metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.174D14, C14.372- 1+4, C14.822+ 1+4, C4⋊Q8⋊12D7, (C4×D7)⋊2Q8, C28⋊Q8⋊45C2, C4.41(Q8×D7), D14.6(C2×Q8), C28.55(C2×Q8), C4⋊C4.124D14, (C2×Q8).86D14, Dic7.7(C2×Q8), Dic7.Q8⋊41C2, D14⋊Q8.4C2, C28.3Q8⋊43C2, C28.6Q8⋊24C2, C42⋊D7.8C2, Dic7⋊Q8⋊27C2, C14.49(C22×Q8), (C2×C28).106C23, (C2×C14).273C24, (C4×C28).214C22, D14⋊C4.52C22, D14⋊3Q8.12C2, C2.86(D4⋊6D14), C4⋊Dic7.252C22, (Q8×C14).140C22, C22.294(C23×D7), Dic7⋊C4.167C22, C7⋊5(C23.41C23), (C2×Dic7).144C23, (C4×Dic7).162C22, (C22×D7).234C23, C2.38(Q8.10D14), (C2×Dic14).191C22, C2.32(C2×Q8×D7), (C7×C4⋊Q8)⋊15C2, (D7×C4⋊C4).13C2, C4⋊C4⋊7D7.15C2, (C2×C4×D7).146C22, (C7×C4⋊C4).216C22, (C2×C4).219(C22×D7), SmallGroup(448,1182)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.174D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2b2, ab=ba, cac-1=dad-1=a-1, cbc-1=b-1, dbd-1=a2b-1, dcd-1=c13 >
Subgroups: 844 in 206 conjugacy classes, 103 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, Q8, C23, D7, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×Q8, C2×Q8, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C4⋊C4, C42⋊C2, C22⋊Q8, C42.C2, C4⋊Q8, C4⋊Q8, Dic14, C4×D7, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C23.41C23, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, D14⋊C4, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×C4×D7, Q8×C14, C28.6Q8, C42⋊D7, C28⋊Q8, Dic7.Q8, C28.3Q8, D7×C4⋊C4, C4⋊C4⋊7D7, D14⋊Q8, Dic7⋊Q8, D14⋊3Q8, C7×C4⋊Q8, C42.174D14
Quotients: C1, C2, C22, Q8, C23, D7, C2×Q8, C24, D14, C22×Q8, 2+ 1+4, 2- 1+4, C22×D7, C23.41C23, Q8×D7, C23×D7, D4⋊6D14, C2×Q8×D7, Q8.10D14, C42.174D14
►On 224 points
Generators in S224
(1 174 55 65)(2 66 56 175)(3 176 29 67)(4 68 30 177)(5 178 31 69)(6 70 32 179)(7 180 33 71)(8 72 34 181)(9 182 35 73)(10 74 36 183)(11 184 37 75)(12 76 38 185)(13 186 39 77)(14 78 40 187)(15 188 41 79)(16 80 42 189)(17 190 43 81)(18 82 44 191)(19 192 45 83)(20 84 46 193)(21 194 47 57)(22 58 48 195)(23 196 49 59)(24 60 50 169)(25 170 51 61)(26 62 52 171)(27 172 53 63)(28 64 54 173)(85 122 152 203)(86 204 153 123)(87 124 154 205)(88 206 155 125)(89 126 156 207)(90 208 157 127)(91 128 158 209)(92 210 159 129)(93 130 160 211)(94 212 161 131)(95 132 162 213)(96 214 163 133)(97 134 164 215)(98 216 165 135)(99 136 166 217)(100 218 167 137)(101 138 168 219)(102 220 141 139)(103 140 142 221)(104 222 143 113)(105 114 144 223)(106 224 145 115)(107 116 146 197)(108 198 147 117)(109 118 148 199)(110 200 149 119)(111 120 150 201)(112 202 151 121)
(1 87 41 168)(2 141 42 88)(3 89 43 142)(4 143 44 90)(5 91 45 144)(6 145 46 92)(7 93 47 146)(8 147 48 94)(9 95 49 148)(10 149 50 96)(11 97 51 150)(12 151 52 98)(13 99 53 152)(14 153 54 100)(15 101 55 154)(16 155 56 102)(17 103 29 156)(18 157 30 104)(19 105 31 158)(20 159 32 106)(21 107 33 160)(22 161 34 108)(23 109 35 162)(24 163 36 110)(25 111 37 164)(26 165 38 112)(27 85 39 166)(28 167 40 86)(57 197 180 130)(58 131 181 198)(59 199 182 132)(60 133 183 200)(61 201 184 134)(62 135 185 202)(63 203 186 136)(64 137 187 204)(65 205 188 138)(66 139 189 206)(67 207 190 140)(68 113 191 208)(69 209 192 114)(70 115 193 210)(71 211 194 116)(72 117 195 212)(73 213 196 118)(74 119 169 214)(75 215 170 120)(76 121 171 216)(77 217 172 122)(78 123 173 218)(79 219 174 124)(80 125 175 220)(81 221 176 126)(82 127 177 222)(83 223 178 128)(84 129 179 224)
(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 38 43 52)(30 51 44 37)(31 36 45 50)(32 49 46 35)(33 34 47 48)(39 56 53 42)(40 41 54 55)(57 58 71 72)(59 84 73 70)(60 69 74 83)(61 82 75 68)(62 67 76 81)(63 80 77 66)(64 65 78 79)(85 141 99 155)(86 154 100 168)(87 167 101 153)(88 152 102 166)(89 165 103 151)(90 150 104 164)(91 163 105 149)(92 148 106 162)(93 161 107 147)(94 146 108 160)(95 159 109 145)(96 144 110 158)(97 157 111 143)(98 142 112 156)(113 215 127 201)(114 200 128 214)(115 213 129 199)(116 198 130 212)(117 211 131 197)(118 224 132 210)(119 209 133 223)(120 222 134 208)(121 207 135 221)(122 220 136 206)(123 205 137 219)(124 218 138 204)(125 203 139 217)(126 216 140 202)(169 178 183 192)(170 191 184 177)(171 176 185 190)(172 189 186 175)(173 174 187 188)(179 196 193 182)(180 181 194 195)
G:=sub<Sym(224)| (1,174,55,65)(2,66,56,175)(3,176,29,67)(4,68,30,177)(5,178,31,69)(6,70,32,179)(7,180,33,71)(8,72,34,181)(9,182,35,73)(10,74,36,183)(11,184,37,75)(12,76,38,185)(13,186,39,77)(14,78,40,187)(15,188,41,79)(16,80,42,189)(17,190,43,81)(18,82,44,191)(19,192,45,83)(20,84,46,193)(21,194,47,57)(22,58,48,195)(23,196,49,59)(24,60,50,169)(25,170,51,61)(26,62,52,171)(27,172,53,63)(28,64,54,173)(85,122,152,203)(86,204,153,123)(87,124,154,205)(88,206,155,125)(89,126,156,207)(90,208,157,127)(91,128,158,209)(92,210,159,129)(93,130,160,211)(94,212,161,131)(95,132,162,213)(96,214,163,133)(97,134,164,215)(98,216,165,135)(99,136,166,217)(100,218,167,137)(101,138,168,219)(102,220,141,139)(103,140,142,221)(104,222,143,113)(105,114,144,223)(106,224,145,115)(107,116,146,197)(108,198,147,117)(109,118,148,199)(110,200,149,119)(111,120,150,201)(112,202,151,121), (1,87,41,168)(2,141,42,88)(3,89,43,142)(4,143,44,90)(5,91,45,144)(6,145,46,92)(7,93,47,146)(8,147,48,94)(9,95,49,148)(10,149,50,96)(11,97,51,150)(12,151,52,98)(13,99,53,152)(14,153,54,100)(15,101,55,154)(16,155,56,102)(17,103,29,156)(18,157,30,104)(19,105,31,158)(20,159,32,106)(21,107,33,160)(22,161,34,108)(23,109,35,162)(24,163,36,110)(25,111,37,164)(26,165,38,112)(27,85,39,166)(28,167,40,86)(57,197,180,130)(58,131,181,198)(59,199,182,132)(60,133,183,200)(61,201,184,134)(62,135,185,202)(63,203,186,136)(64,137,187,204)(65,205,188,138)(66,139,189,206)(67,207,190,140)(68,113,191,208)(69,209,192,114)(70,115,193,210)(71,211,194,116)(72,117,195,212)(73,213,196,118)(74,119,169,214)(75,215,170,120)(76,121,171,216)(77,217,172,122)(78,123,173,218)(79,219,174,124)(80,125,175,220)(81,221,176,126)(82,127,177,222)(83,223,178,128)(84,129,179,224), (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)(29,38,43,52)(30,51,44,37)(31,36,45,50)(32,49,46,35)(33,34,47,48)(39,56,53,42)(40,41,54,55)(57,58,71,72)(59,84,73,70)(60,69,74,83)(61,82,75,68)(62,67,76,81)(63,80,77,66)(64,65,78,79)(85,141,99,155)(86,154,100,168)(87,167,101,153)(88,152,102,166)(89,165,103,151)(90,150,104,164)(91,163,105,149)(92,148,106,162)(93,161,107,147)(94,146,108,160)(95,159,109,145)(96,144,110,158)(97,157,111,143)(98,142,112,156)(113,215,127,201)(114,200,128,214)(115,213,129,199)(116,198,130,212)(117,211,131,197)(118,224,132,210)(119,209,133,223)(120,222,134,208)(121,207,135,221)(122,220,136,206)(123,205,137,219)(124,218,138,204)(125,203,139,217)(126,216,140,202)(169,178,183,192)(170,191,184,177)(171,176,185,190)(172,189,186,175)(173,174,187,188)(179,196,193,182)(180,181,194,195)>;
G:=Group( (1,174,55,65)(2,66,56,175)(3,176,29,67)(4,68,30,177)(5,178,31,69)(6,70,32,179)(7,180,33,71)(8,72,34,181)(9,182,35,73)(10,74,36,183)(11,184,37,75)(12,76,38,185)(13,186,39,77)(14,78,40,187)(15,188,41,79)(16,80,42,189)(17,190,43,81)(18,82,44,191)(19,192,45,83)(20,84,46,193)(21,194,47,57)(22,58,48,195)(23,196,49,59)(24,60,50,169)(25,170,51,61)(26,62,52,171)(27,172,53,63)(28,64,54,173)(85,122,152,203)(86,204,153,123)(87,124,154,205)(88,206,155,125)(89,126,156,207)(90,208,157,127)(91,128,158,209)(92,210,159,129)(93,130,160,211)(94,212,161,131)(95,132,162,213)(96,214,163,133)(97,134,164,215)(98,216,165,135)(99,136,166,217)(100,218,167,137)(101,138,168,219)(102,220,141,139)(103,140,142,221)(104,222,143,113)(105,114,144,223)(106,224,145,115)(107,116,146,197)(108,198,147,117)(109,118,148,199)(110,200,149,119)(111,120,150,201)(112,202,151,121), (1,87,41,168)(2,141,42,88)(3,89,43,142)(4,143,44,90)(5,91,45,144)(6,145,46,92)(7,93,47,146)(8,147,48,94)(9,95,49,148)(10,149,50,96)(11,97,51,150)(12,151,52,98)(13,99,53,152)(14,153,54,100)(15,101,55,154)(16,155,56,102)(17,103,29,156)(18,157,30,104)(19,105,31,158)(20,159,32,106)(21,107,33,160)(22,161,34,108)(23,109,35,162)(24,163,36,110)(25,111,37,164)(26,165,38,112)(27,85,39,166)(28,167,40,86)(57,197,180,130)(58,131,181,198)(59,199,182,132)(60,133,183,200)(61,201,184,134)(62,135,185,202)(63,203,186,136)(64,137,187,204)(65,205,188,138)(66,139,189,206)(67,207,190,140)(68,113,191,208)(69,209,192,114)(70,115,193,210)(71,211,194,116)(72,117,195,212)(73,213,196,118)(74,119,169,214)(75,215,170,120)(76,121,171,216)(77,217,172,122)(78,123,173,218)(79,219,174,124)(80,125,175,220)(81,221,176,126)(82,127,177,222)(83,223,178,128)(84,129,179,224), (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)(29,38,43,52)(30,51,44,37)(31,36,45,50)(32,49,46,35)(33,34,47,48)(39,56,53,42)(40,41,54,55)(57,58,71,72)(59,84,73,70)(60,69,74,83)(61,82,75,68)(62,67,76,81)(63,80,77,66)(64,65,78,79)(85,141,99,155)(86,154,100,168)(87,167,101,153)(88,152,102,166)(89,165,103,151)(90,150,104,164)(91,163,105,149)(92,148,106,162)(93,161,107,147)(94,146,108,160)(95,159,109,145)(96,144,110,158)(97,157,111,143)(98,142,112,156)(113,215,127,201)(114,200,128,214)(115,213,129,199)(116,198,130,212)(117,211,131,197)(118,224,132,210)(119,209,133,223)(120,222,134,208)(121,207,135,221)(122,220,136,206)(123,205,137,219)(124,218,138,204)(125,203,139,217)(126,216,140,202)(169,178,183,192)(170,191,184,177)(171,176,185,190)(172,189,186,175)(173,174,187,188)(179,196,193,182)(180,181,194,195) );
G=PermutationGroup([[(1,174,55,65),(2,66,56,175),(3,176,29,67),(4,68,30,177),(5,178,31,69),(6,70,32,179),(7,180,33,71),(8,72,34,181),(9,182,35,73),(10,74,36,183),(11,184,37,75),(12,76,38,185),(13,186,39,77),(14,78,40,187),(15,188,41,79),(16,80,42,189),(17,190,43,81),(18,82,44,191),(19,192,45,83),(20,84,46,193),(21,194,47,57),(22,58,48,195),(23,196,49,59),(24,60,50,169),(25,170,51,61),(26,62,52,171),(27,172,53,63),(28,64,54,173),(85,122,152,203),(86,204,153,123),(87,124,154,205),(88,206,155,125),(89,126,156,207),(90,208,157,127),(91,128,158,209),(92,210,159,129),(93,130,160,211),(94,212,161,131),(95,132,162,213),(96,214,163,133),(97,134,164,215),(98,216,165,135),(99,136,166,217),(100,218,167,137),(101,138,168,219),(102,220,141,139),(103,140,142,221),(104,222,143,113),(105,114,144,223),(106,224,145,115),(107,116,146,197),(108,198,147,117),(109,118,148,199),(110,200,149,119),(111,120,150,201),(112,202,151,121)], [(1,87,41,168),(2,141,42,88),(3,89,43,142),(4,143,44,90),(5,91,45,144),(6,145,46,92),(7,93,47,146),(8,147,48,94),(9,95,49,148),(10,149,50,96),(11,97,51,150),(12,151,52,98),(13,99,53,152),(14,153,54,100),(15,101,55,154),(16,155,56,102),(17,103,29,156),(18,157,30,104),(19,105,31,158),(20,159,32,106),(21,107,33,160),(22,161,34,108),(23,109,35,162),(24,163,36,110),(25,111,37,164),(26,165,38,112),(27,85,39,166),(28,167,40,86),(57,197,180,130),(58,131,181,198),(59,199,182,132),(60,133,183,200),(61,201,184,134),(62,135,185,202),(63,203,186,136),(64,137,187,204),(65,205,188,138),(66,139,189,206),(67,207,190,140),(68,113,191,208),(69,209,192,114),(70,115,193,210),(71,211,194,116),(72,117,195,212),(73,213,196,118),(74,119,169,214),(75,215,170,120),(76,121,171,216),(77,217,172,122),(78,123,173,218),(79,219,174,124),(80,125,175,220),(81,221,176,126),(82,127,177,222),(83,223,178,128),(84,129,179,224)], [(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),(29,38,43,52),(30,51,44,37),(31,36,45,50),(32,49,46,35),(33,34,47,48),(39,56,53,42),(40,41,54,55),(57,58,71,72),(59,84,73,70),(60,69,74,83),(61,82,75,68),(62,67,76,81),(63,80,77,66),(64,65,78,79),(85,141,99,155),(86,154,100,168),(87,167,101,153),(88,152,102,166),(89,165,103,151),(90,150,104,164),(91,163,105,149),(92,148,106,162),(93,161,107,147),(94,146,108,160),(95,159,109,145),(96,144,110,158),(97,157,111,143),(98,142,112,156),(113,215,127,201),(114,200,128,214),(115,213,129,199),(116,198,130,212),(117,211,131,197),(118,224,132,210),(119,209,133,223),(120,222,134,208),(121,207,135,221),(122,220,136,206),(123,205,137,219),(124,218,138,204),(125,203,139,217),(126,216,140,202),(169,178,183,192),(170,191,184,177),(171,176,185,190),(172,189,186,175),(173,174,187,188),(179,196,193,182),(180,181,194,195)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | ··· | 4H | 4I | 4J | 4K | ··· | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 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 | Q8 | D7 | D14 | D14 | D14 | 2+ 1+4 | 2- 1+4 | Q8×D7 | D4⋊6D14 | Q8.10D14 |
| kernel | C42.174D14 | C28.6Q8 | C42⋊D7 | C28⋊Q8 | Dic7.Q8 | C28.3Q8 | D7×C4⋊C4 | C4⋊C4⋊7D7 | D14⋊Q8 | Dic7⋊Q8 | D14⋊3Q8 | C7×C4⋊Q8 | C4×D7 | C4⋊Q8 | C42 | C4⋊C4 | C2×Q8 | C14 | C14 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 2 | 2 | 1 | 4 | 3 | 3 | 12 | 6 | 1 | 1 | 6 | 6 | 6 |
Matrix representation of C42.174D14 ►in GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 21 | 8 | 17 |
| 0 | 0 | 11 | 0 | 11 | 17 |
| 0 | 0 | 5 | 3 | 6 | 8 |
| 0 | 0 | 25 | 10 | 8 | 6 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 2 | 0 | 14 |
| 0 | 0 | 17 | 24 | 15 | 4 |
| 0 | 0 | 26 | 25 | 18 | 27 |
| 0 | 0 | 4 | 0 | 2 | 11 |
| 18 | 20 | 0 | 0 | 0 | 0 |
| 20 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 13 | 14 | 8 | 13 |
| 0 | 0 | 19 | 5 | 15 | 20 |
| 0 | 0 | 1 | 10 | 28 | 15 |
| 0 | 0 | 27 | 8 | 1 | 12 |
| 18 | 20 | 0 | 0 | 0 | 0 |
| 20 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 24 | 12 | 16 | 21 |
| 0 | 0 | 18 | 21 | 9 | 14 |
| 0 | 0 | 13 | 21 | 14 | 1 |
| 0 | 0 | 27 | 8 | 17 | 28 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,17,11,5,25,0,0,21,0,3,10,0,0,8,11,6,8,0,0,17,17,8,6],[0,28,0,0,0,0,1,0,0,0,0,0,0,0,5,17,26,4,0,0,2,24,25,0,0,0,0,15,18,2,0,0,14,4,27,11],[18,20,0,0,0,0,20,11,0,0,0,0,0,0,13,19,1,27,0,0,14,5,10,8,0,0,8,15,28,1,0,0,13,20,15,12],[18,20,0,0,0,0,20,11,0,0,0,0,0,0,24,18,13,27,0,0,12,21,21,8,0,0,16,9,14,17,0,0,21,14,1,28] >;
C42.174D14 in GAP, Magma, Sage, TeX
C_4^2._{174}D_{14} % in TeX
G:=Group("C4^2.174D14"); // GroupNames label
G:=SmallGroup(448,1182);
// by ID
G=gap.SmallGroup(448,1182);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,268,675,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^2*b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=b^-1,d*b*d^-1=a^2*b^-1,d*c*d^-1=c^13>;
// generators/relations