metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.158D14, C14.322- 1+4, C14.1362+ 1+4, C4⋊D28⋊35C2, C4⋊C4.115D14, C42.C2⋊14D7, D14⋊Q8⋊38C2, C4.D28⋊32C2, D14.5D4⋊37C2, (C2×C28).191C23, (C4×C28).225C22, (C2×C14).244C24, D14⋊C4.74C22, C2.61(D4⋊8D14), (C2×D28).167C22, Dic7⋊C4.55C22, C22.265(C23×D7), C7⋊5(C22.56C24), (C2×Dic14).42C22, (C2×Dic7).126C23, (C22×D7).109C23, C2.33(Q8.10D14), (C7×C42.C2)⋊17C2, (C2×C4×D7).134C22, (C7×C4⋊C4).199C22, (C2×C4).208(C22×D7), SmallGroup(448,1153)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.158D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2, ab=ba, cac-1=a-1b2, dad-1=a-1, cbc-1=b-1, dbd-1=a2b-1, dcd-1=c13 >
Subgroups: 1244 in 220 conjugacy classes, 91 normal (13 characteristic)
C1, C2, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, Dic7, C28, D14, C2×C14, C4⋊D4, C22⋊Q8, C22.D4, C4.4D4, C42.C2, Dic14, C4×D7, D28, C2×Dic7, C2×C28, C2×C28, C22×D7, C22.56C24, Dic7⋊C4, D14⋊C4, C4×C28, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C4.D28, D14.5D4, C4⋊D28, D14⋊Q8, C7×C42.C2, C42.158D14
Quotients: C1, C2, C22, C23, D7, C24, D14, 2+ 1+4, 2- 1+4, C22×D7, C22.56C24, C23×D7, Q8.10D14, D4⋊8D14, C42.158D14
►On 224 points
Generators in S224
(1 223 15 209)(2 131 16 117)(3 197 17 211)(4 133 18 119)(5 199 19 213)(6 135 20 121)(7 201 21 215)(8 137 22 123)(9 203 23 217)(10 139 24 125)(11 205 25 219)(12 113 26 127)(13 207 27 221)(14 115 28 129)(29 75 43 61)(30 189 44 175)(31 77 45 63)(32 191 46 177)(33 79 47 65)(34 193 48 179)(35 81 49 67)(36 195 50 181)(37 83 51 69)(38 169 52 183)(39 57 53 71)(40 171 54 185)(41 59 55 73)(42 173 56 187)(58 93 72 107)(60 95 74 109)(62 97 76 111)(64 99 78 85)(66 101 80 87)(68 103 82 89)(70 105 84 91)(86 178 100 192)(88 180 102 194)(90 182 104 196)(92 184 106 170)(94 186 108 172)(96 188 110 174)(98 190 112 176)(114 145 128 159)(116 147 130 161)(118 149 132 163)(120 151 134 165)(122 153 136 167)(124 155 138 141)(126 157 140 143)(142 218 156 204)(144 220 158 206)(146 222 160 208)(148 224 162 210)(150 198 164 212)(152 200 166 214)(154 202 168 216)
(1 76 161 175)(2 176 162 77)(3 78 163 177)(4 178 164 79)(5 80 165 179)(6 180 166 81)(7 82 167 181)(8 182 168 83)(9 84 141 183)(10 184 142 57)(11 58 143 185)(12 186 144 59)(13 60 145 187)(14 188 146 61)(15 62 147 189)(16 190 148 63)(17 64 149 191)(18 192 150 65)(19 66 151 193)(20 194 152 67)(21 68 153 195)(22 196 154 69)(23 70 155 169)(24 170 156 71)(25 72 157 171)(26 172 158 73)(27 74 159 173)(28 174 160 75)(29 115 110 222)(30 223 111 116)(31 117 112 224)(32 197 85 118)(33 119 86 198)(34 199 87 120)(35 121 88 200)(36 201 89 122)(37 123 90 202)(38 203 91 124)(39 125 92 204)(40 205 93 126)(41 127 94 206)(42 207 95 128)(43 129 96 208)(44 209 97 130)(45 131 98 210)(46 211 99 132)(47 133 100 212)(48 213 101 134)(49 135 102 214)(50 215 103 136)(51 137 104 216)(52 217 105 138)(53 139 106 218)(54 219 107 140)(55 113 108 220)(56 221 109 114)
(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 36 15 50)(2 49 16 35)(3 34 17 48)(4 47 18 33)(5 32 19 46)(6 45 20 31)(7 30 21 44)(8 43 22 29)(9 56 23 42)(10 41 24 55)(11 54 25 40)(12 39 26 53)(13 52 27 38)(14 37 28 51)(57 113 71 127)(58 126 72 140)(59 139 73 125)(60 124 74 138)(61 137 75 123)(62 122 76 136)(63 135 77 121)(64 120 78 134)(65 133 79 119)(66 118 80 132)(67 131 81 117)(68 116 82 130)(69 129 83 115)(70 114 84 128)(85 151 99 165)(86 164 100 150)(87 149 101 163)(88 162 102 148)(89 147 103 161)(90 160 104 146)(91 145 105 159)(92 158 106 144)(93 143 107 157)(94 156 108 142)(95 141 109 155)(96 154 110 168)(97 167 111 153)(98 152 112 166)(169 221 183 207)(170 206 184 220)(171 219 185 205)(172 204 186 218)(173 217 187 203)(174 202 188 216)(175 215 189 201)(176 200 190 214)(177 213 191 199)(178 198 192 212)(179 211 193 197)(180 224 194 210)(181 209 195 223)(182 222 196 208)
G:=sub<Sym(224)| (1,223,15,209)(2,131,16,117)(3,197,17,211)(4,133,18,119)(5,199,19,213)(6,135,20,121)(7,201,21,215)(8,137,22,123)(9,203,23,217)(10,139,24,125)(11,205,25,219)(12,113,26,127)(13,207,27,221)(14,115,28,129)(29,75,43,61)(30,189,44,175)(31,77,45,63)(32,191,46,177)(33,79,47,65)(34,193,48,179)(35,81,49,67)(36,195,50,181)(37,83,51,69)(38,169,52,183)(39,57,53,71)(40,171,54,185)(41,59,55,73)(42,173,56,187)(58,93,72,107)(60,95,74,109)(62,97,76,111)(64,99,78,85)(66,101,80,87)(68,103,82,89)(70,105,84,91)(86,178,100,192)(88,180,102,194)(90,182,104,196)(92,184,106,170)(94,186,108,172)(96,188,110,174)(98,190,112,176)(114,145,128,159)(116,147,130,161)(118,149,132,163)(120,151,134,165)(122,153,136,167)(124,155,138,141)(126,157,140,143)(142,218,156,204)(144,220,158,206)(146,222,160,208)(148,224,162,210)(150,198,164,212)(152,200,166,214)(154,202,168,216), (1,76,161,175)(2,176,162,77)(3,78,163,177)(4,178,164,79)(5,80,165,179)(6,180,166,81)(7,82,167,181)(8,182,168,83)(9,84,141,183)(10,184,142,57)(11,58,143,185)(12,186,144,59)(13,60,145,187)(14,188,146,61)(15,62,147,189)(16,190,148,63)(17,64,149,191)(18,192,150,65)(19,66,151,193)(20,194,152,67)(21,68,153,195)(22,196,154,69)(23,70,155,169)(24,170,156,71)(25,72,157,171)(26,172,158,73)(27,74,159,173)(28,174,160,75)(29,115,110,222)(30,223,111,116)(31,117,112,224)(32,197,85,118)(33,119,86,198)(34,199,87,120)(35,121,88,200)(36,201,89,122)(37,123,90,202)(38,203,91,124)(39,125,92,204)(40,205,93,126)(41,127,94,206)(42,207,95,128)(43,129,96,208)(44,209,97,130)(45,131,98,210)(46,211,99,132)(47,133,100,212)(48,213,101,134)(49,135,102,214)(50,215,103,136)(51,137,104,216)(52,217,105,138)(53,139,106,218)(54,219,107,140)(55,113,108,220)(56,221,109,114), (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), (1,36,15,50)(2,49,16,35)(3,34,17,48)(4,47,18,33)(5,32,19,46)(6,45,20,31)(7,30,21,44)(8,43,22,29)(9,56,23,42)(10,41,24,55)(11,54,25,40)(12,39,26,53)(13,52,27,38)(14,37,28,51)(57,113,71,127)(58,126,72,140)(59,139,73,125)(60,124,74,138)(61,137,75,123)(62,122,76,136)(63,135,77,121)(64,120,78,134)(65,133,79,119)(66,118,80,132)(67,131,81,117)(68,116,82,130)(69,129,83,115)(70,114,84,128)(85,151,99,165)(86,164,100,150)(87,149,101,163)(88,162,102,148)(89,147,103,161)(90,160,104,146)(91,145,105,159)(92,158,106,144)(93,143,107,157)(94,156,108,142)(95,141,109,155)(96,154,110,168)(97,167,111,153)(98,152,112,166)(169,221,183,207)(170,206,184,220)(171,219,185,205)(172,204,186,218)(173,217,187,203)(174,202,188,216)(175,215,189,201)(176,200,190,214)(177,213,191,199)(178,198,192,212)(179,211,193,197)(180,224,194,210)(181,209,195,223)(182,222,196,208)>;
G:=Group( (1,223,15,209)(2,131,16,117)(3,197,17,211)(4,133,18,119)(5,199,19,213)(6,135,20,121)(7,201,21,215)(8,137,22,123)(9,203,23,217)(10,139,24,125)(11,205,25,219)(12,113,26,127)(13,207,27,221)(14,115,28,129)(29,75,43,61)(30,189,44,175)(31,77,45,63)(32,191,46,177)(33,79,47,65)(34,193,48,179)(35,81,49,67)(36,195,50,181)(37,83,51,69)(38,169,52,183)(39,57,53,71)(40,171,54,185)(41,59,55,73)(42,173,56,187)(58,93,72,107)(60,95,74,109)(62,97,76,111)(64,99,78,85)(66,101,80,87)(68,103,82,89)(70,105,84,91)(86,178,100,192)(88,180,102,194)(90,182,104,196)(92,184,106,170)(94,186,108,172)(96,188,110,174)(98,190,112,176)(114,145,128,159)(116,147,130,161)(118,149,132,163)(120,151,134,165)(122,153,136,167)(124,155,138,141)(126,157,140,143)(142,218,156,204)(144,220,158,206)(146,222,160,208)(148,224,162,210)(150,198,164,212)(152,200,166,214)(154,202,168,216), (1,76,161,175)(2,176,162,77)(3,78,163,177)(4,178,164,79)(5,80,165,179)(6,180,166,81)(7,82,167,181)(8,182,168,83)(9,84,141,183)(10,184,142,57)(11,58,143,185)(12,186,144,59)(13,60,145,187)(14,188,146,61)(15,62,147,189)(16,190,148,63)(17,64,149,191)(18,192,150,65)(19,66,151,193)(20,194,152,67)(21,68,153,195)(22,196,154,69)(23,70,155,169)(24,170,156,71)(25,72,157,171)(26,172,158,73)(27,74,159,173)(28,174,160,75)(29,115,110,222)(30,223,111,116)(31,117,112,224)(32,197,85,118)(33,119,86,198)(34,199,87,120)(35,121,88,200)(36,201,89,122)(37,123,90,202)(38,203,91,124)(39,125,92,204)(40,205,93,126)(41,127,94,206)(42,207,95,128)(43,129,96,208)(44,209,97,130)(45,131,98,210)(46,211,99,132)(47,133,100,212)(48,213,101,134)(49,135,102,214)(50,215,103,136)(51,137,104,216)(52,217,105,138)(53,139,106,218)(54,219,107,140)(55,113,108,220)(56,221,109,114), (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), (1,36,15,50)(2,49,16,35)(3,34,17,48)(4,47,18,33)(5,32,19,46)(6,45,20,31)(7,30,21,44)(8,43,22,29)(9,56,23,42)(10,41,24,55)(11,54,25,40)(12,39,26,53)(13,52,27,38)(14,37,28,51)(57,113,71,127)(58,126,72,140)(59,139,73,125)(60,124,74,138)(61,137,75,123)(62,122,76,136)(63,135,77,121)(64,120,78,134)(65,133,79,119)(66,118,80,132)(67,131,81,117)(68,116,82,130)(69,129,83,115)(70,114,84,128)(85,151,99,165)(86,164,100,150)(87,149,101,163)(88,162,102,148)(89,147,103,161)(90,160,104,146)(91,145,105,159)(92,158,106,144)(93,143,107,157)(94,156,108,142)(95,141,109,155)(96,154,110,168)(97,167,111,153)(98,152,112,166)(169,221,183,207)(170,206,184,220)(171,219,185,205)(172,204,186,218)(173,217,187,203)(174,202,188,216)(175,215,189,201)(176,200,190,214)(177,213,191,199)(178,198,192,212)(179,211,193,197)(180,224,194,210)(181,209,195,223)(182,222,196,208) );
G=PermutationGroup([[(1,223,15,209),(2,131,16,117),(3,197,17,211),(4,133,18,119),(5,199,19,213),(6,135,20,121),(7,201,21,215),(8,137,22,123),(9,203,23,217),(10,139,24,125),(11,205,25,219),(12,113,26,127),(13,207,27,221),(14,115,28,129),(29,75,43,61),(30,189,44,175),(31,77,45,63),(32,191,46,177),(33,79,47,65),(34,193,48,179),(35,81,49,67),(36,195,50,181),(37,83,51,69),(38,169,52,183),(39,57,53,71),(40,171,54,185),(41,59,55,73),(42,173,56,187),(58,93,72,107),(60,95,74,109),(62,97,76,111),(64,99,78,85),(66,101,80,87),(68,103,82,89),(70,105,84,91),(86,178,100,192),(88,180,102,194),(90,182,104,196),(92,184,106,170),(94,186,108,172),(96,188,110,174),(98,190,112,176),(114,145,128,159),(116,147,130,161),(118,149,132,163),(120,151,134,165),(122,153,136,167),(124,155,138,141),(126,157,140,143),(142,218,156,204),(144,220,158,206),(146,222,160,208),(148,224,162,210),(150,198,164,212),(152,200,166,214),(154,202,168,216)], [(1,76,161,175),(2,176,162,77),(3,78,163,177),(4,178,164,79),(5,80,165,179),(6,180,166,81),(7,82,167,181),(8,182,168,83),(9,84,141,183),(10,184,142,57),(11,58,143,185),(12,186,144,59),(13,60,145,187),(14,188,146,61),(15,62,147,189),(16,190,148,63),(17,64,149,191),(18,192,150,65),(19,66,151,193),(20,194,152,67),(21,68,153,195),(22,196,154,69),(23,70,155,169),(24,170,156,71),(25,72,157,171),(26,172,158,73),(27,74,159,173),(28,174,160,75),(29,115,110,222),(30,223,111,116),(31,117,112,224),(32,197,85,118),(33,119,86,198),(34,199,87,120),(35,121,88,200),(36,201,89,122),(37,123,90,202),(38,203,91,124),(39,125,92,204),(40,205,93,126),(41,127,94,206),(42,207,95,128),(43,129,96,208),(44,209,97,130),(45,131,98,210),(46,211,99,132),(47,133,100,212),(48,213,101,134),(49,135,102,214),(50,215,103,136),(51,137,104,216),(52,217,105,138),(53,139,106,218),(54,219,107,140),(55,113,108,220),(56,221,109,114)], [(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)], [(1,36,15,50),(2,49,16,35),(3,34,17,48),(4,47,18,33),(5,32,19,46),(6,45,20,31),(7,30,21,44),(8,43,22,29),(9,56,23,42),(10,41,24,55),(11,54,25,40),(12,39,26,53),(13,52,27,38),(14,37,28,51),(57,113,71,127),(58,126,72,140),(59,139,73,125),(60,124,74,138),(61,137,75,123),(62,122,76,136),(63,135,77,121),(64,120,78,134),(65,133,79,119),(66,118,80,132),(67,131,81,117),(68,116,82,130),(69,129,83,115),(70,114,84,128),(85,151,99,165),(86,164,100,150),(87,149,101,163),(88,162,102,148),(89,147,103,161),(90,160,104,146),(91,145,105,159),(92,158,106,144),(93,143,107,157),(94,156,108,142),(95,141,109,155),(96,154,110,168),(97,167,111,153),(98,152,112,166),(169,221,183,207),(170,206,184,220),(171,219,185,205),(172,204,186,218),(173,217,187,203),(174,202,188,216),(175,215,189,201),(176,200,190,214),(177,213,191,199),(178,198,192,212),(179,211,193,197),(180,224,194,210),(181,209,195,223),(182,222,196,208)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | ··· | 4G | 4H | 4I | 4J | 4K | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 28 | 28 | 4 | ··· | 4 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | + | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | D7 | D14 | D14 | 2+ 1+4 | 2- 1+4 | Q8.10D14 | D4⋊8D14 |
| kernel | C42.158D14 | C4.D28 | D14.5D4 | C4⋊D28 | D14⋊Q8 | C7×C42.C2 | C42.C2 | C42 | C4⋊C4 | C14 | C14 | C2 | C2 |
| # reps | 1 | 2 | 4 | 4 | 4 | 1 | 3 | 3 | 18 | 2 | 1 | 6 | 12 |
Matrix representation of C42.158D14 ►in GL8(𝔽29)
| 5 | 4 | 27 | 0 | 0 | 0 | 0 | 0 |
| 15 | 5 | 0 | 27 | 0 | 0 | 0 | 0 |
| 14 | 20 | 24 | 25 | 0 | 0 | 0 | 0 |
| 17 | 14 | 14 | 24 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 11 | 0 |
| 0 | 0 | 0 | 0 | 28 | 17 | 10 | 22 |
| 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 14 | 8 | 13 | 12 |
| 18 | 14 | 0 | 0 | 0 | 0 | 0 | 0 |
| 8 | 11 | 0 | 0 | 0 | 0 | 0 | 0 |
| 27 | 15 | 18 | 14 | 0 | 0 | 0 | 0 |
| 9 | 2 | 8 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 16 | 9 | 22 |
| 0 | 0 | 0 | 0 | 12 | 13 | 20 | 20 |
| 26 | 14 | 14 | 6 | 0 | 0 | 0 | 0 |
| 14 | 10 | 20 | 11 | 0 | 0 | 0 | 0 |
| 6 | 5 | 27 | 9 | 0 | 0 | 0 | 0 |
| 8 | 25 | 23 | 24 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 15 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 26 | 6 | 2 |
| 0 | 0 | 0 | 0 | 21 | 0 | 14 | 0 |
| 0 | 0 | 0 | 0 | 24 | 25 | 25 | 3 |
| 9 | 25 | 6 | 20 | 0 | 0 | 0 | 0 |
| 21 | 19 | 27 | 23 | 0 | 0 | 0 | 0 |
| 8 | 4 | 11 | 9 | 0 | 0 | 0 | 0 |
| 18 | 16 | 11 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 13 | 12 | 10 |
| 0 | 0 | 0 | 0 | 28 | 17 | 10 | 22 |
| 0 | 0 | 0 | 0 | 1 | 13 | 20 | 7 |
| 0 | 0 | 0 | 0 | 9 | 4 | 18 | 4 |
G:=sub<GL(8,GF(29))| [5,15,14,17,0,0,0,0,4,5,20,14,0,0,0,0,27,0,24,14,0,0,0,0,0,27,25,24,0,0,0,0,0,0,0,0,1,28,0,14,0,0,0,0,0,17,0,8,0,0,0,0,11,10,28,13,0,0,0,0,0,22,0,12],[18,8,27,9,0,0,0,0,14,11,15,2,0,0,0,0,0,0,18,8,0,0,0,0,0,0,14,11,0,0,0,0,0,0,0,0,28,13,28,12,0,0,0,0,11,1,16,13,0,0,0,0,0,0,9,20,0,0,0,0,0,0,22,20],[26,14,6,8,0,0,0,0,14,10,5,25,0,0,0,0,14,20,27,23,0,0,0,0,6,11,9,24,0,0,0,0,0,0,0,0,15,0,21,24,0,0,0,0,0,26,0,25,0,0,0,0,28,6,14,25,0,0,0,0,0,2,0,3],[9,21,8,18,0,0,0,0,25,19,4,16,0,0,0,0,6,27,11,11,0,0,0,0,20,23,9,19,0,0,0,0,0,0,0,0,17,28,1,9,0,0,0,0,13,17,13,4,0,0,0,0,12,10,20,18,0,0,0,0,10,22,7,4] >;
C42.158D14 in GAP, Magma, Sage, TeX
C_4^2._{158}D_{14} % in TeX
G:=Group("C4^2.158D14"); // GroupNames label
G:=SmallGroup(448,1153);
// by ID
G=gap.SmallGroup(448,1153);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,758,555,100,675,570,136,18822]);
// 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^-1*b^2,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