metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.113D14, C14.192+ 1+4, (C4×D4)⋊20D7, (D4×C28)⋊22C2, (C4×D28)⋊32C2, C28⋊2D4⋊9C2, D14⋊D4⋊9C2, C4⋊C4.318D14, (C2×D4).219D14, C4.65(C4○D28), C28.6Q8⋊16C2, (C22×C4).47D14, D14.29(C4○D4), C28.110(C4○D4), (C2×C28).700C23, (C4×C28).157C22, (C2×C14).102C24, D14⋊C4.86C22, C22⋊C4.115D14, C23.D14⋊8C2, C2.20(D4⋊6D14), C23.99(C22×D7), (C2×D28).213C22, (D4×C14).262C22, C4⋊Dic7.200C22, (C2×Dic7).43C23, (C22×D7).36C23, C22.127(C23×D7), C23.D7.14C22, C23.23D14⋊17C2, Dic7⋊C4.100C22, (C22×C14).172C23, (C22×C28).364C22, C7⋊4(C22.47C24), (C4×Dic7).205C22, (D7×C4⋊C4)⋊16C2, (C4×C7⋊D4)⋊44C2, C2.25(D7×C4○D4), C4⋊C4⋊7D7⋊15C2, C2.51(C2×C4○D28), (C2×C4×D7).66C22, C14.142(C2×C4○D4), (C7×C4⋊C4).331C22, (C2×C4).285(C22×D7), (C2×C7⋊D4).17C22, (C7×C22⋊C4).126C22, SmallGroup(448,1011)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.113D14
G = < a,b,c,d | a4=b4=1, c14=d2=b2, ab=ba, cac-1=dad-1=a-1, bc=cb, dbd-1=a2b-1, dcd-1=c13 >
Subgroups: 1076 in 238 conjugacy classes, 97 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C4⋊C4, C42⋊C2, C4×D4, C4×D4, C4⋊D4, C22.D4, C42.C2, C42⋊2C2, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C22.47C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×C4×D7, C2×C4×D7, C2×D28, C2×C7⋊D4, C22×C28, D4×C14, C28.6Q8, C4×D28, C23.D14, D14⋊D4, D7×C4⋊C4, C4⋊C4⋊7D7, C4×C7⋊D4, C23.23D14, C28⋊2D4, D4×C28, C42.113D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.47C24, C4○D28, C23×D7, C2×C4○D28, D4⋊6D14, D7×C4○D4, C42.113D14
►On 224 points
Generators in S224
(1 61 123 207)(2 208 124 62)(3 63 125 209)(4 210 126 64)(5 65 127 211)(6 212 128 66)(7 67 129 213)(8 214 130 68)(9 69 131 215)(10 216 132 70)(11 71 133 217)(12 218 134 72)(13 73 135 219)(14 220 136 74)(15 75 137 221)(16 222 138 76)(17 77 139 223)(18 224 140 78)(19 79 113 197)(20 198 114 80)(21 81 115 199)(22 200 116 82)(23 83 117 201)(24 202 118 84)(25 57 119 203)(26 204 120 58)(27 59 121 205)(28 206 122 60)(29 101 157 193)(30 194 158 102)(31 103 159 195)(32 196 160 104)(33 105 161 169)(34 170 162 106)(35 107 163 171)(36 172 164 108)(37 109 165 173)(38 174 166 110)(39 111 167 175)(40 176 168 112)(41 85 141 177)(42 178 142 86)(43 87 143 179)(44 180 144 88)(45 89 145 181)(46 182 146 90)(47 91 147 183)(48 184 148 92)(49 93 149 185)(50 186 150 94)(51 95 151 187)(52 188 152 96)(53 97 153 189)(54 190 154 98)(55 99 155 191)(56 192 156 100)
(1 47 15 33)(2 48 16 34)(3 49 17 35)(4 50 18 36)(5 51 19 37)(6 52 20 38)(7 53 21 39)(8 54 22 40)(9 55 23 41)(10 56 24 42)(11 29 25 43)(12 30 26 44)(13 31 27 45)(14 32 28 46)(57 87 71 101)(58 88 72 102)(59 89 73 103)(60 90 74 104)(61 91 75 105)(62 92 76 106)(63 93 77 107)(64 94 78 108)(65 95 79 109)(66 96 80 110)(67 97 81 111)(68 98 82 112)(69 99 83 85)(70 100 84 86)(113 165 127 151)(114 166 128 152)(115 167 129 153)(116 168 130 154)(117 141 131 155)(118 142 132 156)(119 143 133 157)(120 144 134 158)(121 145 135 159)(122 146 136 160)(123 147 137 161)(124 148 138 162)(125 149 139 163)(126 150 140 164)(169 207 183 221)(170 208 184 222)(171 209 185 223)(172 210 186 224)(173 211 187 197)(174 212 188 198)(175 213 189 199)(176 214 190 200)(177 215 191 201)(178 216 192 202)(179 217 193 203)(180 218 194 204)(181 219 195 205)(182 220 196 206)
(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)
(1 136 15 122)(2 121 16 135)(3 134 17 120)(4 119 18 133)(5 132 19 118)(6 117 20 131)(7 130 21 116)(8 115 22 129)(9 128 23 114)(10 113 24 127)(11 126 25 140)(12 139 26 125)(13 124 27 138)(14 137 28 123)(29 36 43 50)(30 49 44 35)(31 34 45 48)(32 47 46 33)(37 56 51 42)(38 41 52 55)(39 54 53 40)(57 224 71 210)(58 209 72 223)(59 222 73 208)(60 207 74 221)(61 220 75 206)(62 205 76 219)(63 218 77 204)(64 203 78 217)(65 216 79 202)(66 201 80 215)(67 214 81 200)(68 199 82 213)(69 212 83 198)(70 197 84 211)(85 96 99 110)(86 109 100 95)(87 94 101 108)(88 107 102 93)(89 92 103 106)(90 105 104 91)(97 112 111 98)(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)(169 196 183 182)(170 181 184 195)(171 194 185 180)(172 179 186 193)(173 192 187 178)(174 177 188 191)(175 190 189 176)
G:=sub<Sym(224)| (1,61,123,207)(2,208,124,62)(3,63,125,209)(4,210,126,64)(5,65,127,211)(6,212,128,66)(7,67,129,213)(8,214,130,68)(9,69,131,215)(10,216,132,70)(11,71,133,217)(12,218,134,72)(13,73,135,219)(14,220,136,74)(15,75,137,221)(16,222,138,76)(17,77,139,223)(18,224,140,78)(19,79,113,197)(20,198,114,80)(21,81,115,199)(22,200,116,82)(23,83,117,201)(24,202,118,84)(25,57,119,203)(26,204,120,58)(27,59,121,205)(28,206,122,60)(29,101,157,193)(30,194,158,102)(31,103,159,195)(32,196,160,104)(33,105,161,169)(34,170,162,106)(35,107,163,171)(36,172,164,108)(37,109,165,173)(38,174,166,110)(39,111,167,175)(40,176,168,112)(41,85,141,177)(42,178,142,86)(43,87,143,179)(44,180,144,88)(45,89,145,181)(46,182,146,90)(47,91,147,183)(48,184,148,92)(49,93,149,185)(50,186,150,94)(51,95,151,187)(52,188,152,96)(53,97,153,189)(54,190,154,98)(55,99,155,191)(56,192,156,100), (1,47,15,33)(2,48,16,34)(3,49,17,35)(4,50,18,36)(5,51,19,37)(6,52,20,38)(7,53,21,39)(8,54,22,40)(9,55,23,41)(10,56,24,42)(11,29,25,43)(12,30,26,44)(13,31,27,45)(14,32,28,46)(57,87,71,101)(58,88,72,102)(59,89,73,103)(60,90,74,104)(61,91,75,105)(62,92,76,106)(63,93,77,107)(64,94,78,108)(65,95,79,109)(66,96,80,110)(67,97,81,111)(68,98,82,112)(69,99,83,85)(70,100,84,86)(113,165,127,151)(114,166,128,152)(115,167,129,153)(116,168,130,154)(117,141,131,155)(118,142,132,156)(119,143,133,157)(120,144,134,158)(121,145,135,159)(122,146,136,160)(123,147,137,161)(124,148,138,162)(125,149,139,163)(126,150,140,164)(169,207,183,221)(170,208,184,222)(171,209,185,223)(172,210,186,224)(173,211,187,197)(174,212,188,198)(175,213,189,199)(176,214,190,200)(177,215,191,201)(178,216,192,202)(179,217,193,203)(180,218,194,204)(181,219,195,205)(182,220,196,206), (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), (1,136,15,122)(2,121,16,135)(3,134,17,120)(4,119,18,133)(5,132,19,118)(6,117,20,131)(7,130,21,116)(8,115,22,129)(9,128,23,114)(10,113,24,127)(11,126,25,140)(12,139,26,125)(13,124,27,138)(14,137,28,123)(29,36,43,50)(30,49,44,35)(31,34,45,48)(32,47,46,33)(37,56,51,42)(38,41,52,55)(39,54,53,40)(57,224,71,210)(58,209,72,223)(59,222,73,208)(60,207,74,221)(61,220,75,206)(62,205,76,219)(63,218,77,204)(64,203,78,217)(65,216,79,202)(66,201,80,215)(67,214,81,200)(68,199,82,213)(69,212,83,198)(70,197,84,211)(85,96,99,110)(86,109,100,95)(87,94,101,108)(88,107,102,93)(89,92,103,106)(90,105,104,91)(97,112,111,98)(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)(169,196,183,182)(170,181,184,195)(171,194,185,180)(172,179,186,193)(173,192,187,178)(174,177,188,191)(175,190,189,176)>;
G:=Group( (1,61,123,207)(2,208,124,62)(3,63,125,209)(4,210,126,64)(5,65,127,211)(6,212,128,66)(7,67,129,213)(8,214,130,68)(9,69,131,215)(10,216,132,70)(11,71,133,217)(12,218,134,72)(13,73,135,219)(14,220,136,74)(15,75,137,221)(16,222,138,76)(17,77,139,223)(18,224,140,78)(19,79,113,197)(20,198,114,80)(21,81,115,199)(22,200,116,82)(23,83,117,201)(24,202,118,84)(25,57,119,203)(26,204,120,58)(27,59,121,205)(28,206,122,60)(29,101,157,193)(30,194,158,102)(31,103,159,195)(32,196,160,104)(33,105,161,169)(34,170,162,106)(35,107,163,171)(36,172,164,108)(37,109,165,173)(38,174,166,110)(39,111,167,175)(40,176,168,112)(41,85,141,177)(42,178,142,86)(43,87,143,179)(44,180,144,88)(45,89,145,181)(46,182,146,90)(47,91,147,183)(48,184,148,92)(49,93,149,185)(50,186,150,94)(51,95,151,187)(52,188,152,96)(53,97,153,189)(54,190,154,98)(55,99,155,191)(56,192,156,100), (1,47,15,33)(2,48,16,34)(3,49,17,35)(4,50,18,36)(5,51,19,37)(6,52,20,38)(7,53,21,39)(8,54,22,40)(9,55,23,41)(10,56,24,42)(11,29,25,43)(12,30,26,44)(13,31,27,45)(14,32,28,46)(57,87,71,101)(58,88,72,102)(59,89,73,103)(60,90,74,104)(61,91,75,105)(62,92,76,106)(63,93,77,107)(64,94,78,108)(65,95,79,109)(66,96,80,110)(67,97,81,111)(68,98,82,112)(69,99,83,85)(70,100,84,86)(113,165,127,151)(114,166,128,152)(115,167,129,153)(116,168,130,154)(117,141,131,155)(118,142,132,156)(119,143,133,157)(120,144,134,158)(121,145,135,159)(122,146,136,160)(123,147,137,161)(124,148,138,162)(125,149,139,163)(126,150,140,164)(169,207,183,221)(170,208,184,222)(171,209,185,223)(172,210,186,224)(173,211,187,197)(174,212,188,198)(175,213,189,199)(176,214,190,200)(177,215,191,201)(178,216,192,202)(179,217,193,203)(180,218,194,204)(181,219,195,205)(182,220,196,206), (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), (1,136,15,122)(2,121,16,135)(3,134,17,120)(4,119,18,133)(5,132,19,118)(6,117,20,131)(7,130,21,116)(8,115,22,129)(9,128,23,114)(10,113,24,127)(11,126,25,140)(12,139,26,125)(13,124,27,138)(14,137,28,123)(29,36,43,50)(30,49,44,35)(31,34,45,48)(32,47,46,33)(37,56,51,42)(38,41,52,55)(39,54,53,40)(57,224,71,210)(58,209,72,223)(59,222,73,208)(60,207,74,221)(61,220,75,206)(62,205,76,219)(63,218,77,204)(64,203,78,217)(65,216,79,202)(66,201,80,215)(67,214,81,200)(68,199,82,213)(69,212,83,198)(70,197,84,211)(85,96,99,110)(86,109,100,95)(87,94,101,108)(88,107,102,93)(89,92,103,106)(90,105,104,91)(97,112,111,98)(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)(169,196,183,182)(170,181,184,195)(171,194,185,180)(172,179,186,193)(173,192,187,178)(174,177,188,191)(175,190,189,176) );
G=PermutationGroup([[(1,61,123,207),(2,208,124,62),(3,63,125,209),(4,210,126,64),(5,65,127,211),(6,212,128,66),(7,67,129,213),(8,214,130,68),(9,69,131,215),(10,216,132,70),(11,71,133,217),(12,218,134,72),(13,73,135,219),(14,220,136,74),(15,75,137,221),(16,222,138,76),(17,77,139,223),(18,224,140,78),(19,79,113,197),(20,198,114,80),(21,81,115,199),(22,200,116,82),(23,83,117,201),(24,202,118,84),(25,57,119,203),(26,204,120,58),(27,59,121,205),(28,206,122,60),(29,101,157,193),(30,194,158,102),(31,103,159,195),(32,196,160,104),(33,105,161,169),(34,170,162,106),(35,107,163,171),(36,172,164,108),(37,109,165,173),(38,174,166,110),(39,111,167,175),(40,176,168,112),(41,85,141,177),(42,178,142,86),(43,87,143,179),(44,180,144,88),(45,89,145,181),(46,182,146,90),(47,91,147,183),(48,184,148,92),(49,93,149,185),(50,186,150,94),(51,95,151,187),(52,188,152,96),(53,97,153,189),(54,190,154,98),(55,99,155,191),(56,192,156,100)], [(1,47,15,33),(2,48,16,34),(3,49,17,35),(4,50,18,36),(5,51,19,37),(6,52,20,38),(7,53,21,39),(8,54,22,40),(9,55,23,41),(10,56,24,42),(11,29,25,43),(12,30,26,44),(13,31,27,45),(14,32,28,46),(57,87,71,101),(58,88,72,102),(59,89,73,103),(60,90,74,104),(61,91,75,105),(62,92,76,106),(63,93,77,107),(64,94,78,108),(65,95,79,109),(66,96,80,110),(67,97,81,111),(68,98,82,112),(69,99,83,85),(70,100,84,86),(113,165,127,151),(114,166,128,152),(115,167,129,153),(116,168,130,154),(117,141,131,155),(118,142,132,156),(119,143,133,157),(120,144,134,158),(121,145,135,159),(122,146,136,160),(123,147,137,161),(124,148,138,162),(125,149,139,163),(126,150,140,164),(169,207,183,221),(170,208,184,222),(171,209,185,223),(172,210,186,224),(173,211,187,197),(174,212,188,198),(175,213,189,199),(176,214,190,200),(177,215,191,201),(178,216,192,202),(179,217,193,203),(180,218,194,204),(181,219,195,205),(182,220,196,206)], [(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)], [(1,136,15,122),(2,121,16,135),(3,134,17,120),(4,119,18,133),(5,132,19,118),(6,117,20,131),(7,130,21,116),(8,115,22,129),(9,128,23,114),(10,113,24,127),(11,126,25,140),(12,139,26,125),(13,124,27,138),(14,137,28,123),(29,36,43,50),(30,49,44,35),(31,34,45,48),(32,47,46,33),(37,56,51,42),(38,41,52,55),(39,54,53,40),(57,224,71,210),(58,209,72,223),(59,222,73,208),(60,207,74,221),(61,220,75,206),(62,205,76,219),(63,218,77,204),(64,203,78,217),(65,216,79,202),(66,201,80,215),(67,214,81,200),(68,199,82,213),(69,212,83,198),(70,197,84,211),(85,96,99,110),(86,109,100,95),(87,94,101,108),(88,107,102,93),(89,92,103,106),(90,105,104,91),(97,112,111,98),(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),(169,196,183,182),(170,181,184,195),(171,194,185,180),(172,179,186,193),(173,192,187,178),(174,177,188,191),(175,190,189,176)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | ··· | 4H | 4I | 4J | 4K | 4L | ··· | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 14 | 14 | 28 | 2 | ··· | 2 | 4 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | D14 | D14 | C4○D28 | 2+ 1+4 | D4⋊6D14 | D7×C4○D4 |
| kernel | C42.113D14 | C28.6Q8 | C4×D28 | C23.D14 | D14⋊D4 | D7×C4⋊C4 | C4⋊C4⋊7D7 | C4×C7⋊D4 | C23.23D14 | C28⋊2D4 | D4×C28 | C4×D4 | C28 | D14 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C4 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 2 | 1 | 3 | 4 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of C42.113D14 ►in GL4(𝔽29) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 16 | 13 |
| 0 | 0 | 7 | 13 |
| 22 | 24 | 0 | 0 |
| 10 | 7 | 0 | 0 |
| 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 17 |
| 2 | 19 | 0 | 0 |
| 20 | 1 | 0 | 0 |
| 0 | 0 | 11 | 18 |
| 0 | 0 | 19 | 18 |
| 16 | 16 | 0 | 0 |
| 22 | 13 | 0 | 0 |
| 0 | 0 | 18 | 11 |
| 0 | 0 | 10 | 11 |
G:=sub<GL(4,GF(29))| [1,0,0,0,0,1,0,0,0,0,16,7,0,0,13,13],[22,10,0,0,24,7,0,0,0,0,17,0,0,0,0,17],[2,20,0,0,19,1,0,0,0,0,11,19,0,0,18,18],[16,22,0,0,16,13,0,0,0,0,18,10,0,0,11,11] >;
C42.113D14 in GAP, Magma, Sage, TeX
C_4^2._{113}D_{14} % in TeX
G:=Group("C4^2.113D14"); // GroupNames label
G:=SmallGroup(448,1011);
// by ID
G=gap.SmallGroup(448,1011);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,387,100,1571,570,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,b*c=c*b,d*b*d^-1=a^2*b^-1,d*c*d^-1=c^13>;
// generators/relations