metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.82D14, C4⋊Q8⋊7D7, C4⋊C4.85D14, (C2×C28).296D4, C28.84(C4○D4), C14.Q16⋊42C2, C4.D28.9C2, C14.D8.16C2, C14.99(C8⋊C22), (C4×C28).136C22, (C2×C28).407C23, C4.17(Q8⋊2D7), C42.D7⋊15C2, C14.59(C4.4D4), (C2×D28).110C22, C14.98(C8.C22), C2.20(D4.D14), C2.19(C28.C23), C2.12(C28.23D4), C7⋊5(C42.28C22), (C2×Dic14).114C22, (C7×C4⋊Q8)⋊7C2, (C2×C14).538(C2×D4), (C2×C4).74(C7⋊D4), (C2×C7⋊C8).139C22, (C7×C4⋊C4).132C22, (C2×C4).504(C22×D7), C22.210(C2×C7⋊D4), SmallGroup(448,623)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.82D14
G = < a,b,c,d | a4=b4=1, c14=a2b2, d2=a2b, ab=ba, cac-1=a-1, dad-1=ab2, cbc-1=b-1, bd=db, dcd-1=b-1c13 >
Subgroups: 524 in 100 conjugacy classes, 39 normal (25 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×D4, C2×Q8, Dic7, C28, C28, D14, C2×C14, C8⋊C4, D4⋊C4, Q8⋊C4, C4.4D4, C4⋊Q8, C7⋊C8, Dic14, D28, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C42.28C22, C2×C7⋊C8, D14⋊C4, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×D28, Q8×C14, C42.D7, C14.D8, C14.Q16, C4.D28, C7×C4⋊Q8, C42.82D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4.4D4, C8⋊C22, C8.C22, C7⋊D4, C22×D7, C42.28C22, Q8⋊2D7, C2×C7⋊D4, D4.D14, C28.C23, C28.23D4, C42.82D14
►On 224 points
Generators in S224
(1 139 69 178)(2 179 70 140)(3 113 71 180)(4 181 72 114)(5 115 73 182)(6 183 74 116)(7 117 75 184)(8 185 76 118)(9 119 77 186)(10 187 78 120)(11 121 79 188)(12 189 80 122)(13 123 81 190)(14 191 82 124)(15 125 83 192)(16 193 84 126)(17 127 57 194)(18 195 58 128)(19 129 59 196)(20 169 60 130)(21 131 61 170)(22 171 62 132)(23 133 63 172)(24 173 64 134)(25 135 65 174)(26 175 66 136)(27 137 67 176)(28 177 68 138)(29 145 107 219)(30 220 108 146)(31 147 109 221)(32 222 110 148)(33 149 111 223)(34 224 112 150)(35 151 85 197)(36 198 86 152)(37 153 87 199)(38 200 88 154)(39 155 89 201)(40 202 90 156)(41 157 91 203)(42 204 92 158)(43 159 93 205)(44 206 94 160)(45 161 95 207)(46 208 96 162)(47 163 97 209)(48 210 98 164)(49 165 99 211)(50 212 100 166)(51 167 101 213)(52 214 102 168)(53 141 103 215)(54 216 104 142)(55 143 105 217)(56 218 106 144)
(1 37 83 101)(2 102 84 38)(3 39 57 103)(4 104 58 40)(5 41 59 105)(6 106 60 42)(7 43 61 107)(8 108 62 44)(9 45 63 109)(10 110 64 46)(11 47 65 111)(12 112 66 48)(13 49 67 85)(14 86 68 50)(15 51 69 87)(16 88 70 52)(17 53 71 89)(18 90 72 54)(19 55 73 91)(20 92 74 56)(21 29 75 93)(22 94 76 30)(23 31 77 95)(24 96 78 32)(25 33 79 97)(26 98 80 34)(27 35 81 99)(28 100 82 36)(113 155 194 215)(114 216 195 156)(115 157 196 217)(116 218 169 158)(117 159 170 219)(118 220 171 160)(119 161 172 221)(120 222 173 162)(121 163 174 223)(122 224 175 164)(123 165 176 197)(124 198 177 166)(125 167 178 199)(126 200 179 168)(127 141 180 201)(128 202 181 142)(129 143 182 203)(130 204 183 144)(131 145 184 205)(132 206 185 146)(133 147 186 207)(134 208 187 148)(135 149 188 209)(136 210 189 150)(137 151 190 211)(138 212 191 152)(139 153 192 213)(140 214 193 154)
(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 87 36 83 68 51 100)(2 99 52 67 84 35 88 13)(3 12 89 34 57 66 53 98)(4 97 54 65 58 33 90 11)(5 10 91 32 59 64 55 96)(6 95 56 63 60 31 92 9)(7 8 93 30 61 62 29 94)(15 28 101 50 69 82 37 86)(16 85 38 81 70 49 102 27)(17 26 103 48 71 80 39 112)(18 111 40 79 72 47 104 25)(19 24 105 46 73 78 41 110)(20 109 42 77 74 45 106 23)(21 22 107 44 75 76 43 108)(113 136 201 164 194 189 141 224)(114 223 142 188 195 163 202 135)(115 134 203 162 196 187 143 222)(116 221 144 186 169 161 204 133)(117 132 205 160 170 185 145 220)(118 219 146 184 171 159 206 131)(119 130 207 158 172 183 147 218)(120 217 148 182 173 157 208 129)(121 128 209 156 174 181 149 216)(122 215 150 180 175 155 210 127)(123 126 211 154 176 179 151 214)(124 213 152 178 177 153 212 125)(137 140 197 168 190 193 165 200)(138 199 166 192 191 167 198 139)
G:=sub<Sym(224)| (1,139,69,178)(2,179,70,140)(3,113,71,180)(4,181,72,114)(5,115,73,182)(6,183,74,116)(7,117,75,184)(8,185,76,118)(9,119,77,186)(10,187,78,120)(11,121,79,188)(12,189,80,122)(13,123,81,190)(14,191,82,124)(15,125,83,192)(16,193,84,126)(17,127,57,194)(18,195,58,128)(19,129,59,196)(20,169,60,130)(21,131,61,170)(22,171,62,132)(23,133,63,172)(24,173,64,134)(25,135,65,174)(26,175,66,136)(27,137,67,176)(28,177,68,138)(29,145,107,219)(30,220,108,146)(31,147,109,221)(32,222,110,148)(33,149,111,223)(34,224,112,150)(35,151,85,197)(36,198,86,152)(37,153,87,199)(38,200,88,154)(39,155,89,201)(40,202,90,156)(41,157,91,203)(42,204,92,158)(43,159,93,205)(44,206,94,160)(45,161,95,207)(46,208,96,162)(47,163,97,209)(48,210,98,164)(49,165,99,211)(50,212,100,166)(51,167,101,213)(52,214,102,168)(53,141,103,215)(54,216,104,142)(55,143,105,217)(56,218,106,144), (1,37,83,101)(2,102,84,38)(3,39,57,103)(4,104,58,40)(5,41,59,105)(6,106,60,42)(7,43,61,107)(8,108,62,44)(9,45,63,109)(10,110,64,46)(11,47,65,111)(12,112,66,48)(13,49,67,85)(14,86,68,50)(15,51,69,87)(16,88,70,52)(17,53,71,89)(18,90,72,54)(19,55,73,91)(20,92,74,56)(21,29,75,93)(22,94,76,30)(23,31,77,95)(24,96,78,32)(25,33,79,97)(26,98,80,34)(27,35,81,99)(28,100,82,36)(113,155,194,215)(114,216,195,156)(115,157,196,217)(116,218,169,158)(117,159,170,219)(118,220,171,160)(119,161,172,221)(120,222,173,162)(121,163,174,223)(122,224,175,164)(123,165,176,197)(124,198,177,166)(125,167,178,199)(126,200,179,168)(127,141,180,201)(128,202,181,142)(129,143,182,203)(130,204,183,144)(131,145,184,205)(132,206,185,146)(133,147,186,207)(134,208,187,148)(135,149,188,209)(136,210,189,150)(137,151,190,211)(138,212,191,152)(139,153,192,213)(140,214,193,154), (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), (1,14,87,36,83,68,51,100)(2,99,52,67,84,35,88,13)(3,12,89,34,57,66,53,98)(4,97,54,65,58,33,90,11)(5,10,91,32,59,64,55,96)(6,95,56,63,60,31,92,9)(7,8,93,30,61,62,29,94)(15,28,101,50,69,82,37,86)(16,85,38,81,70,49,102,27)(17,26,103,48,71,80,39,112)(18,111,40,79,72,47,104,25)(19,24,105,46,73,78,41,110)(20,109,42,77,74,45,106,23)(21,22,107,44,75,76,43,108)(113,136,201,164,194,189,141,224)(114,223,142,188,195,163,202,135)(115,134,203,162,196,187,143,222)(116,221,144,186,169,161,204,133)(117,132,205,160,170,185,145,220)(118,219,146,184,171,159,206,131)(119,130,207,158,172,183,147,218)(120,217,148,182,173,157,208,129)(121,128,209,156,174,181,149,216)(122,215,150,180,175,155,210,127)(123,126,211,154,176,179,151,214)(124,213,152,178,177,153,212,125)(137,140,197,168,190,193,165,200)(138,199,166,192,191,167,198,139)>;
G:=Group( (1,139,69,178)(2,179,70,140)(3,113,71,180)(4,181,72,114)(5,115,73,182)(6,183,74,116)(7,117,75,184)(8,185,76,118)(9,119,77,186)(10,187,78,120)(11,121,79,188)(12,189,80,122)(13,123,81,190)(14,191,82,124)(15,125,83,192)(16,193,84,126)(17,127,57,194)(18,195,58,128)(19,129,59,196)(20,169,60,130)(21,131,61,170)(22,171,62,132)(23,133,63,172)(24,173,64,134)(25,135,65,174)(26,175,66,136)(27,137,67,176)(28,177,68,138)(29,145,107,219)(30,220,108,146)(31,147,109,221)(32,222,110,148)(33,149,111,223)(34,224,112,150)(35,151,85,197)(36,198,86,152)(37,153,87,199)(38,200,88,154)(39,155,89,201)(40,202,90,156)(41,157,91,203)(42,204,92,158)(43,159,93,205)(44,206,94,160)(45,161,95,207)(46,208,96,162)(47,163,97,209)(48,210,98,164)(49,165,99,211)(50,212,100,166)(51,167,101,213)(52,214,102,168)(53,141,103,215)(54,216,104,142)(55,143,105,217)(56,218,106,144), (1,37,83,101)(2,102,84,38)(3,39,57,103)(4,104,58,40)(5,41,59,105)(6,106,60,42)(7,43,61,107)(8,108,62,44)(9,45,63,109)(10,110,64,46)(11,47,65,111)(12,112,66,48)(13,49,67,85)(14,86,68,50)(15,51,69,87)(16,88,70,52)(17,53,71,89)(18,90,72,54)(19,55,73,91)(20,92,74,56)(21,29,75,93)(22,94,76,30)(23,31,77,95)(24,96,78,32)(25,33,79,97)(26,98,80,34)(27,35,81,99)(28,100,82,36)(113,155,194,215)(114,216,195,156)(115,157,196,217)(116,218,169,158)(117,159,170,219)(118,220,171,160)(119,161,172,221)(120,222,173,162)(121,163,174,223)(122,224,175,164)(123,165,176,197)(124,198,177,166)(125,167,178,199)(126,200,179,168)(127,141,180,201)(128,202,181,142)(129,143,182,203)(130,204,183,144)(131,145,184,205)(132,206,185,146)(133,147,186,207)(134,208,187,148)(135,149,188,209)(136,210,189,150)(137,151,190,211)(138,212,191,152)(139,153,192,213)(140,214,193,154), (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), (1,14,87,36,83,68,51,100)(2,99,52,67,84,35,88,13)(3,12,89,34,57,66,53,98)(4,97,54,65,58,33,90,11)(5,10,91,32,59,64,55,96)(6,95,56,63,60,31,92,9)(7,8,93,30,61,62,29,94)(15,28,101,50,69,82,37,86)(16,85,38,81,70,49,102,27)(17,26,103,48,71,80,39,112)(18,111,40,79,72,47,104,25)(19,24,105,46,73,78,41,110)(20,109,42,77,74,45,106,23)(21,22,107,44,75,76,43,108)(113,136,201,164,194,189,141,224)(114,223,142,188,195,163,202,135)(115,134,203,162,196,187,143,222)(116,221,144,186,169,161,204,133)(117,132,205,160,170,185,145,220)(118,219,146,184,171,159,206,131)(119,130,207,158,172,183,147,218)(120,217,148,182,173,157,208,129)(121,128,209,156,174,181,149,216)(122,215,150,180,175,155,210,127)(123,126,211,154,176,179,151,214)(124,213,152,178,177,153,212,125)(137,140,197,168,190,193,165,200)(138,199,166,192,191,167,198,139) );
G=PermutationGroup([[(1,139,69,178),(2,179,70,140),(3,113,71,180),(4,181,72,114),(5,115,73,182),(6,183,74,116),(7,117,75,184),(8,185,76,118),(9,119,77,186),(10,187,78,120),(11,121,79,188),(12,189,80,122),(13,123,81,190),(14,191,82,124),(15,125,83,192),(16,193,84,126),(17,127,57,194),(18,195,58,128),(19,129,59,196),(20,169,60,130),(21,131,61,170),(22,171,62,132),(23,133,63,172),(24,173,64,134),(25,135,65,174),(26,175,66,136),(27,137,67,176),(28,177,68,138),(29,145,107,219),(30,220,108,146),(31,147,109,221),(32,222,110,148),(33,149,111,223),(34,224,112,150),(35,151,85,197),(36,198,86,152),(37,153,87,199),(38,200,88,154),(39,155,89,201),(40,202,90,156),(41,157,91,203),(42,204,92,158),(43,159,93,205),(44,206,94,160),(45,161,95,207),(46,208,96,162),(47,163,97,209),(48,210,98,164),(49,165,99,211),(50,212,100,166),(51,167,101,213),(52,214,102,168),(53,141,103,215),(54,216,104,142),(55,143,105,217),(56,218,106,144)], [(1,37,83,101),(2,102,84,38),(3,39,57,103),(4,104,58,40),(5,41,59,105),(6,106,60,42),(7,43,61,107),(8,108,62,44),(9,45,63,109),(10,110,64,46),(11,47,65,111),(12,112,66,48),(13,49,67,85),(14,86,68,50),(15,51,69,87),(16,88,70,52),(17,53,71,89),(18,90,72,54),(19,55,73,91),(20,92,74,56),(21,29,75,93),(22,94,76,30),(23,31,77,95),(24,96,78,32),(25,33,79,97),(26,98,80,34),(27,35,81,99),(28,100,82,36),(113,155,194,215),(114,216,195,156),(115,157,196,217),(116,218,169,158),(117,159,170,219),(118,220,171,160),(119,161,172,221),(120,222,173,162),(121,163,174,223),(122,224,175,164),(123,165,176,197),(124,198,177,166),(125,167,178,199),(126,200,179,168),(127,141,180,201),(128,202,181,142),(129,143,182,203),(130,204,183,144),(131,145,184,205),(132,206,185,146),(133,147,186,207),(134,208,187,148),(135,149,188,209),(136,210,189,150),(137,151,190,211),(138,212,191,152),(139,153,192,213),(140,214,193,154)], [(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)], [(1,14,87,36,83,68,51,100),(2,99,52,67,84,35,88,13),(3,12,89,34,57,66,53,98),(4,97,54,65,58,33,90,11),(5,10,91,32,59,64,55,96),(6,95,56,63,60,31,92,9),(7,8,93,30,61,62,29,94),(15,28,101,50,69,82,37,86),(16,85,38,81,70,49,102,27),(17,26,103,48,71,80,39,112),(18,111,40,79,72,47,104,25),(19,24,105,46,73,78,41,110),(20,109,42,77,74,45,106,23),(21,22,107,44,75,76,43,108),(113,136,201,164,194,189,141,224),(114,223,142,188,195,163,202,135),(115,134,203,162,196,187,143,222),(116,221,144,186,169,161,204,133),(117,132,205,160,170,185,145,220),(118,219,146,184,171,159,206,131),(119,130,207,158,172,183,147,218),(120,217,148,182,173,157,208,129),(121,128,209,156,174,181,149,216),(122,215,150,180,175,155,210,127),(123,126,211,154,176,179,151,214),(124,213,152,178,177,153,212,125),(137,140,197,168,190,193,165,200),(138,199,166,192,191,167,198,139)]])
58 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 56 | 2 | 2 | 4 | 4 | 8 | 8 | 56 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
58 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | - | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | C7⋊D4 | C8⋊C22 | C8.C22 | Q8⋊2D7 | D4.D14 | C28.C23 |
| kernel | C42.82D14 | C42.D7 | C14.D8 | C14.Q16 | C4.D28 | C7×C4⋊Q8 | C2×C28 | C4⋊Q8 | C28 | C42 | C4⋊C4 | C2×C4 | C14 | C14 | C4 | C2 | C2 |
| # reps | 1 | 1 | 2 | 2 | 1 | 1 | 2 | 3 | 4 | 3 | 6 | 12 | 1 | 1 | 6 | 6 | 6 |
Matrix representation of C42.82D14 ►in GL6(𝔽113)
| 98 | 15 | 0 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 29 | 7 | 58 | 14 |
| 0 | 0 | 106 | 84 | 99 | 55 |
| 0 | 0 | 84 | 106 | 84 | 106 |
| 0 | 0 | 7 | 29 | 7 | 29 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 111 | 0 |
| 0 | 0 | 0 | 112 | 0 | 111 |
| 0 | 0 | 1 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 | 0 | 1 |
| 1 | 112 | 0 | 0 | 0 | 0 |
| 2 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 82 | 31 | 84 | 33 |
| 0 | 0 | 82 | 35 | 80 | 85 |
| 0 | 0 | 73 | 42 | 31 | 82 |
| 0 | 0 | 71 | 64 | 31 | 78 |
| 112 | 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 111 | 111 | 80 | 29 |
| 0 | 0 | 63 | 2 | 28 | 33 |
| 0 | 0 | 73 | 42 | 31 | 82 |
| 0 | 0 | 99 | 40 | 35 | 82 |
G:=sub<GL(6,GF(113))| [98,0,0,0,0,0,15,15,0,0,0,0,0,0,29,106,84,7,0,0,7,84,106,29,0,0,58,99,84,7,0,0,14,55,106,29],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,1,0,0,0,0,112,0,1,0,0,111,0,1,0,0,0,0,111,0,1],[1,2,0,0,0,0,112,112,0,0,0,0,0,0,82,82,73,71,0,0,31,35,42,64,0,0,84,80,31,31,0,0,33,85,82,78],[112,0,0,0,0,0,1,1,0,0,0,0,0,0,111,63,73,99,0,0,111,2,42,40,0,0,80,28,31,35,0,0,29,33,82,82] >;
C42.82D14 in GAP, Magma, Sage, TeX
C_4^2._{82}D_{14} % in TeX
G:=Group("C4^2.82D14"); // GroupNames label
G:=SmallGroup(448,623);
// by ID
G=gap.SmallGroup(448,623);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,344,254,555,100,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=a^2*b^2,d^2=a^2*b,a*b=b*a,c*a*c^-1=a^-1,d*a*d^-1=a*b^2,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=b^-1*c^13>;
// generators/relations