metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.155D14, C14.972- 1+4, C4⋊C4.211D14, C28⋊2Q8⋊33C2, C42.C2⋊11D7, (C2×C28).92C23, C28.3Q8⋊37C2, C42⋊D7.7C2, Dic7⋊3Q8⋊38C2, C28.131(C4○D4), (C2×C14).241C24, (C4×C28).200C22, D14⋊2Q8.12C2, C4.20(Q8⋊2D7), D14⋊C4.112C22, C4⋊Dic7.244C22, C22.262(C23×D7), Dic7⋊C4.124C22, C7⋊5(C22.35C24), (C2×Dic7).261C23, (C4×Dic7).146C22, (C22×D7).106C23, C2.60(D4.10D14), (C2×Dic14).182C22, C4⋊C4⋊D7.3C2, C14.118(C2×C4○D4), C2.25(C2×Q8⋊2D7), (C7×C42.C2)⋊14C2, (C2×C4×D7).131C22, (C7×C4⋊C4).196C22, (C2×C4).206(C22×D7), SmallGroup(448,1150)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.155D14
G = < a,b,c,d | a4=b4=1, c14=b2, d2=a2, ab=ba, cac-1=dad-1=a-1, cbc-1=a2b-1, dbd-1=b-1, dcd-1=a2b2c13 >
Subgroups: 764 in 192 conjugacy classes, 95 normal (19 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, Q8, C23, D7, C14, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×Q8, Dic7, C28, C28, D14, C2×C14, C42⋊C2, C4×Q8, C22⋊Q8, C42.C2, C42.C2, C42⋊2C2, C4⋊Q8, Dic14, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C22.35C24, C4×Dic7, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C4×C28, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C28⋊2Q8, C42⋊D7, Dic7⋊3Q8, C28.3Q8, D14⋊2Q8, C4⋊C4⋊D7, C7×C42.C2, C42.155D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2- 1+4, C22×D7, C22.35C24, Q8⋊2D7, C23×D7, C2×Q8⋊2D7, D4.10D14, C42.155D14
►On 224 points
Generators in S224
(1 73 112 129)(2 130 85 74)(3 75 86 131)(4 132 87 76)(5 77 88 133)(6 134 89 78)(7 79 90 135)(8 136 91 80)(9 81 92 137)(10 138 93 82)(11 83 94 139)(12 140 95 84)(13 57 96 113)(14 114 97 58)(15 59 98 115)(16 116 99 60)(17 61 100 117)(18 118 101 62)(19 63 102 119)(20 120 103 64)(21 65 104 121)(22 122 105 66)(23 67 106 123)(24 124 107 68)(25 69 108 125)(26 126 109 70)(27 71 110 127)(28 128 111 72)(29 180 209 167)(30 168 210 181)(31 182 211 141)(32 142 212 183)(33 184 213 143)(34 144 214 185)(35 186 215 145)(36 146 216 187)(37 188 217 147)(38 148 218 189)(39 190 219 149)(40 150 220 191)(41 192 221 151)(42 152 222 193)(43 194 223 153)(44 154 224 195)(45 196 197 155)(46 156 198 169)(47 170 199 157)(48 158 200 171)(49 172 201 159)(50 160 202 173)(51 174 203 161)(52 162 204 175)(53 176 205 163)(54 164 206 177)(55 178 207 165)(56 166 208 179)
(1 157 15 143)(2 185 16 171)(3 159 17 145)(4 187 18 173)(5 161 19 147)(6 189 20 175)(7 163 21 149)(8 191 22 177)(9 165 23 151)(10 193 24 179)(11 167 25 153)(12 195 26 181)(13 141 27 155)(14 169 28 183)(29 69 43 83)(30 140 44 126)(31 71 45 57)(32 114 46 128)(33 73 47 59)(34 116 48 130)(35 75 49 61)(36 118 50 132)(37 77 51 63)(38 120 52 134)(39 79 53 65)(40 122 54 136)(41 81 55 67)(42 124 56 138)(58 198 72 212)(60 200 74 214)(62 202 76 216)(64 204 78 218)(66 206 80 220)(68 208 82 222)(70 210 84 224)(85 144 99 158)(86 172 100 186)(87 146 101 160)(88 174 102 188)(89 148 103 162)(90 176 104 190)(91 150 105 164)(92 178 106 192)(93 152 107 166)(94 180 108 194)(95 154 109 168)(96 182 110 196)(97 156 111 142)(98 184 112 170)(113 211 127 197)(115 213 129 199)(117 215 131 201)(119 217 133 203)(121 219 135 205)(123 221 137 207)(125 223 139 209)
(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 14 112 97)(2 96 85 13)(3 12 86 95)(4 94 87 11)(5 10 88 93)(6 92 89 9)(7 8 90 91)(15 28 98 111)(16 110 99 27)(17 26 100 109)(18 108 101 25)(19 24 102 107)(20 106 103 23)(21 22 104 105)(29 202 209 50)(30 49 210 201)(31 200 211 48)(32 47 212 199)(33 198 213 46)(34 45 214 197)(35 224 215 44)(36 43 216 223)(37 222 217 42)(38 41 218 221)(39 220 219 40)(51 208 203 56)(52 55 204 207)(53 206 205 54)(57 74 113 130)(58 129 114 73)(59 72 115 128)(60 127 116 71)(61 70 117 126)(62 125 118 69)(63 68 119 124)(64 123 120 67)(65 66 121 122)(75 84 131 140)(76 139 132 83)(77 82 133 138)(78 137 134 81)(79 80 135 136)(141 171 182 158)(142 157 183 170)(143 169 184 156)(144 155 185 196)(145 195 186 154)(146 153 187 194)(147 193 188 152)(148 151 189 192)(149 191 190 150)(159 181 172 168)(160 167 173 180)(161 179 174 166)(162 165 175 178)(163 177 176 164)
G:=sub<Sym(224)| (1,73,112,129)(2,130,85,74)(3,75,86,131)(4,132,87,76)(5,77,88,133)(6,134,89,78)(7,79,90,135)(8,136,91,80)(9,81,92,137)(10,138,93,82)(11,83,94,139)(12,140,95,84)(13,57,96,113)(14,114,97,58)(15,59,98,115)(16,116,99,60)(17,61,100,117)(18,118,101,62)(19,63,102,119)(20,120,103,64)(21,65,104,121)(22,122,105,66)(23,67,106,123)(24,124,107,68)(25,69,108,125)(26,126,109,70)(27,71,110,127)(28,128,111,72)(29,180,209,167)(30,168,210,181)(31,182,211,141)(32,142,212,183)(33,184,213,143)(34,144,214,185)(35,186,215,145)(36,146,216,187)(37,188,217,147)(38,148,218,189)(39,190,219,149)(40,150,220,191)(41,192,221,151)(42,152,222,193)(43,194,223,153)(44,154,224,195)(45,196,197,155)(46,156,198,169)(47,170,199,157)(48,158,200,171)(49,172,201,159)(50,160,202,173)(51,174,203,161)(52,162,204,175)(53,176,205,163)(54,164,206,177)(55,178,207,165)(56,166,208,179), (1,157,15,143)(2,185,16,171)(3,159,17,145)(4,187,18,173)(5,161,19,147)(6,189,20,175)(7,163,21,149)(8,191,22,177)(9,165,23,151)(10,193,24,179)(11,167,25,153)(12,195,26,181)(13,141,27,155)(14,169,28,183)(29,69,43,83)(30,140,44,126)(31,71,45,57)(32,114,46,128)(33,73,47,59)(34,116,48,130)(35,75,49,61)(36,118,50,132)(37,77,51,63)(38,120,52,134)(39,79,53,65)(40,122,54,136)(41,81,55,67)(42,124,56,138)(58,198,72,212)(60,200,74,214)(62,202,76,216)(64,204,78,218)(66,206,80,220)(68,208,82,222)(70,210,84,224)(85,144,99,158)(86,172,100,186)(87,146,101,160)(88,174,102,188)(89,148,103,162)(90,176,104,190)(91,150,105,164)(92,178,106,192)(93,152,107,166)(94,180,108,194)(95,154,109,168)(96,182,110,196)(97,156,111,142)(98,184,112,170)(113,211,127,197)(115,213,129,199)(117,215,131,201)(119,217,133,203)(121,219,135,205)(123,221,137,207)(125,223,139,209), (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), (1,14,112,97)(2,96,85,13)(3,12,86,95)(4,94,87,11)(5,10,88,93)(6,92,89,9)(7,8,90,91)(15,28,98,111)(16,110,99,27)(17,26,100,109)(18,108,101,25)(19,24,102,107)(20,106,103,23)(21,22,104,105)(29,202,209,50)(30,49,210,201)(31,200,211,48)(32,47,212,199)(33,198,213,46)(34,45,214,197)(35,224,215,44)(36,43,216,223)(37,222,217,42)(38,41,218,221)(39,220,219,40)(51,208,203,56)(52,55,204,207)(53,206,205,54)(57,74,113,130)(58,129,114,73)(59,72,115,128)(60,127,116,71)(61,70,117,126)(62,125,118,69)(63,68,119,124)(64,123,120,67)(65,66,121,122)(75,84,131,140)(76,139,132,83)(77,82,133,138)(78,137,134,81)(79,80,135,136)(141,171,182,158)(142,157,183,170)(143,169,184,156)(144,155,185,196)(145,195,186,154)(146,153,187,194)(147,193,188,152)(148,151,189,192)(149,191,190,150)(159,181,172,168)(160,167,173,180)(161,179,174,166)(162,165,175,178)(163,177,176,164)>;
G:=Group( (1,73,112,129)(2,130,85,74)(3,75,86,131)(4,132,87,76)(5,77,88,133)(6,134,89,78)(7,79,90,135)(8,136,91,80)(9,81,92,137)(10,138,93,82)(11,83,94,139)(12,140,95,84)(13,57,96,113)(14,114,97,58)(15,59,98,115)(16,116,99,60)(17,61,100,117)(18,118,101,62)(19,63,102,119)(20,120,103,64)(21,65,104,121)(22,122,105,66)(23,67,106,123)(24,124,107,68)(25,69,108,125)(26,126,109,70)(27,71,110,127)(28,128,111,72)(29,180,209,167)(30,168,210,181)(31,182,211,141)(32,142,212,183)(33,184,213,143)(34,144,214,185)(35,186,215,145)(36,146,216,187)(37,188,217,147)(38,148,218,189)(39,190,219,149)(40,150,220,191)(41,192,221,151)(42,152,222,193)(43,194,223,153)(44,154,224,195)(45,196,197,155)(46,156,198,169)(47,170,199,157)(48,158,200,171)(49,172,201,159)(50,160,202,173)(51,174,203,161)(52,162,204,175)(53,176,205,163)(54,164,206,177)(55,178,207,165)(56,166,208,179), (1,157,15,143)(2,185,16,171)(3,159,17,145)(4,187,18,173)(5,161,19,147)(6,189,20,175)(7,163,21,149)(8,191,22,177)(9,165,23,151)(10,193,24,179)(11,167,25,153)(12,195,26,181)(13,141,27,155)(14,169,28,183)(29,69,43,83)(30,140,44,126)(31,71,45,57)(32,114,46,128)(33,73,47,59)(34,116,48,130)(35,75,49,61)(36,118,50,132)(37,77,51,63)(38,120,52,134)(39,79,53,65)(40,122,54,136)(41,81,55,67)(42,124,56,138)(58,198,72,212)(60,200,74,214)(62,202,76,216)(64,204,78,218)(66,206,80,220)(68,208,82,222)(70,210,84,224)(85,144,99,158)(86,172,100,186)(87,146,101,160)(88,174,102,188)(89,148,103,162)(90,176,104,190)(91,150,105,164)(92,178,106,192)(93,152,107,166)(94,180,108,194)(95,154,109,168)(96,182,110,196)(97,156,111,142)(98,184,112,170)(113,211,127,197)(115,213,129,199)(117,215,131,201)(119,217,133,203)(121,219,135,205)(123,221,137,207)(125,223,139,209), (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), (1,14,112,97)(2,96,85,13)(3,12,86,95)(4,94,87,11)(5,10,88,93)(6,92,89,9)(7,8,90,91)(15,28,98,111)(16,110,99,27)(17,26,100,109)(18,108,101,25)(19,24,102,107)(20,106,103,23)(21,22,104,105)(29,202,209,50)(30,49,210,201)(31,200,211,48)(32,47,212,199)(33,198,213,46)(34,45,214,197)(35,224,215,44)(36,43,216,223)(37,222,217,42)(38,41,218,221)(39,220,219,40)(51,208,203,56)(52,55,204,207)(53,206,205,54)(57,74,113,130)(58,129,114,73)(59,72,115,128)(60,127,116,71)(61,70,117,126)(62,125,118,69)(63,68,119,124)(64,123,120,67)(65,66,121,122)(75,84,131,140)(76,139,132,83)(77,82,133,138)(78,137,134,81)(79,80,135,136)(141,171,182,158)(142,157,183,170)(143,169,184,156)(144,155,185,196)(145,195,186,154)(146,153,187,194)(147,193,188,152)(148,151,189,192)(149,191,190,150)(159,181,172,168)(160,167,173,180)(161,179,174,166)(162,165,175,178)(163,177,176,164) );
G=PermutationGroup([[(1,73,112,129),(2,130,85,74),(3,75,86,131),(4,132,87,76),(5,77,88,133),(6,134,89,78),(7,79,90,135),(8,136,91,80),(9,81,92,137),(10,138,93,82),(11,83,94,139),(12,140,95,84),(13,57,96,113),(14,114,97,58),(15,59,98,115),(16,116,99,60),(17,61,100,117),(18,118,101,62),(19,63,102,119),(20,120,103,64),(21,65,104,121),(22,122,105,66),(23,67,106,123),(24,124,107,68),(25,69,108,125),(26,126,109,70),(27,71,110,127),(28,128,111,72),(29,180,209,167),(30,168,210,181),(31,182,211,141),(32,142,212,183),(33,184,213,143),(34,144,214,185),(35,186,215,145),(36,146,216,187),(37,188,217,147),(38,148,218,189),(39,190,219,149),(40,150,220,191),(41,192,221,151),(42,152,222,193),(43,194,223,153),(44,154,224,195),(45,196,197,155),(46,156,198,169),(47,170,199,157),(48,158,200,171),(49,172,201,159),(50,160,202,173),(51,174,203,161),(52,162,204,175),(53,176,205,163),(54,164,206,177),(55,178,207,165),(56,166,208,179)], [(1,157,15,143),(2,185,16,171),(3,159,17,145),(4,187,18,173),(5,161,19,147),(6,189,20,175),(7,163,21,149),(8,191,22,177),(9,165,23,151),(10,193,24,179),(11,167,25,153),(12,195,26,181),(13,141,27,155),(14,169,28,183),(29,69,43,83),(30,140,44,126),(31,71,45,57),(32,114,46,128),(33,73,47,59),(34,116,48,130),(35,75,49,61),(36,118,50,132),(37,77,51,63),(38,120,52,134),(39,79,53,65),(40,122,54,136),(41,81,55,67),(42,124,56,138),(58,198,72,212),(60,200,74,214),(62,202,76,216),(64,204,78,218),(66,206,80,220),(68,208,82,222),(70,210,84,224),(85,144,99,158),(86,172,100,186),(87,146,101,160),(88,174,102,188),(89,148,103,162),(90,176,104,190),(91,150,105,164),(92,178,106,192),(93,152,107,166),(94,180,108,194),(95,154,109,168),(96,182,110,196),(97,156,111,142),(98,184,112,170),(113,211,127,197),(115,213,129,199),(117,215,131,201),(119,217,133,203),(121,219,135,205),(123,221,137,207),(125,223,139,209)], [(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)], [(1,14,112,97),(2,96,85,13),(3,12,86,95),(4,94,87,11),(5,10,88,93),(6,92,89,9),(7,8,90,91),(15,28,98,111),(16,110,99,27),(17,26,100,109),(18,108,101,25),(19,24,102,107),(20,106,103,23),(21,22,104,105),(29,202,209,50),(30,49,210,201),(31,200,211,48),(32,47,212,199),(33,198,213,46),(34,45,214,197),(35,224,215,44),(36,43,216,223),(37,222,217,42),(38,41,218,221),(39,220,219,40),(51,208,203,56),(52,55,204,207),(53,206,205,54),(57,74,113,130),(58,129,114,73),(59,72,115,128),(60,127,116,71),(61,70,117,126),(62,125,118,69),(63,68,119,124),(64,123,120,67),(65,66,121,122),(75,84,131,140),(76,139,132,83),(77,82,133,138),(78,137,134,81),(79,80,135,136),(141,171,182,158),(142,157,183,170),(143,169,184,156),(144,155,185,196),(145,195,186,154),(146,153,187,194),(147,193,188,152),(148,151,189,192),(149,191,190,150),(159,181,172,168),(160,167,173,180),(161,179,174,166),(162,165,175,178),(163,177,176,164)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | ··· | 4H | 4I | 4J | 4K | 4L | 4M | ··· | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 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 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | - | + | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | 2- 1+4 | Q8⋊2D7 | D4.10D14 |
| kernel | C42.155D14 | C28⋊2Q8 | C42⋊D7 | Dic7⋊3Q8 | C28.3Q8 | D14⋊2Q8 | C4⋊C4⋊D7 | C7×C42.C2 | C42.C2 | C28 | C42 | C4⋊C4 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 4 | 2 | 4 | 1 | 3 | 4 | 3 | 18 | 2 | 6 | 12 |
Matrix representation of C42.155D14 ►in GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 26 | 10 |
| 0 | 0 | 0 | 28 | 19 | 3 |
| 0 | 0 | 13 | 5 | 1 | 0 |
| 0 | 0 | 24 | 16 | 0 | 1 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 1 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 24 | 27 | 0 |
| 0 | 0 | 5 | 13 | 0 | 27 |
| 0 | 0 | 28 | 0 | 13 | 5 |
| 0 | 0 | 0 | 28 | 24 | 16 |
| 1 | 5 | 0 | 0 | 0 | 0 |
| 17 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 27 | 1 | 1 |
| 0 | 0 | 2 | 24 | 28 | 19 |
| 0 | 0 | 7 | 7 | 27 | 2 |
| 0 | 0 | 22 | 17 | 27 | 5 |
| 28 | 24 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 2 | 28 | 28 |
| 0 | 0 | 24 | 2 | 10 | 1 |
| 0 | 0 | 7 | 7 | 27 | 2 |
| 0 | 0 | 17 | 22 | 24 | 2 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,13,24,0,0,0,28,5,16,0,0,26,19,1,0,0,0,10,3,0,1],[12,1,0,0,0,0,0,17,0,0,0,0,0,0,16,5,28,0,0,0,24,13,0,28,0,0,27,0,13,24,0,0,0,27,5,16],[1,17,0,0,0,0,5,28,0,0,0,0,0,0,2,2,7,22,0,0,27,24,7,17,0,0,1,28,27,27,0,0,1,19,2,5],[28,0,0,0,0,0,24,1,0,0,0,0,0,0,27,24,7,17,0,0,2,2,7,22,0,0,28,10,27,24,0,0,28,1,2,2] >;
C42.155D14 in GAP, Magma, Sage, TeX
C_4^2._{155}D_{14} % in TeX
G:=Group("C4^2.155D14"); // GroupNames label
G:=SmallGroup(448,1150);
// by ID
G=gap.SmallGroup(448,1150);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,758,219,268,675,297,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=b^2,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=a^2*b^2*c^13>;
// generators/relations