metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.164D14, C14.1412+ 1+4, C14.1022- 1+4, C28⋊Q8⋊41C2, C4⋊C4.119D14, C4.D28⋊9C2, C42⋊2C2⋊7D7, D14⋊Q8⋊45C2, D14⋊2Q8⋊42C2, (C4×Dic14)⋊16C2, D14⋊D4.5C2, (C4×C28).36C22, C22⋊C4.82D14, Dic7⋊4D4⋊38C2, D14.5D4⋊43C2, (C2×C28).605C23, (C2×C14).254C24, D14⋊C4.47C22, (C2×D28).37C22, C2.66(D4⋊8D14), C23.60(C22×D7), Dic7.16(C4○D4), Dic7.D4⋊47C2, C22⋊Dic14⋊47C2, C22.D28⋊31C2, C4⋊Dic7.319C22, (C22×C14).68C23, C22.275(C23×D7), C23.D7.69C22, Dic7⋊C4.127C22, (C2×Dic7).267C23, (C4×Dic7).219C22, (C22×D7).113C23, C2.66(D4.10D14), C7⋊10(C22.36C24), (C2×Dic14).256C22, (C22×Dic7).154C22, C4⋊C4⋊D7⋊44C2, C4⋊C4⋊7D7⋊42C2, C2.101(D7×C4○D4), (C7×C42⋊2C2)⋊9C2, C14.212(C2×C4○D4), (C2×C4×D7).136C22, (C7×C4⋊C4).206C22, (C2×C4).210(C22×D7), (C2×C7⋊D4).74C22, (C7×C22⋊C4).79C22, SmallGroup(448,1163)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.164D14
G = < a,b,c,d | a4=b4=1, c14=d2=b2, ab=ba, cac-1=ab2, dad-1=a-1, cbc-1=a2b-1, dbd-1=a2b, dcd-1=c13 >
Subgroups: 1036 in 216 conjugacy classes, 93 normal (91 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, Dic7, Dic7, C28, D14, C2×C14, C2×C14, C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22.D4, C4.4D4, C42⋊2C2, C42⋊2C2, C4⋊Q8, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C22×D7, C22×C14, C22.36C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C22×Dic7, C2×C7⋊D4, C4×Dic14, C4.D28, C22⋊Dic14, Dic7⋊4D4, D14⋊D4, Dic7.D4, C22.D28, C28⋊Q8, C4⋊C4⋊7D7, D14.5D4, D14⋊Q8, D14⋊2Q8, C4⋊C4⋊D7, C7×C42⋊2C2, C42.164D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, 2- 1+4, C22×D7, C22.36C24, C23×D7, D7×C4○D4, D4⋊8D14, D4.10D14, C42.164D14
►On 224 points
Generators in S224
(1 118 166 68)(2 133 167 83)(3 120 168 70)(4 135 141 57)(5 122 142 72)(6 137 143 59)(7 124 144 74)(8 139 145 61)(9 126 146 76)(10 113 147 63)(11 128 148 78)(12 115 149 65)(13 130 150 80)(14 117 151 67)(15 132 152 82)(16 119 153 69)(17 134 154 84)(18 121 155 71)(19 136 156 58)(20 123 157 73)(21 138 158 60)(22 125 159 75)(23 140 160 62)(24 127 161 77)(25 114 162 64)(26 129 163 79)(27 116 164 66)(28 131 165 81)(29 170 210 97)(30 185 211 112)(31 172 212 99)(32 187 213 86)(33 174 214 101)(34 189 215 88)(35 176 216 103)(36 191 217 90)(37 178 218 105)(38 193 219 92)(39 180 220 107)(40 195 221 94)(41 182 222 109)(42 169 223 96)(43 184 224 111)(44 171 197 98)(45 186 198 85)(46 173 199 100)(47 188 200 87)(48 175 201 102)(49 190 202 89)(50 177 203 104)(51 192 204 91)(52 179 205 106)(53 194 206 93)(54 181 207 108)(55 196 208 95)(56 183 209 110)
(1 139 15 125)(2 76 16 62)(3 113 17 127)(4 78 18 64)(5 115 19 129)(6 80 20 66)(7 117 21 131)(8 82 22 68)(9 119 23 133)(10 84 24 70)(11 121 25 135)(12 58 26 72)(13 123 27 137)(14 60 28 74)(29 90 43 104)(30 178 44 192)(31 92 45 106)(32 180 46 194)(33 94 47 108)(34 182 48 196)(35 96 49 110)(36 184 50 170)(37 98 51 112)(38 186 52 172)(39 100 53 86)(40 188 54 174)(41 102 55 88)(42 190 56 176)(57 148 71 162)(59 150 73 164)(61 152 75 166)(63 154 77 168)(65 156 79 142)(67 158 81 144)(69 160 83 146)(85 205 99 219)(87 207 101 221)(89 209 103 223)(91 211 105 197)(93 213 107 199)(95 215 109 201)(97 217 111 203)(114 141 128 155)(116 143 130 157)(118 145 132 159)(120 147 134 161)(122 149 136 163)(124 151 138 165)(126 153 140 167)(169 202 183 216)(171 204 185 218)(173 206 187 220)(175 208 189 222)(177 210 191 224)(179 212 193 198)(181 214 195 200)
(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)
(1 215 15 201)(2 200 16 214)(3 213 17 199)(4 198 18 212)(5 211 19 197)(6 224 20 210)(7 209 21 223)(8 222 22 208)(9 207 23 221)(10 220 24 206)(11 205 25 219)(12 218 26 204)(13 203 27 217)(14 216 28 202)(29 143 43 157)(30 156 44 142)(31 141 45 155)(32 154 46 168)(33 167 47 153)(34 152 48 166)(35 165 49 151)(36 150 50 164)(37 163 51 149)(38 148 52 162)(39 161 53 147)(40 146 54 160)(41 159 55 145)(42 144 56 158)(57 85 71 99)(58 98 72 112)(59 111 73 97)(60 96 74 110)(61 109 75 95)(62 94 76 108)(63 107 77 93)(64 92 78 106)(65 105 79 91)(66 90 80 104)(67 103 81 89)(68 88 82 102)(69 101 83 87)(70 86 84 100)(113 180 127 194)(114 193 128 179)(115 178 129 192)(116 191 130 177)(117 176 131 190)(118 189 132 175)(119 174 133 188)(120 187 134 173)(121 172 135 186)(122 185 136 171)(123 170 137 184)(124 183 138 169)(125 196 139 182)(126 181 140 195)
G:=sub<Sym(224)| (1,118,166,68)(2,133,167,83)(3,120,168,70)(4,135,141,57)(5,122,142,72)(6,137,143,59)(7,124,144,74)(8,139,145,61)(9,126,146,76)(10,113,147,63)(11,128,148,78)(12,115,149,65)(13,130,150,80)(14,117,151,67)(15,132,152,82)(16,119,153,69)(17,134,154,84)(18,121,155,71)(19,136,156,58)(20,123,157,73)(21,138,158,60)(22,125,159,75)(23,140,160,62)(24,127,161,77)(25,114,162,64)(26,129,163,79)(27,116,164,66)(28,131,165,81)(29,170,210,97)(30,185,211,112)(31,172,212,99)(32,187,213,86)(33,174,214,101)(34,189,215,88)(35,176,216,103)(36,191,217,90)(37,178,218,105)(38,193,219,92)(39,180,220,107)(40,195,221,94)(41,182,222,109)(42,169,223,96)(43,184,224,111)(44,171,197,98)(45,186,198,85)(46,173,199,100)(47,188,200,87)(48,175,201,102)(49,190,202,89)(50,177,203,104)(51,192,204,91)(52,179,205,106)(53,194,206,93)(54,181,207,108)(55,196,208,95)(56,183,209,110), (1,139,15,125)(2,76,16,62)(3,113,17,127)(4,78,18,64)(5,115,19,129)(6,80,20,66)(7,117,21,131)(8,82,22,68)(9,119,23,133)(10,84,24,70)(11,121,25,135)(12,58,26,72)(13,123,27,137)(14,60,28,74)(29,90,43,104)(30,178,44,192)(31,92,45,106)(32,180,46,194)(33,94,47,108)(34,182,48,196)(35,96,49,110)(36,184,50,170)(37,98,51,112)(38,186,52,172)(39,100,53,86)(40,188,54,174)(41,102,55,88)(42,190,56,176)(57,148,71,162)(59,150,73,164)(61,152,75,166)(63,154,77,168)(65,156,79,142)(67,158,81,144)(69,160,83,146)(85,205,99,219)(87,207,101,221)(89,209,103,223)(91,211,105,197)(93,213,107,199)(95,215,109,201)(97,217,111,203)(114,141,128,155)(116,143,130,157)(118,145,132,159)(120,147,134,161)(122,149,136,163)(124,151,138,165)(126,153,140,167)(169,202,183,216)(171,204,185,218)(173,206,187,220)(175,208,189,222)(177,210,191,224)(179,212,193,198)(181,214,195,200), (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), (1,215,15,201)(2,200,16,214)(3,213,17,199)(4,198,18,212)(5,211,19,197)(6,224,20,210)(7,209,21,223)(8,222,22,208)(9,207,23,221)(10,220,24,206)(11,205,25,219)(12,218,26,204)(13,203,27,217)(14,216,28,202)(29,143,43,157)(30,156,44,142)(31,141,45,155)(32,154,46,168)(33,167,47,153)(34,152,48,166)(35,165,49,151)(36,150,50,164)(37,163,51,149)(38,148,52,162)(39,161,53,147)(40,146,54,160)(41,159,55,145)(42,144,56,158)(57,85,71,99)(58,98,72,112)(59,111,73,97)(60,96,74,110)(61,109,75,95)(62,94,76,108)(63,107,77,93)(64,92,78,106)(65,105,79,91)(66,90,80,104)(67,103,81,89)(68,88,82,102)(69,101,83,87)(70,86,84,100)(113,180,127,194)(114,193,128,179)(115,178,129,192)(116,191,130,177)(117,176,131,190)(118,189,132,175)(119,174,133,188)(120,187,134,173)(121,172,135,186)(122,185,136,171)(123,170,137,184)(124,183,138,169)(125,196,139,182)(126,181,140,195)>;
G:=Group( (1,118,166,68)(2,133,167,83)(3,120,168,70)(4,135,141,57)(5,122,142,72)(6,137,143,59)(7,124,144,74)(8,139,145,61)(9,126,146,76)(10,113,147,63)(11,128,148,78)(12,115,149,65)(13,130,150,80)(14,117,151,67)(15,132,152,82)(16,119,153,69)(17,134,154,84)(18,121,155,71)(19,136,156,58)(20,123,157,73)(21,138,158,60)(22,125,159,75)(23,140,160,62)(24,127,161,77)(25,114,162,64)(26,129,163,79)(27,116,164,66)(28,131,165,81)(29,170,210,97)(30,185,211,112)(31,172,212,99)(32,187,213,86)(33,174,214,101)(34,189,215,88)(35,176,216,103)(36,191,217,90)(37,178,218,105)(38,193,219,92)(39,180,220,107)(40,195,221,94)(41,182,222,109)(42,169,223,96)(43,184,224,111)(44,171,197,98)(45,186,198,85)(46,173,199,100)(47,188,200,87)(48,175,201,102)(49,190,202,89)(50,177,203,104)(51,192,204,91)(52,179,205,106)(53,194,206,93)(54,181,207,108)(55,196,208,95)(56,183,209,110), (1,139,15,125)(2,76,16,62)(3,113,17,127)(4,78,18,64)(5,115,19,129)(6,80,20,66)(7,117,21,131)(8,82,22,68)(9,119,23,133)(10,84,24,70)(11,121,25,135)(12,58,26,72)(13,123,27,137)(14,60,28,74)(29,90,43,104)(30,178,44,192)(31,92,45,106)(32,180,46,194)(33,94,47,108)(34,182,48,196)(35,96,49,110)(36,184,50,170)(37,98,51,112)(38,186,52,172)(39,100,53,86)(40,188,54,174)(41,102,55,88)(42,190,56,176)(57,148,71,162)(59,150,73,164)(61,152,75,166)(63,154,77,168)(65,156,79,142)(67,158,81,144)(69,160,83,146)(85,205,99,219)(87,207,101,221)(89,209,103,223)(91,211,105,197)(93,213,107,199)(95,215,109,201)(97,217,111,203)(114,141,128,155)(116,143,130,157)(118,145,132,159)(120,147,134,161)(122,149,136,163)(124,151,138,165)(126,153,140,167)(169,202,183,216)(171,204,185,218)(173,206,187,220)(175,208,189,222)(177,210,191,224)(179,212,193,198)(181,214,195,200), (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), (1,215,15,201)(2,200,16,214)(3,213,17,199)(4,198,18,212)(5,211,19,197)(6,224,20,210)(7,209,21,223)(8,222,22,208)(9,207,23,221)(10,220,24,206)(11,205,25,219)(12,218,26,204)(13,203,27,217)(14,216,28,202)(29,143,43,157)(30,156,44,142)(31,141,45,155)(32,154,46,168)(33,167,47,153)(34,152,48,166)(35,165,49,151)(36,150,50,164)(37,163,51,149)(38,148,52,162)(39,161,53,147)(40,146,54,160)(41,159,55,145)(42,144,56,158)(57,85,71,99)(58,98,72,112)(59,111,73,97)(60,96,74,110)(61,109,75,95)(62,94,76,108)(63,107,77,93)(64,92,78,106)(65,105,79,91)(66,90,80,104)(67,103,81,89)(68,88,82,102)(69,101,83,87)(70,86,84,100)(113,180,127,194)(114,193,128,179)(115,178,129,192)(116,191,130,177)(117,176,131,190)(118,189,132,175)(119,174,133,188)(120,187,134,173)(121,172,135,186)(122,185,136,171)(123,170,137,184)(124,183,138,169)(125,196,139,182)(126,181,140,195) );
G=PermutationGroup([[(1,118,166,68),(2,133,167,83),(3,120,168,70),(4,135,141,57),(5,122,142,72),(6,137,143,59),(7,124,144,74),(8,139,145,61),(9,126,146,76),(10,113,147,63),(11,128,148,78),(12,115,149,65),(13,130,150,80),(14,117,151,67),(15,132,152,82),(16,119,153,69),(17,134,154,84),(18,121,155,71),(19,136,156,58),(20,123,157,73),(21,138,158,60),(22,125,159,75),(23,140,160,62),(24,127,161,77),(25,114,162,64),(26,129,163,79),(27,116,164,66),(28,131,165,81),(29,170,210,97),(30,185,211,112),(31,172,212,99),(32,187,213,86),(33,174,214,101),(34,189,215,88),(35,176,216,103),(36,191,217,90),(37,178,218,105),(38,193,219,92),(39,180,220,107),(40,195,221,94),(41,182,222,109),(42,169,223,96),(43,184,224,111),(44,171,197,98),(45,186,198,85),(46,173,199,100),(47,188,200,87),(48,175,201,102),(49,190,202,89),(50,177,203,104),(51,192,204,91),(52,179,205,106),(53,194,206,93),(54,181,207,108),(55,196,208,95),(56,183,209,110)], [(1,139,15,125),(2,76,16,62),(3,113,17,127),(4,78,18,64),(5,115,19,129),(6,80,20,66),(7,117,21,131),(8,82,22,68),(9,119,23,133),(10,84,24,70),(11,121,25,135),(12,58,26,72),(13,123,27,137),(14,60,28,74),(29,90,43,104),(30,178,44,192),(31,92,45,106),(32,180,46,194),(33,94,47,108),(34,182,48,196),(35,96,49,110),(36,184,50,170),(37,98,51,112),(38,186,52,172),(39,100,53,86),(40,188,54,174),(41,102,55,88),(42,190,56,176),(57,148,71,162),(59,150,73,164),(61,152,75,166),(63,154,77,168),(65,156,79,142),(67,158,81,144),(69,160,83,146),(85,205,99,219),(87,207,101,221),(89,209,103,223),(91,211,105,197),(93,213,107,199),(95,215,109,201),(97,217,111,203),(114,141,128,155),(116,143,130,157),(118,145,132,159),(120,147,134,161),(122,149,136,163),(124,151,138,165),(126,153,140,167),(169,202,183,216),(171,204,185,218),(173,206,187,220),(175,208,189,222),(177,210,191,224),(179,212,193,198),(181,214,195,200)], [(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)], [(1,215,15,201),(2,200,16,214),(3,213,17,199),(4,198,18,212),(5,211,19,197),(6,224,20,210),(7,209,21,223),(8,222,22,208),(9,207,23,221),(10,220,24,206),(11,205,25,219),(12,218,26,204),(13,203,27,217),(14,216,28,202),(29,143,43,157),(30,156,44,142),(31,141,45,155),(32,154,46,168),(33,167,47,153),(34,152,48,166),(35,165,49,151),(36,150,50,164),(37,163,51,149),(38,148,52,162),(39,161,53,147),(40,146,54,160),(41,159,55,145),(42,144,56,158),(57,85,71,99),(58,98,72,112),(59,111,73,97),(60,96,74,110),(61,109,75,95),(62,94,76,108),(63,107,77,93),(64,92,78,106),(65,105,79,91),(66,90,80,104),(67,103,81,89),(68,88,82,102),(69,101,83,87),(70,86,84,100),(113,180,127,194),(114,193,128,179),(115,178,129,192),(116,191,130,177),(117,176,131,190),(118,189,132,175),(119,174,133,188),(120,187,134,173),(121,172,135,186),(122,185,136,171),(123,170,137,184),(124,183,138,169),(125,196,139,182),(126,181,140,195)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | ··· | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 14J | 14K | 14L | 28A | ··· | 28R | 28S | ··· | 28AA |
| order | 1 | 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 | 28 | 28 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | 2+ 1+4 | 2- 1+4 | D7×C4○D4 | D4⋊8D14 | D4.10D14 |
| kernel | C42.164D14 | C4×Dic14 | C4.D28 | C22⋊Dic14 | Dic7⋊4D4 | D14⋊D4 | Dic7.D4 | C22.D28 | C28⋊Q8 | C4⋊C4⋊7D7 | D14.5D4 | D14⋊Q8 | D14⋊2Q8 | C4⋊C4⋊D7 | C7×C42⋊2C2 | C42⋊2C2 | Dic7 | C42 | C22⋊C4 | C4⋊C4 | C14 | C14 | C2 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 3 | 9 | 9 | 1 | 1 | 6 | 6 | 6 |
Matrix representation of C42.164D14 ►in GL6(𝔽29)
| 12 | 18 | 0 | 0 | 0 | 0 |
| 13 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 11 | 0 | 0 |
| 0 | 0 | 18 | 2 | 0 | 0 |
| 0 | 0 | 0 | 0 | 26 | 11 |
| 0 | 0 | 0 | 0 | 7 | 3 |
| 28 | 13 | 0 | 0 | 0 | 0 |
| 11 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 11 | 4 | 1 |
| 0 | 0 | 18 | 2 | 24 | 15 |
| 0 | 0 | 25 | 8 | 3 | 18 |
| 0 | 0 | 18 | 26 | 22 | 26 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 13 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 8 | 8 | 23 |
| 0 | 0 | 21 | 3 | 6 | 0 |
| 0 | 0 | 0 | 0 | 27 | 21 |
| 0 | 0 | 0 | 0 | 16 | 20 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 27 | 0 | 0 |
| 0 | 0 | 2 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 5 |
| 0 | 0 | 0 | 0 | 0 | 28 |
G:=sub<GL(6,GF(29))| [12,13,0,0,0,0,18,17,0,0,0,0,0,0,27,18,0,0,0,0,11,2,0,0,0,0,0,0,26,7,0,0,0,0,11,3],[28,11,0,0,0,0,13,1,0,0,0,0,0,0,27,18,25,18,0,0,11,2,8,26,0,0,4,24,3,22,0,0,1,15,18,26],[12,13,0,0,0,0,0,17,0,0,0,0,0,0,8,21,0,0,0,0,8,3,0,0,0,0,8,6,27,16,0,0,23,0,21,20],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,11,2,0,0,0,0,27,18,0,0,0,0,0,0,1,0,0,0,0,0,5,28] >;
C42.164D14 in GAP, Magma, Sage, TeX
C_4^2._{164}D_{14} % in TeX
G:=Group("C4^2.164D14"); // GroupNames label
G:=SmallGroup(448,1163);
// by ID
G=gap.SmallGroup(448,1163);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,758,219,268,675,570,80,18822]);
// 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=a*b^2,d*a*d^-1=a^-1,c*b*c^-1=a^2*b^-1,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations