metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.152D14, C14.962- 1+4, C42.C2⋊8D7, C4⋊C4.208D14, (C4×D28).25C2, D14⋊2Q8⋊38C2, (C4×Dic14)⋊48C2, (C2×C28).90C23, C28.3Q8⋊35C2, D14.25(C4○D4), C28.129(C4○D4), (C4×C28).197C22, (C2×C14).238C24, C4.38(Q8⋊2D7), D14.5D4.3C2, D14⋊C4.138C22, (C2×D28).225C22, C4⋊Dic7.243C22, C22.259(C23×D7), Dic7⋊C4.123C22, (C4×Dic7).144C22, (C2×Dic7).123C23, (C22×D7).103C23, C2.58(D4.10D14), C7⋊10(C22.46C24), (C2×Dic14).299C22, (D7×C4⋊C4)⋊38C2, C2.89(D7×C4○D4), C4⋊C4⋊7D7⋊37C2, C4⋊C4⋊D7⋊36C2, C14.200(C2×C4○D4), C2.23(C2×Q8⋊2D7), (C7×C42.C2)⋊11C2, (C2×C4×D7).128C22, (C2×C4).81(C22×D7), (C7×C4⋊C4).193C22, SmallGroup(448,1147)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.152D14
G = < a,b,c,d | a4=b4=1, c14=d2=b2, ab=ba, cac-1=dad-1=a-1, cbc-1=a2b-1, dbd-1=a2b, dcd-1=c13 >
Subgroups: 924 in 214 conjugacy classes, 97 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, Dic7, C28, C28, D14, D14, C2×C14, C2×C4⋊C4, C42⋊C2, C4×D4, C4×Q8, C22⋊Q8, C22.D4, C42.C2, C42.C2, C42⋊2C2, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C22.46C24, C4×Dic7, 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, C2×D28, C4×Dic14, C4×D28, C28.3Q8, D7×C4⋊C4, C4⋊C4⋊7D7, C4⋊C4⋊7D7, D14.5D4, D14⋊2Q8, C4⋊C4⋊D7, C7×C42.C2, C42.152D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2- 1+4, C22×D7, C22.46C24, Q8⋊2D7, C23×D7, C2×Q8⋊2D7, D7×C4○D4, D4.10D14, C42.152D14
►On 224 points
Generators in S224
(1 94 209 74)(2 75 210 95)(3 96 211 76)(4 77 212 97)(5 98 213 78)(6 79 214 99)(7 100 215 80)(8 81 216 101)(9 102 217 82)(10 83 218 103)(11 104 219 84)(12 57 220 105)(13 106 221 58)(14 59 222 107)(15 108 223 60)(16 61 224 109)(17 110 197 62)(18 63 198 111)(19 112 199 64)(20 65 200 85)(21 86 201 66)(22 67 202 87)(23 88 203 68)(24 69 204 89)(25 90 205 70)(26 71 206 91)(27 92 207 72)(28 73 208 93)(29 166 114 182)(30 183 115 167)(31 168 116 184)(32 185 117 141)(33 142 118 186)(34 187 119 143)(35 144 120 188)(36 189 121 145)(37 146 122 190)(38 191 123 147)(39 148 124 192)(40 193 125 149)(41 150 126 194)(42 195 127 151)(43 152 128 196)(44 169 129 153)(45 154 130 170)(46 171 131 155)(47 156 132 172)(48 173 133 157)(49 158 134 174)(50 175 135 159)(51 160 136 176)(52 177 137 161)(53 162 138 178)(54 179 139 163)(55 164 140 180)(56 181 113 165)
(1 175 15 189)(2 146 16 160)(3 177 17 191)(4 148 18 162)(5 179 19 193)(6 150 20 164)(7 181 21 195)(8 152 22 166)(9 183 23 169)(10 154 24 168)(11 185 25 171)(12 156 26 142)(13 187 27 173)(14 158 28 144)(29 101 43 87)(30 68 44 82)(31 103 45 89)(32 70 46 84)(33 105 47 91)(34 72 48 58)(35 107 49 93)(36 74 50 60)(37 109 51 95)(38 76 52 62)(39 111 53 97)(40 78 54 64)(41 85 55 99)(42 80 56 66)(57 132 71 118)(59 134 73 120)(61 136 75 122)(63 138 77 124)(65 140 79 126)(67 114 81 128)(69 116 83 130)(86 127 100 113)(88 129 102 115)(90 131 104 117)(92 133 106 119)(94 135 108 121)(96 137 110 123)(98 139 112 125)(141 205 155 219)(143 207 157 221)(145 209 159 223)(147 211 161 197)(149 213 163 199)(151 215 165 201)(153 217 167 203)(170 204 184 218)(172 206 186 220)(174 208 188 222)(176 210 190 224)(178 212 192 198)(180 214 194 200)(182 216 196 202)
(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 56 43 42)(30 41 44 55)(31 54 45 40)(32 39 46 53)(33 52 47 38)(34 37 48 51)(35 50 49 36)(57 62 71 76)(58 75 72 61)(59 60 73 74)(63 84 77 70)(64 69 78 83)(65 82 79 68)(66 67 80 81)(85 102 99 88)(86 87 100 101)(89 98 103 112)(90 111 104 97)(91 96 105 110)(92 109 106 95)(93 94 107 108)(113 128 127 114)(115 126 129 140)(116 139 130 125)(117 124 131 138)(118 137 132 123)(119 122 133 136)(120 135 134 121)(141 148 155 162)(142 161 156 147)(143 146 157 160)(144 159 158 145)(149 168 163 154)(150 153 164 167)(151 166 165 152)(169 180 183 194)(170 193 184 179)(171 178 185 192)(172 191 186 177)(173 176 187 190)(174 189 188 175)(181 196 195 182)(197 206 211 220)(198 219 212 205)(199 204 213 218)(200 217 214 203)(201 202 215 216)(207 224 221 210)(208 209 222 223)
G:=sub<Sym(224)| (1,94,209,74)(2,75,210,95)(3,96,211,76)(4,77,212,97)(5,98,213,78)(6,79,214,99)(7,100,215,80)(8,81,216,101)(9,102,217,82)(10,83,218,103)(11,104,219,84)(12,57,220,105)(13,106,221,58)(14,59,222,107)(15,108,223,60)(16,61,224,109)(17,110,197,62)(18,63,198,111)(19,112,199,64)(20,65,200,85)(21,86,201,66)(22,67,202,87)(23,88,203,68)(24,69,204,89)(25,90,205,70)(26,71,206,91)(27,92,207,72)(28,73,208,93)(29,166,114,182)(30,183,115,167)(31,168,116,184)(32,185,117,141)(33,142,118,186)(34,187,119,143)(35,144,120,188)(36,189,121,145)(37,146,122,190)(38,191,123,147)(39,148,124,192)(40,193,125,149)(41,150,126,194)(42,195,127,151)(43,152,128,196)(44,169,129,153)(45,154,130,170)(46,171,131,155)(47,156,132,172)(48,173,133,157)(49,158,134,174)(50,175,135,159)(51,160,136,176)(52,177,137,161)(53,162,138,178)(54,179,139,163)(55,164,140,180)(56,181,113,165), (1,175,15,189)(2,146,16,160)(3,177,17,191)(4,148,18,162)(5,179,19,193)(6,150,20,164)(7,181,21,195)(8,152,22,166)(9,183,23,169)(10,154,24,168)(11,185,25,171)(12,156,26,142)(13,187,27,173)(14,158,28,144)(29,101,43,87)(30,68,44,82)(31,103,45,89)(32,70,46,84)(33,105,47,91)(34,72,48,58)(35,107,49,93)(36,74,50,60)(37,109,51,95)(38,76,52,62)(39,111,53,97)(40,78,54,64)(41,85,55,99)(42,80,56,66)(57,132,71,118)(59,134,73,120)(61,136,75,122)(63,138,77,124)(65,140,79,126)(67,114,81,128)(69,116,83,130)(86,127,100,113)(88,129,102,115)(90,131,104,117)(92,133,106,119)(94,135,108,121)(96,137,110,123)(98,139,112,125)(141,205,155,219)(143,207,157,221)(145,209,159,223)(147,211,161,197)(149,213,163,199)(151,215,165,201)(153,217,167,203)(170,204,184,218)(172,206,186,220)(174,208,188,222)(176,210,190,224)(178,212,192,198)(180,214,194,200)(182,216,196,202), (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)(29,56,43,42)(30,41,44,55)(31,54,45,40)(32,39,46,53)(33,52,47,38)(34,37,48,51)(35,50,49,36)(57,62,71,76)(58,75,72,61)(59,60,73,74)(63,84,77,70)(64,69,78,83)(65,82,79,68)(66,67,80,81)(85,102,99,88)(86,87,100,101)(89,98,103,112)(90,111,104,97)(91,96,105,110)(92,109,106,95)(93,94,107,108)(113,128,127,114)(115,126,129,140)(116,139,130,125)(117,124,131,138)(118,137,132,123)(119,122,133,136)(120,135,134,121)(141,148,155,162)(142,161,156,147)(143,146,157,160)(144,159,158,145)(149,168,163,154)(150,153,164,167)(151,166,165,152)(169,180,183,194)(170,193,184,179)(171,178,185,192)(172,191,186,177)(173,176,187,190)(174,189,188,175)(181,196,195,182)(197,206,211,220)(198,219,212,205)(199,204,213,218)(200,217,214,203)(201,202,215,216)(207,224,221,210)(208,209,222,223)>;
G:=Group( (1,94,209,74)(2,75,210,95)(3,96,211,76)(4,77,212,97)(5,98,213,78)(6,79,214,99)(7,100,215,80)(8,81,216,101)(9,102,217,82)(10,83,218,103)(11,104,219,84)(12,57,220,105)(13,106,221,58)(14,59,222,107)(15,108,223,60)(16,61,224,109)(17,110,197,62)(18,63,198,111)(19,112,199,64)(20,65,200,85)(21,86,201,66)(22,67,202,87)(23,88,203,68)(24,69,204,89)(25,90,205,70)(26,71,206,91)(27,92,207,72)(28,73,208,93)(29,166,114,182)(30,183,115,167)(31,168,116,184)(32,185,117,141)(33,142,118,186)(34,187,119,143)(35,144,120,188)(36,189,121,145)(37,146,122,190)(38,191,123,147)(39,148,124,192)(40,193,125,149)(41,150,126,194)(42,195,127,151)(43,152,128,196)(44,169,129,153)(45,154,130,170)(46,171,131,155)(47,156,132,172)(48,173,133,157)(49,158,134,174)(50,175,135,159)(51,160,136,176)(52,177,137,161)(53,162,138,178)(54,179,139,163)(55,164,140,180)(56,181,113,165), (1,175,15,189)(2,146,16,160)(3,177,17,191)(4,148,18,162)(5,179,19,193)(6,150,20,164)(7,181,21,195)(8,152,22,166)(9,183,23,169)(10,154,24,168)(11,185,25,171)(12,156,26,142)(13,187,27,173)(14,158,28,144)(29,101,43,87)(30,68,44,82)(31,103,45,89)(32,70,46,84)(33,105,47,91)(34,72,48,58)(35,107,49,93)(36,74,50,60)(37,109,51,95)(38,76,52,62)(39,111,53,97)(40,78,54,64)(41,85,55,99)(42,80,56,66)(57,132,71,118)(59,134,73,120)(61,136,75,122)(63,138,77,124)(65,140,79,126)(67,114,81,128)(69,116,83,130)(86,127,100,113)(88,129,102,115)(90,131,104,117)(92,133,106,119)(94,135,108,121)(96,137,110,123)(98,139,112,125)(141,205,155,219)(143,207,157,221)(145,209,159,223)(147,211,161,197)(149,213,163,199)(151,215,165,201)(153,217,167,203)(170,204,184,218)(172,206,186,220)(174,208,188,222)(176,210,190,224)(178,212,192,198)(180,214,194,200)(182,216,196,202), (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)(29,56,43,42)(30,41,44,55)(31,54,45,40)(32,39,46,53)(33,52,47,38)(34,37,48,51)(35,50,49,36)(57,62,71,76)(58,75,72,61)(59,60,73,74)(63,84,77,70)(64,69,78,83)(65,82,79,68)(66,67,80,81)(85,102,99,88)(86,87,100,101)(89,98,103,112)(90,111,104,97)(91,96,105,110)(92,109,106,95)(93,94,107,108)(113,128,127,114)(115,126,129,140)(116,139,130,125)(117,124,131,138)(118,137,132,123)(119,122,133,136)(120,135,134,121)(141,148,155,162)(142,161,156,147)(143,146,157,160)(144,159,158,145)(149,168,163,154)(150,153,164,167)(151,166,165,152)(169,180,183,194)(170,193,184,179)(171,178,185,192)(172,191,186,177)(173,176,187,190)(174,189,188,175)(181,196,195,182)(197,206,211,220)(198,219,212,205)(199,204,213,218)(200,217,214,203)(201,202,215,216)(207,224,221,210)(208,209,222,223) );
G=PermutationGroup([[(1,94,209,74),(2,75,210,95),(3,96,211,76),(4,77,212,97),(5,98,213,78),(6,79,214,99),(7,100,215,80),(8,81,216,101),(9,102,217,82),(10,83,218,103),(11,104,219,84),(12,57,220,105),(13,106,221,58),(14,59,222,107),(15,108,223,60),(16,61,224,109),(17,110,197,62),(18,63,198,111),(19,112,199,64),(20,65,200,85),(21,86,201,66),(22,67,202,87),(23,88,203,68),(24,69,204,89),(25,90,205,70),(26,71,206,91),(27,92,207,72),(28,73,208,93),(29,166,114,182),(30,183,115,167),(31,168,116,184),(32,185,117,141),(33,142,118,186),(34,187,119,143),(35,144,120,188),(36,189,121,145),(37,146,122,190),(38,191,123,147),(39,148,124,192),(40,193,125,149),(41,150,126,194),(42,195,127,151),(43,152,128,196),(44,169,129,153),(45,154,130,170),(46,171,131,155),(47,156,132,172),(48,173,133,157),(49,158,134,174),(50,175,135,159),(51,160,136,176),(52,177,137,161),(53,162,138,178),(54,179,139,163),(55,164,140,180),(56,181,113,165)], [(1,175,15,189),(2,146,16,160),(3,177,17,191),(4,148,18,162),(5,179,19,193),(6,150,20,164),(7,181,21,195),(8,152,22,166),(9,183,23,169),(10,154,24,168),(11,185,25,171),(12,156,26,142),(13,187,27,173),(14,158,28,144),(29,101,43,87),(30,68,44,82),(31,103,45,89),(32,70,46,84),(33,105,47,91),(34,72,48,58),(35,107,49,93),(36,74,50,60),(37,109,51,95),(38,76,52,62),(39,111,53,97),(40,78,54,64),(41,85,55,99),(42,80,56,66),(57,132,71,118),(59,134,73,120),(61,136,75,122),(63,138,77,124),(65,140,79,126),(67,114,81,128),(69,116,83,130),(86,127,100,113),(88,129,102,115),(90,131,104,117),(92,133,106,119),(94,135,108,121),(96,137,110,123),(98,139,112,125),(141,205,155,219),(143,207,157,221),(145,209,159,223),(147,211,161,197),(149,213,163,199),(151,215,165,201),(153,217,167,203),(170,204,184,218),(172,206,186,220),(174,208,188,222),(176,210,190,224),(178,212,192,198),(180,214,194,200),(182,216,196,202)], [(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),(29,56,43,42),(30,41,44,55),(31,54,45,40),(32,39,46,53),(33,52,47,38),(34,37,48,51),(35,50,49,36),(57,62,71,76),(58,75,72,61),(59,60,73,74),(63,84,77,70),(64,69,78,83),(65,82,79,68),(66,67,80,81),(85,102,99,88),(86,87,100,101),(89,98,103,112),(90,111,104,97),(91,96,105,110),(92,109,106,95),(93,94,107,108),(113,128,127,114),(115,126,129,140),(116,139,130,125),(117,124,131,138),(118,137,132,123),(119,122,133,136),(120,135,134,121),(141,148,155,162),(142,161,156,147),(143,146,157,160),(144,159,158,145),(149,168,163,154),(150,153,164,167),(151,166,165,152),(169,180,183,194),(170,193,184,179),(171,178,185,192),(172,191,186,177),(173,176,187,190),(174,189,188,175),(181,196,195,182),(197,206,211,220),(198,219,212,205),(199,204,213,218),(200,217,214,203),(201,202,215,216),(207,224,221,210),(208,209,222,223)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | ··· | 4I | 4J | ··· | 4O | 4P | 4Q | 4R | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 28 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | 2- 1+4 | Q8⋊2D7 | D7×C4○D4 | D4.10D14 |
| kernel | C42.152D14 | C4×Dic14 | C4×D28 | C28.3Q8 | D7×C4⋊C4 | C4⋊C4⋊7D7 | D14.5D4 | D14⋊2Q8 | C4⋊C4⋊D7 | C7×C42.C2 | C42.C2 | C28 | D14 | C42 | C4⋊C4 | C14 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 1 | 3 | 2 | 2 | 2 | 1 | 3 | 4 | 4 | 3 | 18 | 1 | 6 | 6 | 6 |
Matrix representation of C42.152D14 ►in GL6(𝔽29)
| 12 | 28 | 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 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 28 | 17 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 12 | 28 | 0 | 0 | 0 | 0 |
| 27 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 10 | 0 | 0 |
| 0 | 0 | 19 | 22 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 12 | 28 | 0 | 0 | 0 | 0 |
| 27 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 10 | 0 | 0 |
| 0 | 0 | 22 | 19 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,28,17,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[28,0,0,0,0,0,17,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,0,28,0,0,0,0,1,0],[12,27,0,0,0,0,28,17,0,0,0,0,0,0,10,19,0,0,0,0,10,22,0,0,0,0,0,0,12,0,0,0,0,0,0,17],[12,27,0,0,0,0,28,17,0,0,0,0,0,0,10,22,0,0,0,0,10,19,0,0,0,0,0,0,12,0,0,0,0,0,0,12] >;
C42.152D14 in GAP, Magma, Sage, TeX
C_4^2._{152}D_{14} % in TeX
G:=Group("C4^2.152D14"); // GroupNames label
G:=SmallGroup(448,1147);
// by ID
G=gap.SmallGroup(448,1147);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,268,1571,297,192,18822]);
// 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,c*b*c^-1=a^2*b^-1,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations