metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.141D14, C14.902- 1+4, C4.33(D4×D7), (C4×D7).12D4, C4.4D4⋊9D7, C28.62(C2×D4), C28⋊2Q8⋊30C2, D14.46(C2×D4), (C2×D4).172D14, C42⋊D7⋊20C2, (C2×C28).80C23, (C2×Q8).136D14, C22⋊C4.35D14, Dic7.51(C2×D4), C14.89(C22×D4), Dic7⋊Q8⋊24C2, D14.D4⋊41C2, C28.17D4⋊24C2, (C2×C14).219C24, (C4×C28).185C22, C4⋊Dic7.51C22, C23.41(C22×D7), D14⋊C4.110C22, C22⋊Dic14⋊40C2, (D4×C14).154C22, (C22×C14).49C23, (Q8×C14).126C22, C22.240(C23×D7), C23.D7.54C22, Dic7⋊C4.120C22, C7⋊4(C23.38C23), (C2×Dic7).114C23, (C4×Dic7).133C22, (C22×D7).214C23, C2.51(D4.10D14), (C2×Dic14).177C22, (C22×Dic7).142C22, (C2×Q8×D7)⋊10C2, C2.62(C2×D4×D7), (C2×D4⋊2D7).9C2, (C7×C4.4D4)⋊11C2, (C2×C4×D7).120C22, (C2×C4).194(C22×D7), (C2×C7⋊D4).59C22, (C7×C22⋊C4).64C22, SmallGroup(448,1128)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.141D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2, ab=ba, cac-1=dad-1=a-1, cbc-1=a2b-1, dbd-1=b-1, dcd-1=c13 >
Subgroups: 1196 in 270 conjugacy classes, 103 normal (29 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C42⋊C2, C22⋊Q8, C22.D4, C4.4D4, C4.4D4, C4⋊Q8, C22×Q8, C2×C4○D4, Dic14, C4×D7, C4×D7, C2×Dic7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C7×Q8, C22×D7, C22×C14, C23.38C23, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C2×Dic14, C2×Dic14, C2×C4×D7, C2×C4×D7, D4⋊2D7, Q8×D7, C22×Dic7, C2×C7⋊D4, D4×C14, Q8×C14, C28⋊2Q8, C42⋊D7, C22⋊Dic14, D14.D4, C28.17D4, Dic7⋊Q8, C7×C4.4D4, C2×D4⋊2D7, C2×Q8×D7, C42.141D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C24, D14, C22×D4, 2- 1+4, C22×D7, C23.38C23, D4×D7, C23×D7, C2×D4×D7, D4.10D14, C42.141D14
►On 224 points
Generators in S224
(1 155 15 141)(2 142 16 156)(3 157 17 143)(4 144 18 158)(5 159 19 145)(6 146 20 160)(7 161 21 147)(8 148 22 162)(9 163 23 149)(10 150 24 164)(11 165 25 151)(12 152 26 166)(13 167 27 153)(14 154 28 168)(29 83 43 69)(30 70 44 84)(31 57 45 71)(32 72 46 58)(33 59 47 73)(34 74 48 60)(35 61 49 75)(36 76 50 62)(37 63 51 77)(38 78 52 64)(39 65 53 79)(40 80 54 66)(41 67 55 81)(42 82 56 68)(85 178 99 192)(86 193 100 179)(87 180 101 194)(88 195 102 181)(89 182 103 196)(90 169 104 183)(91 184 105 170)(92 171 106 185)(93 186 107 172)(94 173 108 187)(95 188 109 174)(96 175 110 189)(97 190 111 176)(98 177 112 191)(113 202 127 216)(114 217 128 203)(115 204 129 218)(116 219 130 205)(117 206 131 220)(118 221 132 207)(119 208 133 222)(120 223 134 209)(121 210 135 224)(122 197 136 211)(123 212 137 198)(124 199 138 213)(125 214 139 200)(126 201 140 215)
(1 218 30 188)(2 175 31 205)(3 220 32 190)(4 177 33 207)(5 222 34 192)(6 179 35 209)(7 224 36 194)(8 181 37 211)(9 198 38 196)(10 183 39 213)(11 200 40 170)(12 185 41 215)(13 202 42 172)(14 187 43 217)(15 204 44 174)(16 189 45 219)(17 206 46 176)(18 191 47 221)(19 208 48 178)(20 193 49 223)(21 210 50 180)(22 195 51 197)(23 212 52 182)(24 169 53 199)(25 214 54 184)(26 171 55 201)(27 216 56 186)(28 173 29 203)(57 116 142 110)(58 97 143 131)(59 118 144 112)(60 99 145 133)(61 120 146 86)(62 101 147 135)(63 122 148 88)(64 103 149 137)(65 124 150 90)(66 105 151 139)(67 126 152 92)(68 107 153 113)(69 128 154 94)(70 109 155 115)(71 130 156 96)(72 111 157 117)(73 132 158 98)(74 85 159 119)(75 134 160 100)(76 87 161 121)(77 136 162 102)(78 89 163 123)(79 138 164 104)(80 91 165 125)(81 140 166 106)(82 93 167 127)(83 114 168 108)(84 95 141 129)
(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 15 28)(2 27 16 13)(3 12 17 26)(4 25 18 11)(5 10 19 24)(6 23 20 9)(7 8 21 22)(29 30 43 44)(31 56 45 42)(32 41 46 55)(33 54 47 40)(34 39 48 53)(35 52 49 38)(36 37 50 51)(57 82 71 68)(58 67 72 81)(59 80 73 66)(60 65 74 79)(61 78 75 64)(62 63 76 77)(69 70 83 84)(85 104 99 90)(86 89 100 103)(87 102 101 88)(91 98 105 112)(92 111 106 97)(93 96 107 110)(94 109 108 95)(113 116 127 130)(114 129 128 115)(117 140 131 126)(118 125 132 139)(119 138 133 124)(120 123 134 137)(121 136 135 122)(141 154 155 168)(142 167 156 153)(143 152 157 166)(144 165 158 151)(145 150 159 164)(146 163 160 149)(147 148 161 162)(169 192 183 178)(170 177 184 191)(171 190 185 176)(172 175 186 189)(173 188 187 174)(179 182 193 196)(180 195 194 181)(197 224 211 210)(198 209 212 223)(199 222 213 208)(200 207 214 221)(201 220 215 206)(202 205 216 219)(203 218 217 204)
G:=sub<Sym(224)| (1,155,15,141)(2,142,16,156)(3,157,17,143)(4,144,18,158)(5,159,19,145)(6,146,20,160)(7,161,21,147)(8,148,22,162)(9,163,23,149)(10,150,24,164)(11,165,25,151)(12,152,26,166)(13,167,27,153)(14,154,28,168)(29,83,43,69)(30,70,44,84)(31,57,45,71)(32,72,46,58)(33,59,47,73)(34,74,48,60)(35,61,49,75)(36,76,50,62)(37,63,51,77)(38,78,52,64)(39,65,53,79)(40,80,54,66)(41,67,55,81)(42,82,56,68)(85,178,99,192)(86,193,100,179)(87,180,101,194)(88,195,102,181)(89,182,103,196)(90,169,104,183)(91,184,105,170)(92,171,106,185)(93,186,107,172)(94,173,108,187)(95,188,109,174)(96,175,110,189)(97,190,111,176)(98,177,112,191)(113,202,127,216)(114,217,128,203)(115,204,129,218)(116,219,130,205)(117,206,131,220)(118,221,132,207)(119,208,133,222)(120,223,134,209)(121,210,135,224)(122,197,136,211)(123,212,137,198)(124,199,138,213)(125,214,139,200)(126,201,140,215), (1,218,30,188)(2,175,31,205)(3,220,32,190)(4,177,33,207)(5,222,34,192)(6,179,35,209)(7,224,36,194)(8,181,37,211)(9,198,38,196)(10,183,39,213)(11,200,40,170)(12,185,41,215)(13,202,42,172)(14,187,43,217)(15,204,44,174)(16,189,45,219)(17,206,46,176)(18,191,47,221)(19,208,48,178)(20,193,49,223)(21,210,50,180)(22,195,51,197)(23,212,52,182)(24,169,53,199)(25,214,54,184)(26,171,55,201)(27,216,56,186)(28,173,29,203)(57,116,142,110)(58,97,143,131)(59,118,144,112)(60,99,145,133)(61,120,146,86)(62,101,147,135)(63,122,148,88)(64,103,149,137)(65,124,150,90)(66,105,151,139)(67,126,152,92)(68,107,153,113)(69,128,154,94)(70,109,155,115)(71,130,156,96)(72,111,157,117)(73,132,158,98)(74,85,159,119)(75,134,160,100)(76,87,161,121)(77,136,162,102)(78,89,163,123)(79,138,164,104)(80,91,165,125)(81,140,166,106)(82,93,167,127)(83,114,168,108)(84,95,141,129), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,30,43,44)(31,56,45,42)(32,41,46,55)(33,54,47,40)(34,39,48,53)(35,52,49,38)(36,37,50,51)(57,82,71,68)(58,67,72,81)(59,80,73,66)(60,65,74,79)(61,78,75,64)(62,63,76,77)(69,70,83,84)(85,104,99,90)(86,89,100,103)(87,102,101,88)(91,98,105,112)(92,111,106,97)(93,96,107,110)(94,109,108,95)(113,116,127,130)(114,129,128,115)(117,140,131,126)(118,125,132,139)(119,138,133,124)(120,123,134,137)(121,136,135,122)(141,154,155,168)(142,167,156,153)(143,152,157,166)(144,165,158,151)(145,150,159,164)(146,163,160,149)(147,148,161,162)(169,192,183,178)(170,177,184,191)(171,190,185,176)(172,175,186,189)(173,188,187,174)(179,182,193,196)(180,195,194,181)(197,224,211,210)(198,209,212,223)(199,222,213,208)(200,207,214,221)(201,220,215,206)(202,205,216,219)(203,218,217,204)>;
G:=Group( (1,155,15,141)(2,142,16,156)(3,157,17,143)(4,144,18,158)(5,159,19,145)(6,146,20,160)(7,161,21,147)(8,148,22,162)(9,163,23,149)(10,150,24,164)(11,165,25,151)(12,152,26,166)(13,167,27,153)(14,154,28,168)(29,83,43,69)(30,70,44,84)(31,57,45,71)(32,72,46,58)(33,59,47,73)(34,74,48,60)(35,61,49,75)(36,76,50,62)(37,63,51,77)(38,78,52,64)(39,65,53,79)(40,80,54,66)(41,67,55,81)(42,82,56,68)(85,178,99,192)(86,193,100,179)(87,180,101,194)(88,195,102,181)(89,182,103,196)(90,169,104,183)(91,184,105,170)(92,171,106,185)(93,186,107,172)(94,173,108,187)(95,188,109,174)(96,175,110,189)(97,190,111,176)(98,177,112,191)(113,202,127,216)(114,217,128,203)(115,204,129,218)(116,219,130,205)(117,206,131,220)(118,221,132,207)(119,208,133,222)(120,223,134,209)(121,210,135,224)(122,197,136,211)(123,212,137,198)(124,199,138,213)(125,214,139,200)(126,201,140,215), (1,218,30,188)(2,175,31,205)(3,220,32,190)(4,177,33,207)(5,222,34,192)(6,179,35,209)(7,224,36,194)(8,181,37,211)(9,198,38,196)(10,183,39,213)(11,200,40,170)(12,185,41,215)(13,202,42,172)(14,187,43,217)(15,204,44,174)(16,189,45,219)(17,206,46,176)(18,191,47,221)(19,208,48,178)(20,193,49,223)(21,210,50,180)(22,195,51,197)(23,212,52,182)(24,169,53,199)(25,214,54,184)(26,171,55,201)(27,216,56,186)(28,173,29,203)(57,116,142,110)(58,97,143,131)(59,118,144,112)(60,99,145,133)(61,120,146,86)(62,101,147,135)(63,122,148,88)(64,103,149,137)(65,124,150,90)(66,105,151,139)(67,126,152,92)(68,107,153,113)(69,128,154,94)(70,109,155,115)(71,130,156,96)(72,111,157,117)(73,132,158,98)(74,85,159,119)(75,134,160,100)(76,87,161,121)(77,136,162,102)(78,89,163,123)(79,138,164,104)(80,91,165,125)(81,140,166,106)(82,93,167,127)(83,114,168,108)(84,95,141,129), (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), (1,14,15,28)(2,27,16,13)(3,12,17,26)(4,25,18,11)(5,10,19,24)(6,23,20,9)(7,8,21,22)(29,30,43,44)(31,56,45,42)(32,41,46,55)(33,54,47,40)(34,39,48,53)(35,52,49,38)(36,37,50,51)(57,82,71,68)(58,67,72,81)(59,80,73,66)(60,65,74,79)(61,78,75,64)(62,63,76,77)(69,70,83,84)(85,104,99,90)(86,89,100,103)(87,102,101,88)(91,98,105,112)(92,111,106,97)(93,96,107,110)(94,109,108,95)(113,116,127,130)(114,129,128,115)(117,140,131,126)(118,125,132,139)(119,138,133,124)(120,123,134,137)(121,136,135,122)(141,154,155,168)(142,167,156,153)(143,152,157,166)(144,165,158,151)(145,150,159,164)(146,163,160,149)(147,148,161,162)(169,192,183,178)(170,177,184,191)(171,190,185,176)(172,175,186,189)(173,188,187,174)(179,182,193,196)(180,195,194,181)(197,224,211,210)(198,209,212,223)(199,222,213,208)(200,207,214,221)(201,220,215,206)(202,205,216,219)(203,218,217,204) );
G=PermutationGroup([[(1,155,15,141),(2,142,16,156),(3,157,17,143),(4,144,18,158),(5,159,19,145),(6,146,20,160),(7,161,21,147),(8,148,22,162),(9,163,23,149),(10,150,24,164),(11,165,25,151),(12,152,26,166),(13,167,27,153),(14,154,28,168),(29,83,43,69),(30,70,44,84),(31,57,45,71),(32,72,46,58),(33,59,47,73),(34,74,48,60),(35,61,49,75),(36,76,50,62),(37,63,51,77),(38,78,52,64),(39,65,53,79),(40,80,54,66),(41,67,55,81),(42,82,56,68),(85,178,99,192),(86,193,100,179),(87,180,101,194),(88,195,102,181),(89,182,103,196),(90,169,104,183),(91,184,105,170),(92,171,106,185),(93,186,107,172),(94,173,108,187),(95,188,109,174),(96,175,110,189),(97,190,111,176),(98,177,112,191),(113,202,127,216),(114,217,128,203),(115,204,129,218),(116,219,130,205),(117,206,131,220),(118,221,132,207),(119,208,133,222),(120,223,134,209),(121,210,135,224),(122,197,136,211),(123,212,137,198),(124,199,138,213),(125,214,139,200),(126,201,140,215)], [(1,218,30,188),(2,175,31,205),(3,220,32,190),(4,177,33,207),(5,222,34,192),(6,179,35,209),(7,224,36,194),(8,181,37,211),(9,198,38,196),(10,183,39,213),(11,200,40,170),(12,185,41,215),(13,202,42,172),(14,187,43,217),(15,204,44,174),(16,189,45,219),(17,206,46,176),(18,191,47,221),(19,208,48,178),(20,193,49,223),(21,210,50,180),(22,195,51,197),(23,212,52,182),(24,169,53,199),(25,214,54,184),(26,171,55,201),(27,216,56,186),(28,173,29,203),(57,116,142,110),(58,97,143,131),(59,118,144,112),(60,99,145,133),(61,120,146,86),(62,101,147,135),(63,122,148,88),(64,103,149,137),(65,124,150,90),(66,105,151,139),(67,126,152,92),(68,107,153,113),(69,128,154,94),(70,109,155,115),(71,130,156,96),(72,111,157,117),(73,132,158,98),(74,85,159,119),(75,134,160,100),(76,87,161,121),(77,136,162,102),(78,89,163,123),(79,138,164,104),(80,91,165,125),(81,140,166,106),(82,93,167,127),(83,114,168,108),(84,95,141,129)], [(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)], [(1,14,15,28),(2,27,16,13),(3,12,17,26),(4,25,18,11),(5,10,19,24),(6,23,20,9),(7,8,21,22),(29,30,43,44),(31,56,45,42),(32,41,46,55),(33,54,47,40),(34,39,48,53),(35,52,49,38),(36,37,50,51),(57,82,71,68),(58,67,72,81),(59,80,73,66),(60,65,74,79),(61,78,75,64),(62,63,76,77),(69,70,83,84),(85,104,99,90),(86,89,100,103),(87,102,101,88),(91,98,105,112),(92,111,106,97),(93,96,107,110),(94,109,108,95),(113,116,127,130),(114,129,128,115),(117,140,131,126),(118,125,132,139),(119,138,133,124),(120,123,134,137),(121,136,135,122),(141,154,155,168),(142,167,156,153),(143,152,157,166),(144,165,158,151),(145,150,159,164),(146,163,160,149),(147,148,161,162),(169,192,183,178),(170,177,184,191),(171,190,185,176),(172,175,186,189),(173,188,187,174),(179,182,193,196),(180,195,194,181),(197,224,211,210),(198,209,212,223),(199,222,213,208),(200,207,214,221),(201,220,215,206),(202,205,216,219),(203,218,217,204)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4N | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 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 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 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 | D4 | D7 | D14 | D14 | D14 | D14 | 2- 1+4 | D4×D7 | D4.10D14 |
| kernel | C42.141D14 | C28⋊2Q8 | C42⋊D7 | C22⋊Dic14 | D14.D4 | C28.17D4 | Dic7⋊Q8 | C7×C4.4D4 | C2×D4⋊2D7 | C2×Q8×D7 | C4×D7 | C4.4D4 | C42 | C22⋊C4 | C2×D4 | C2×Q8 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 4 | 4 | 1 | 1 | 1 | 1 | 1 | 4 | 3 | 3 | 12 | 3 | 3 | 2 | 6 | 12 |
Matrix representation of C42.141D14 ►in GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 21 | 24 |
| 0 | 0 | 0 | 0 | 13 | 8 |
| 0 | 0 | 21 | 24 | 0 | 0 |
| 0 | 0 | 13 | 8 | 0 | 0 |
| 11 | 7 | 0 | 0 | 0 | 0 |
| 24 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 23 | 25 | 0 | 0 | 0 | 0 |
| 16 | 6 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 10 | 0 | 0 |
| 0 | 0 | 3 | 26 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 19 |
| 0 | 0 | 0 | 0 | 26 | 3 |
| 6 | 4 | 0 | 0 | 0 | 0 |
| 13 | 23 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 10 | 0 | 0 |
| 0 | 0 | 28 | 26 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 10 |
| 0 | 0 | 0 | 0 | 28 | 26 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,21,13,0,0,0,0,24,8,0,0,21,13,0,0,0,0,24,8,0,0],[11,24,0,0,0,0,7,18,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,1,0,0],[23,16,0,0,0,0,25,6,0,0,0,0,0,0,0,3,0,0,0,0,10,26,0,0,0,0,0,0,0,26,0,0,0,0,19,3],[6,13,0,0,0,0,4,23,0,0,0,0,0,0,3,28,0,0,0,0,10,26,0,0,0,0,0,0,3,28,0,0,0,0,10,26] >;
C42.141D14 in GAP, Magma, Sage, TeX
C_4^2._{141}D_{14} % in TeX
G:=Group("C4^2.141D14"); // GroupNames label
G:=SmallGroup(448,1128);
// by ID
G=gap.SmallGroup(448,1128);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,100,675,297,192,18822]);
// 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,c*b*c^-1=a^2*b^-1,d*b*d^-1=b^-1,d*c*d^-1=c^13>;
// generators/relations