51,142,74,92)(52,157,75,107)(53,144,76,94)(54,159,77,109)(55,146,78,96)(56,161,79,111), (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), (1,28,15,14)(2,13,16,27)(3,26,17,12)(4,11,18,25)(5,24,19,10)(6,9,20,23)(7,22,21,8)(29,63,43,77)(30,76,44,62)(31,61,45,75)(32,74,46,60)(33,59,47,73)(34,72,48,58)(35,57,49,71)(36,70,50,84)(37,83,51,69)(38,68,52,82)(39,81,53,67)(40,66,54,80)(41,79,55,65)(42,64,56,78)(85,108,99,94)(86,93,100,107)(87,106,101,92)(88,91,102,105)(89,104,103,90)(95,98,109,112)(96,111,110,97)(113,179,127,193)(114,192,128,178)(115,177,129,191)(116,190,130,176)(117,175,131,189)(118,188,132,174)(119,173,133,187)(120,186,134,172)(121,171,135,185)(122,184,136,170)(123,169,137,183)(124,182,138,196)(125,195,139,181)(126,180,140,194)(141,152,155,166)(142,165,156,151)(143,150,157,164)(144,163,158,149)(145,148,159,162)(146,161,160,147)(153,168,167,154)(197,208,211,222)(198,221,212,207)(199,206,213,220)(200,219,214,205)(201,204,215,218)(202,217,216,203)(209,224,223,210)>;
G:=Group( (1,168,15,154)(2,105,16,91)(3,142,17,156)(4,107,18,93)(5,144,19,158)(6,109,20,95)(7,146,21,160)(8,111,22,97)(9,148,23,162)(10,85,24,99)(11,150,25,164)(12,87,26,101)(13,152,27,166)(14,89,28,103)(29,129,43,115)(30,195,44,181)(31,131,45,117)(32,169,46,183)(33,133,47,119)(34,171,48,185)(35,135,49,121)(36,173,50,187)(37,137,51,123)(38,175,52,189)(39,139,53,125)(40,177,54,191)(41,113,55,127)(42,179,56,193)(57,120,71,134)(58,186,72,172)(59,122,73,136)(60,188,74,174)(61,124,75,138)(62,190,76,176)(63,126,77,140)(64,192,78,178)(65,128,79,114)(66,194,80,180)(67,130,81,116)(68,196,82,182)(69,132,83,118)(70,170,84,184)(86,213,100,199)(88,215,102,201)(90,217,104,203)(92,219,106,205)(94,221,108,207)(96,223,110,209)(98,197,112,211)(141,204,155,218)(143,206,157,220)(145,208,159,222)(147,210,161,224)(149,212,163,198)(151,214,165,200)(153,216,167,202), (1,186,203,135)(2,173,204,122)(3,188,205,137)(4,175,206,124)(5,190,207,139)(6,177,208,126)(7,192,209,113)(8,179,210,128)(9,194,211,115)(10,181,212,130)(11,196,213,117)(12,183,214,132)(13,170,215,119)(14,185,216,134)(15,172,217,121)(16,187,218,136)(17,174,219,123)(18,189,220,138)(19,176,221,125)(20,191,222,140)(21,178,223,127)(22,193,224,114)(23,180,197,129)(24,195,198,116)(25,182,199,131)(26,169,200,118)(27,184,201,133)(28,171,202,120)(29,148,80,98)(30,163,81,85)(31,150,82,100)(32,165,83,87)(33,152,84,102)(34,167,57,89)(35,154,58,104)(36,141,59,91)(37,156,60,106)(38,143,61,93)(39,158,62,108)(40,145,63,95)(41,160,64,110)(42,147,65,97)(43,162,66,112)(44,149,67,99)(45,164,68,86)(46,151,69,101)(47,166,70,88)(48,153,71,103)(49,168,72,90)(50,155,73,105)(51,142,74,92)(52,157,75,107)(53,144,76,94)(54,159,77,109)(55,146,78,96)(56,161,79,111), (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), (1,28,15,14)(2,13,16,27)(3,26,17,12)(4,11,18,25)(5,24,19,10)(6,9,20,23)(7,22,21,8)(29,63,43,77)(30,76,44,62)(31,61,45,75)(32,74,46,60)(33,59,47,73)(34,72,48,58)(35,57,49,71)(36,70,50,84)(37,83,51,69)(38,68,52,82)(39,81,53,67)(40,66,54,80)(41,79,55,65)(42,64,56,78)(85,108,99,94)(86,93,100,107)(87,106,101,92)(88,91,102,105)(89,104,103,90)(95,98,109,112)(96,111,110,97)(113,179,127,193)(114,192,128,178)(115,177,129,191)(116,190,130,176)(117,175,131,189)(118,188,132,174)(119,173,133,187)(120,186,134,172)(121,171,135,185)(122,184,136,170)(123,169,137,183)(124,182,138,196)(125,195,139,181)(126,180,140,194)(141,152,155,166)(142,165,156,151)(143,150,157,164)(144,163,158,149)(145,148,159,162)(146,161,160,147)(153,168,167,154)(197,208,211,222)(198,221,212,207)(199,206,213,220)(200,219,214,205)(201,204,215,218)(202,217,216,203)(209,224,223,210) );
G=PermutationGroup([[(1,168,15,154),(2,105,16,91),(3,142,17,156),(4,107,18,93),(5,144,19,158),(6,109,20,95),(7,146,21,160),(8,111,22,97),(9,148,23,162),(10,85,24,99),(11,150,25,164),(12,87,26,101),(13,152,27,166),(14,89,28,103),(29,129,43,115),(30,195,44,181),(31,131,45,117),(32,169,46,183),(33,133,47,119),(34,171,48,185),(35,135,49,121),(36,173,50,187),(37,137,51,123),(38,175,52,189),(39,139,53,125),(40,177,54,191),(41,113,55,127),(42,179,56,193),(57,120,71,134),(58,186,72,172),(59,122,73,136),(60,188,74,174),(61,124,75,138),(62,190,76,176),(63,126,77,140),(64,192,78,178),(65,128,79,114),(66,194,80,180),(67,130,81,116),(68,196,82,182),(69,132,83,118),(70,170,84,184),(86,213,100,199),(88,215,102,201),(90,217,104,203),(92,219,106,205),(94,221,108,207),(96,223,110,209),(98,197,112,211),(141,204,155,218),(143,206,157,220),(145,208,159,222),(147,210,161,224),(149,212,163,198),(151,214,165,200),(153,216,167,202)], [(1,186,203,135),(2,173,204,122),(3,188,205,137),(4,175,206,124),(5,190,207,139),(6,177,208,126),(7,192,209,113),(8,179,210,128),(9,194,211,115),(10,181,212,130),(11,196,213,117),(12,183,214,132),(13,170,215,119),(14,185,216,134),(15,172,217,121),(16,187,218,136),(17,174,219,123),(18,189,220,138),(19,176,221,125),(20,191,222,140),(21,178,223,127),(22,193,224,114),(23,180,197,129),(24,195,198,116),(25,182,199,131),(26,169,200,118),(27,184,201,133),(28,171,202,120),(29,148,80,98),(30,163,81,85),(31,150,82,100),(32,165,83,87),(33,152,84,102),(34,167,57,89),(35,154,58,104),(36,141,59,91),(37,156,60,106),(38,143,61,93),(39,158,62,108),(40,145,63,95),(41,160,64,110),(42,147,65,97),(43,162,66,112),(44,149,67,99),(45,164,68,86),(46,151,69,101),(47,166,70,88),(48,153,71,103),(49,168,72,90),(50,155,73,105),(51,142,74,92),(52,157,75,107),(53,144,76,94),(54,159,77,109),(55,146,78,96),(56,161,79,111)], [(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)], [(1,28,15,14),(2,13,16,27),(3,26,17,12),(4,11,18,25),(5,24,19,10),(6,9,20,23),(7,22,21,8),(29,63,43,77),(30,76,44,62),(31,61,45,75),(32,74,46,60),(33,59,47,73),(34,72,48,58),(35,57,49,71),(36,70,50,84),(37,83,51,69),(38,68,52,82),(39,81,53,67),(40,66,54,80),(41,79,55,65),(42,64,56,78),(85,108,99,94),(86,93,100,107),(87,106,101,92),(88,91,102,105),(89,104,103,90),(95,98,109,112),(96,111,110,97),(113,179,127,193),(114,192,128,178),(115,177,129,191),(116,190,130,176),(117,175,131,189),(118,188,132,174),(119,173,133,187),(120,186,134,172),(121,171,135,185),(122,184,136,170),(123,169,137,183),(124,182,138,196),(125,195,139,181),(126,180,140,194),(141,152,155,166),(142,165,156,151),(143,150,157,164),(144,163,158,149),(145,148,159,162),(146,161,160,147),(153,168,167,154),(197,208,211,222),(198,221,212,207),(199,206,213,220),(200,219,214,205),(201,204,215,218),(202,217,216,203),(209,224,223,210)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4N | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 14J | 14K | 14L | 28A | ··· | 28R | 28S | ··· | 28AA |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 14 | 14 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | 2+ 1+4 | D7×C4○D4 | D4⋊8D14 |
| kernel | C42.163D14 | C42⋊D7 | C4×D28 | Dic7⋊4D4 | D14⋊D4 | C22.D28 | Dic7.Q8 | D7×C4⋊C4 | D28⋊C4 | D14.5D4 | C4⋊D28 | C4⋊C4⋊D7 | C7×C42⋊2C2 | C42⋊2C2 | Dic7 | D14 | C42 | C22⋊C4 | C4⋊C4 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 4 | 3 | 9 | 9 | 1 | 12 | 6 |
Matrix representation of C42.163D14 ►in GL6(𝔽29)
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 14 | 3 |
| 0 | 0 | 0 | 0 | 2 | 15 |
| 28 | 2 | 0 | 0 | 0 | 0 |
| 28 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 23 | 7 |
| 0 | 0 | 0 | 0 | 24 | 6 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 17 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 21 | 0 | 0 |
| 0 | 0 | 11 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 10 | 24 |
| 0 | 0 | 0 | 0 | 26 | 19 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 21 | 0 | 0 |
| 0 | 0 | 15 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 19 | 5 |
| 0 | 0 | 0 | 0 | 3 | 10 |
G:=sub<GL(6,GF(29))| [17,0,0,0,0,0,0,17,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,14,2,0,0,0,0,3,15],[28,28,0,0,0,0,2,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,23,24,0,0,0,0,7,6],[17,17,0,0,0,0,0,12,0,0,0,0,0,0,0,11,0,0,0,0,21,18,0,0,0,0,0,0,10,26,0,0,0,0,24,19],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,11,15,0,0,0,0,21,18,0,0,0,0,0,0,19,3,0,0,0,0,5,10] >;
C42.163D14 in GAP, Magma, Sage, TeX
C_4^2._{163}D_{14} % in TeX
G:=Group("C4^2.163D14"); // GroupNames label
G:=SmallGroup(448,1162);
// by ID
G=gap.SmallGroup(448,1162);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,219,184,1571,297,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1*b^2,c*b*c^-1=a^2*b,d*b*d^-1=a^2*b^-1,d*c*d^-1=c^13>;
// generators/relations