metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.156D14, C14.1342+ 1+4, C28⋊4D4⋊15C2, C4⋊D28⋊34C2, C4⋊C4.113D14, C42.C2⋊12D7, D28⋊C4⋊38C2, C42⋊D7⋊22C2, D14.5D4⋊36C2, C28.132(C4○D4), (C2×C28).189C23, (C2×C14).242C24, (C4×C28).201C22, C4.21(Q8⋊2D7), C2.59(D4⋊8D14), D14⋊C4.113C22, (C2×D28).166C22, C22.263(C23×D7), Dic7⋊C4.125C22, C7⋊6(C22.34C24), (C4×Dic7).147C22, (C2×Dic7).262C23, (C22×D7).107C23, C14.119(C2×C4○D4), C2.26(C2×Q8⋊2D7), (C7×C42.C2)⋊15C2, (C2×C4×D7).132C22, (C7×C4⋊C4).197C22, (C2×C4).594(C22×D7), SmallGroup(448,1151)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.156D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2, ab=ba, cac-1=ab2, dad-1=a-1b2, cbc-1=a2b, dbd-1=a2b-1, dcd-1=c13 >
Subgroups: 1404 in 240 conjugacy classes, 95 normal (19 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, C23, D7, C14, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, Dic7, C28, C28, D14, C2×C14, C42⋊C2, C4×D4, C4⋊D4, C22.D4, C42.C2, C4⋊1D4, C4×D7, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22.34C24, C4×Dic7, Dic7⋊C4, D14⋊C4, C4×C28, C7×C4⋊C4, C2×C4×D7, C2×C4×D7, C2×D28, C42⋊D7, C28⋊4D4, D28⋊C4, D14.5D4, C4⋊D28, C7×C42.C2, C42.156D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.34C24, Q8⋊2D7, C23×D7, C2×Q8⋊2D7, D4⋊8D14, C42.156D14
►On 224 points
Generators in S224
(1 60 15 74)(2 213 16 199)(3 62 17 76)(4 215 18 201)(5 64 19 78)(6 217 20 203)(7 66 21 80)(8 219 22 205)(9 68 23 82)(10 221 24 207)(11 70 25 84)(12 223 26 209)(13 72 27 58)(14 197 28 211)(29 149 43 163)(30 127 44 113)(31 151 45 165)(32 129 46 115)(33 153 47 167)(34 131 48 117)(35 155 49 141)(36 133 50 119)(37 157 51 143)(38 135 52 121)(39 159 53 145)(40 137 54 123)(41 161 55 147)(42 139 56 125)(57 105 71 91)(59 107 73 93)(61 109 75 95)(63 111 77 97)(65 85 79 99)(67 87 81 101)(69 89 83 103)(86 204 100 218)(88 206 102 220)(90 208 104 222)(92 210 106 224)(94 212 108 198)(96 214 110 200)(98 216 112 202)(114 171 128 185)(116 173 130 187)(118 175 132 189)(120 177 134 191)(122 179 136 193)(124 181 138 195)(126 183 140 169)(142 176 156 190)(144 178 158 192)(146 180 160 194)(148 182 162 196)(150 184 164 170)(152 186 166 172)(154 188 168 174)
(1 137 94 160)(2 124 95 147)(3 139 96 162)(4 126 97 149)(5 113 98 164)(6 128 99 151)(7 115 100 166)(8 130 101 153)(9 117 102 168)(10 132 103 155)(11 119 104 142)(12 134 105 157)(13 121 106 144)(14 136 107 159)(15 123 108 146)(16 138 109 161)(17 125 110 148)(18 140 111 163)(19 127 112 150)(20 114 85 165)(21 129 86 152)(22 116 87 167)(23 131 88 154)(24 118 89 141)(25 133 90 156)(26 120 91 143)(27 135 92 158)(28 122 93 145)(29 201 169 77)(30 216 170 64)(31 203 171 79)(32 218 172 66)(33 205 173 81)(34 220 174 68)(35 207 175 83)(36 222 176 70)(37 209 177 57)(38 224 178 72)(39 211 179 59)(40 198 180 74)(41 213 181 61)(42 200 182 76)(43 215 183 63)(44 202 184 78)(45 217 185 65)(46 204 186 80)(47 219 187 67)(48 206 188 82)(49 221 189 69)(50 208 190 84)(51 223 191 71)(52 210 192 58)(53 197 193 73)(54 212 194 60)(55 199 195 75)(56 214 196 62)
(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)
(1 193 15 179)(2 178 16 192)(3 191 17 177)(4 176 18 190)(5 189 19 175)(6 174 20 188)(7 187 21 173)(8 172 22 186)(9 185 23 171)(10 170 24 184)(11 183 25 169)(12 196 26 182)(13 181 27 195)(14 194 28 180)(29 104 43 90)(30 89 44 103)(31 102 45 88)(32 87 46 101)(33 100 47 86)(34 85 48 99)(35 98 49 112)(36 111 50 97)(37 96 51 110)(38 109 52 95)(39 94 53 108)(40 107 54 93)(41 92 55 106)(42 105 56 91)(57 148 71 162)(58 161 72 147)(59 146 73 160)(60 159 74 145)(61 144 75 158)(62 157 76 143)(63 142 77 156)(64 155 78 141)(65 168 79 154)(66 153 80 167)(67 166 81 152)(68 151 82 165)(69 164 83 150)(70 149 84 163)(113 207 127 221)(114 220 128 206)(115 205 129 219)(116 218 130 204)(117 203 131 217)(118 216 132 202)(119 201 133 215)(120 214 134 200)(121 199 135 213)(122 212 136 198)(123 197 137 211)(124 210 138 224)(125 223 139 209)(126 208 140 222)
G:=sub<Sym(224)| (1,60,15,74)(2,213,16,199)(3,62,17,76)(4,215,18,201)(5,64,19,78)(6,217,20,203)(7,66,21,80)(8,219,22,205)(9,68,23,82)(10,221,24,207)(11,70,25,84)(12,223,26,209)(13,72,27,58)(14,197,28,211)(29,149,43,163)(30,127,44,113)(31,151,45,165)(32,129,46,115)(33,153,47,167)(34,131,48,117)(35,155,49,141)(36,133,50,119)(37,157,51,143)(38,135,52,121)(39,159,53,145)(40,137,54,123)(41,161,55,147)(42,139,56,125)(57,105,71,91)(59,107,73,93)(61,109,75,95)(63,111,77,97)(65,85,79,99)(67,87,81,101)(69,89,83,103)(86,204,100,218)(88,206,102,220)(90,208,104,222)(92,210,106,224)(94,212,108,198)(96,214,110,200)(98,216,112,202)(114,171,128,185)(116,173,130,187)(118,175,132,189)(120,177,134,191)(122,179,136,193)(124,181,138,195)(126,183,140,169)(142,176,156,190)(144,178,158,192)(146,180,160,194)(148,182,162,196)(150,184,164,170)(152,186,166,172)(154,188,168,174), (1,137,94,160)(2,124,95,147)(3,139,96,162)(4,126,97,149)(5,113,98,164)(6,128,99,151)(7,115,100,166)(8,130,101,153)(9,117,102,168)(10,132,103,155)(11,119,104,142)(12,134,105,157)(13,121,106,144)(14,136,107,159)(15,123,108,146)(16,138,109,161)(17,125,110,148)(18,140,111,163)(19,127,112,150)(20,114,85,165)(21,129,86,152)(22,116,87,167)(23,131,88,154)(24,118,89,141)(25,133,90,156)(26,120,91,143)(27,135,92,158)(28,122,93,145)(29,201,169,77)(30,216,170,64)(31,203,171,79)(32,218,172,66)(33,205,173,81)(34,220,174,68)(35,207,175,83)(36,222,176,70)(37,209,177,57)(38,224,178,72)(39,211,179,59)(40,198,180,74)(41,213,181,61)(42,200,182,76)(43,215,183,63)(44,202,184,78)(45,217,185,65)(46,204,186,80)(47,219,187,67)(48,206,188,82)(49,221,189,69)(50,208,190,84)(51,223,191,71)(52,210,192,58)(53,197,193,73)(54,212,194,60)(55,199,195,75)(56,214,196,62), (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), (1,193,15,179)(2,178,16,192)(3,191,17,177)(4,176,18,190)(5,189,19,175)(6,174,20,188)(7,187,21,173)(8,172,22,186)(9,185,23,171)(10,170,24,184)(11,183,25,169)(12,196,26,182)(13,181,27,195)(14,194,28,180)(29,104,43,90)(30,89,44,103)(31,102,45,88)(32,87,46,101)(33,100,47,86)(34,85,48,99)(35,98,49,112)(36,111,50,97)(37,96,51,110)(38,109,52,95)(39,94,53,108)(40,107,54,93)(41,92,55,106)(42,105,56,91)(57,148,71,162)(58,161,72,147)(59,146,73,160)(60,159,74,145)(61,144,75,158)(62,157,76,143)(63,142,77,156)(64,155,78,141)(65,168,79,154)(66,153,80,167)(67,166,81,152)(68,151,82,165)(69,164,83,150)(70,149,84,163)(113,207,127,221)(114,220,128,206)(115,205,129,219)(116,218,130,204)(117,203,131,217)(118,216,132,202)(119,201,133,215)(120,214,134,200)(121,199,135,213)(122,212,136,198)(123,197,137,211)(124,210,138,224)(125,223,139,209)(126,208,140,222)>;
G:=Group( (1,60,15,74)(2,213,16,199)(3,62,17,76)(4,215,18,201)(5,64,19,78)(6,217,20,203)(7,66,21,80)(8,219,22,205)(9,68,23,82)(10,221,24,207)(11,70,25,84)(12,223,26,209)(13,72,27,58)(14,197,28,211)(29,149,43,163)(30,127,44,113)(31,151,45,165)(32,129,46,115)(33,153,47,167)(34,131,48,117)(35,155,49,141)(36,133,50,119)(37,157,51,143)(38,135,52,121)(39,159,53,145)(40,137,54,123)(41,161,55,147)(42,139,56,125)(57,105,71,91)(59,107,73,93)(61,109,75,95)(63,111,77,97)(65,85,79,99)(67,87,81,101)(69,89,83,103)(86,204,100,218)(88,206,102,220)(90,208,104,222)(92,210,106,224)(94,212,108,198)(96,214,110,200)(98,216,112,202)(114,171,128,185)(116,173,130,187)(118,175,132,189)(120,177,134,191)(122,179,136,193)(124,181,138,195)(126,183,140,169)(142,176,156,190)(144,178,158,192)(146,180,160,194)(148,182,162,196)(150,184,164,170)(152,186,166,172)(154,188,168,174), (1,137,94,160)(2,124,95,147)(3,139,96,162)(4,126,97,149)(5,113,98,164)(6,128,99,151)(7,115,100,166)(8,130,101,153)(9,117,102,168)(10,132,103,155)(11,119,104,142)(12,134,105,157)(13,121,106,144)(14,136,107,159)(15,123,108,146)(16,138,109,161)(17,125,110,148)(18,140,111,163)(19,127,112,150)(20,114,85,165)(21,129,86,152)(22,116,87,167)(23,131,88,154)(24,118,89,141)(25,133,90,156)(26,120,91,143)(27,135,92,158)(28,122,93,145)(29,201,169,77)(30,216,170,64)(31,203,171,79)(32,218,172,66)(33,205,173,81)(34,220,174,68)(35,207,175,83)(36,222,176,70)(37,209,177,57)(38,224,178,72)(39,211,179,59)(40,198,180,74)(41,213,181,61)(42,200,182,76)(43,215,183,63)(44,202,184,78)(45,217,185,65)(46,204,186,80)(47,219,187,67)(48,206,188,82)(49,221,189,69)(50,208,190,84)(51,223,191,71)(52,210,192,58)(53,197,193,73)(54,212,194,60)(55,199,195,75)(56,214,196,62), (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), (1,193,15,179)(2,178,16,192)(3,191,17,177)(4,176,18,190)(5,189,19,175)(6,174,20,188)(7,187,21,173)(8,172,22,186)(9,185,23,171)(10,170,24,184)(11,183,25,169)(12,196,26,182)(13,181,27,195)(14,194,28,180)(29,104,43,90)(30,89,44,103)(31,102,45,88)(32,87,46,101)(33,100,47,86)(34,85,48,99)(35,98,49,112)(36,111,50,97)(37,96,51,110)(38,109,52,95)(39,94,53,108)(40,107,54,93)(41,92,55,106)(42,105,56,91)(57,148,71,162)(58,161,72,147)(59,146,73,160)(60,159,74,145)(61,144,75,158)(62,157,76,143)(63,142,77,156)(64,155,78,141)(65,168,79,154)(66,153,80,167)(67,166,81,152)(68,151,82,165)(69,164,83,150)(70,149,84,163)(113,207,127,221)(114,220,128,206)(115,205,129,219)(116,218,130,204)(117,203,131,217)(118,216,132,202)(119,201,133,215)(120,214,134,200)(121,199,135,213)(122,212,136,198)(123,197,137,211)(124,210,138,224)(125,223,139,209)(126,208,140,222) );
G=PermutationGroup([[(1,60,15,74),(2,213,16,199),(3,62,17,76),(4,215,18,201),(5,64,19,78),(6,217,20,203),(7,66,21,80),(8,219,22,205),(9,68,23,82),(10,221,24,207),(11,70,25,84),(12,223,26,209),(13,72,27,58),(14,197,28,211),(29,149,43,163),(30,127,44,113),(31,151,45,165),(32,129,46,115),(33,153,47,167),(34,131,48,117),(35,155,49,141),(36,133,50,119),(37,157,51,143),(38,135,52,121),(39,159,53,145),(40,137,54,123),(41,161,55,147),(42,139,56,125),(57,105,71,91),(59,107,73,93),(61,109,75,95),(63,111,77,97),(65,85,79,99),(67,87,81,101),(69,89,83,103),(86,204,100,218),(88,206,102,220),(90,208,104,222),(92,210,106,224),(94,212,108,198),(96,214,110,200),(98,216,112,202),(114,171,128,185),(116,173,130,187),(118,175,132,189),(120,177,134,191),(122,179,136,193),(124,181,138,195),(126,183,140,169),(142,176,156,190),(144,178,158,192),(146,180,160,194),(148,182,162,196),(150,184,164,170),(152,186,166,172),(154,188,168,174)], [(1,137,94,160),(2,124,95,147),(3,139,96,162),(4,126,97,149),(5,113,98,164),(6,128,99,151),(7,115,100,166),(8,130,101,153),(9,117,102,168),(10,132,103,155),(11,119,104,142),(12,134,105,157),(13,121,106,144),(14,136,107,159),(15,123,108,146),(16,138,109,161),(17,125,110,148),(18,140,111,163),(19,127,112,150),(20,114,85,165),(21,129,86,152),(22,116,87,167),(23,131,88,154),(24,118,89,141),(25,133,90,156),(26,120,91,143),(27,135,92,158),(28,122,93,145),(29,201,169,77),(30,216,170,64),(31,203,171,79),(32,218,172,66),(33,205,173,81),(34,220,174,68),(35,207,175,83),(36,222,176,70),(37,209,177,57),(38,224,178,72),(39,211,179,59),(40,198,180,74),(41,213,181,61),(42,200,182,76),(43,215,183,63),(44,202,184,78),(45,217,185,65),(46,204,186,80),(47,219,187,67),(48,206,188,82),(49,221,189,69),(50,208,190,84),(51,223,191,71),(52,210,192,58),(53,197,193,73),(54,212,194,60),(55,199,195,75),(56,214,196,62)], [(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)], [(1,193,15,179),(2,178,16,192),(3,191,17,177),(4,176,18,190),(5,189,19,175),(6,174,20,188),(7,187,21,173),(8,172,22,186),(9,185,23,171),(10,170,24,184),(11,183,25,169),(12,196,26,182),(13,181,27,195),(14,194,28,180),(29,104,43,90),(30,89,44,103),(31,102,45,88),(32,87,46,101),(33,100,47,86),(34,85,48,99),(35,98,49,112),(36,111,50,97),(37,96,51,110),(38,109,52,95),(39,94,53,108),(40,107,54,93),(41,92,55,106),(42,105,56,91),(57,148,71,162),(58,161,72,147),(59,146,73,160),(60,159,74,145),(61,144,75,158),(62,157,76,143),(63,142,77,156),(64,155,78,141),(65,168,79,154),(66,153,80,167),(67,166,81,152),(68,151,82,165),(69,164,83,150),(70,149,84,163),(113,207,127,221),(114,220,128,206),(115,205,129,219),(116,218,130,204),(117,203,131,217),(118,216,132,202),(119,201,133,215),(120,214,134,200),(121,199,135,213),(122,212,136,198),(123,197,137,211),(124,210,138,224),(125,223,139,209),(126,208,140,222)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | ··· | 2H | 4A | 4B | 4C | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | ··· | 28 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 14 | 14 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | 2+ 1+4 | Q8⋊2D7 | D4⋊8D14 |
| kernel | C42.156D14 | C42⋊D7 | C28⋊4D4 | D28⋊C4 | D14.5D4 | C4⋊D28 | C7×C42.C2 | C42.C2 | C28 | C42 | C4⋊C4 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 4 | 6 | 1 | 3 | 4 | 3 | 18 | 2 | 6 | 12 |
Matrix representation of C42.156D14 ►in GL8(𝔽29)
| 1 | 0 | 2 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 2 | 0 | 0 | 0 | 0 |
| 28 | 0 | 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 23 | 14 | 0 | 4 |
| 0 | 0 | 0 | 0 | 20 | 2 | 25 | 11 |
| 0 | 0 | 0 | 0 | 19 | 15 | 22 | 5 |
| 0 | 0 | 0 | 0 | 1 | 14 | 14 | 11 |
| 28 | 0 | 27 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 27 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 19 | 6 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 10 | 0 | 0 |
| 0 | 0 | 0 | 0 | 16 | 14 | 8 | 6 |
| 0 | 0 | 0 | 0 | 14 | 0 | 23 | 21 |
| 10 | 9 | 25 | 1 | 0 | 0 | 0 | 0 |
| 11 | 11 | 27 | 9 | 0 | 0 | 0 | 0 |
| 17 | 6 | 19 | 20 | 0 | 0 | 0 | 0 |
| 17 | 8 | 18 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 27 | 16 | 20 |
| 0 | 0 | 0 | 0 | 16 | 21 | 28 | 13 |
| 0 | 0 | 0 | 0 | 21 | 4 | 6 | 10 |
| 0 | 0 | 0 | 0 | 18 | 12 | 27 | 2 |
| 4 | 22 | 28 | 6 | 0 | 0 | 0 | 0 |
| 9 | 25 | 28 | 1 | 0 | 0 | 0 | 0 |
| 15 | 26 | 5 | 16 | 0 | 0 | 0 | 0 |
| 15 | 14 | 10 | 24 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 14 | 10 | 8 | 28 |
| 0 | 0 | 0 | 0 | 9 | 6 | 21 | 18 |
| 0 | 0 | 0 | 0 | 10 | 24 | 28 | 24 |
| 0 | 0 | 0 | 0 | 17 | 15 | 24 | 10 |
G:=sub<GL(8,GF(29))| [1,0,28,0,0,0,0,0,0,1,0,28,0,0,0,0,2,0,28,0,0,0,0,0,0,2,0,28,0,0,0,0,0,0,0,0,23,20,19,1,0,0,0,0,14,2,15,14,0,0,0,0,0,25,22,14,0,0,0,0,4,11,5,11],[28,0,1,0,0,0,0,0,0,28,0,1,0,0,0,0,27,0,1,0,0,0,0,0,0,27,0,1,0,0,0,0,0,0,0,0,19,17,16,14,0,0,0,0,6,10,14,0,0,0,0,0,0,0,8,23,0,0,0,0,0,0,6,21],[10,11,17,17,0,0,0,0,9,11,6,8,0,0,0,0,25,27,19,18,0,0,0,0,1,9,20,18,0,0,0,0,0,0,0,0,0,16,21,18,0,0,0,0,27,21,4,12,0,0,0,0,16,28,6,27,0,0,0,0,20,13,10,2],[4,9,15,15,0,0,0,0,22,25,26,14,0,0,0,0,28,28,5,10,0,0,0,0,6,1,16,24,0,0,0,0,0,0,0,0,14,9,10,17,0,0,0,0,10,6,24,15,0,0,0,0,8,21,28,24,0,0,0,0,28,18,24,10] >;
C42.156D14 in GAP, Magma, Sage, TeX
C_4^2._{156}D_{14} % in TeX
G:=Group("C4^2.156D14"); // GroupNames label
G:=SmallGroup(448,1151);
// by ID
G=gap.SmallGroup(448,1151);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,219,184,675,570,80,18822]);
// 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=a*b^2,d*a*d^-1=a^-1*b^2,c*b*c^-1=a^2*b,d*b*d^-1=a^2*b^-1,d*c*d^-1=c^13>;
// generators/relations