metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.171D14, C14.342- 1+4, C4⋊Q8⋊9D7, C4.37(D4×D7), (C4×D7).13D4, C28.69(C2×D4), C4⋊C4.122D14, D14.48(C2×D4), D14⋊Q8⋊47C2, C4.D28⋊26C2, C42⋊D7⋊25C2, (C2×Q8).143D14, Dic7.53(C2×D4), C14.98(C22×D4), Dic7⋊Q8⋊26C2, D14.5D4⋊45C2, C28.23D4⋊25C2, (C2×C14).268C24, (C2×C28).101C23, (C4×C28).209C22, D14⋊C4.49C22, (C2×D28).171C22, (Q8×C14).135C22, C22.289(C23×D7), Dic7⋊C4.165C22, C7⋊5(C23.38C23), (C2×Dic7).140C23, (C4×Dic7).159C22, (C22×D7).230C23, C2.35(Q8.10D14), (C2×Dic14).188C22, (C2×Q8×D7)⋊12C2, C2.71(C2×D4×D7), (C7×C4⋊Q8)⋊10C2, (C2×Q8⋊2D7).7C2, (C2×C4×D7).142C22, (C7×C4⋊C4).211C22, (C2×C4).217(C22×D7), SmallGroup(448,1177)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.171D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2, ab=ba, cac-1=dad-1=a-1, cbc-1=b-1, dbd-1=a2b-1, dcd-1=c13 >
Subgroups: 1292 in 270 conjugacy classes, 103 normal (29 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C42⋊C2, C22⋊Q8, C22.D4, C4.4D4, C4⋊Q8, C4⋊Q8, C22×Q8, C2×C4○D4, Dic14, C4×D7, C4×D7, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C22×D7, C23.38C23, C4×Dic7, Dic7⋊C4, D14⋊C4, C4×C28, C7×C4⋊C4, C2×Dic14, C2×Dic14, C2×C4×D7, C2×C4×D7, C2×D28, C2×D28, Q8×D7, Q8⋊2D7, Q8×C14, C42⋊D7, C4.D28, D14.5D4, D14⋊Q8, Dic7⋊Q8, C28.23D4, C7×C4⋊Q8, C2×Q8×D7, C2×Q8⋊2D7, C42.171D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C24, D14, C22×D4, 2- 1+4, C22×D7, C23.38C23, D4×D7, C23×D7, C2×D4×D7, Q8.10D14, C42.171D14
►On 224 points
Generators in S224
(1 57 15 71)(2 72 16 58)(3 59 17 73)(4 74 18 60)(5 61 19 75)(6 76 20 62)(7 63 21 77)(8 78 22 64)(9 65 23 79)(10 80 24 66)(11 67 25 81)(12 82 26 68)(13 69 27 83)(14 84 28 70)(29 158 43 144)(30 145 44 159)(31 160 45 146)(32 147 46 161)(33 162 47 148)(34 149 48 163)(35 164 49 150)(36 151 50 165)(37 166 51 152)(38 153 52 167)(39 168 53 154)(40 155 54 141)(41 142 55 156)(42 157 56 143)(85 192 99 178)(86 179 100 193)(87 194 101 180)(88 181 102 195)(89 196 103 182)(90 183 104 169)(91 170 105 184)(92 185 106 171)(93 172 107 186)(94 187 108 173)(95 174 109 188)(96 189 110 175)(97 176 111 190)(98 191 112 177)(113 217 127 203)(114 204 128 218)(115 219 129 205)(116 206 130 220)(117 221 131 207)(118 208 132 222)(119 223 133 209)(120 210 134 224)(121 197 135 211)(122 212 136 198)(123 199 137 213)(124 214 138 200)(125 201 139 215)(126 216 140 202)
(1 193 127 34)(2 35 128 194)(3 195 129 36)(4 37 130 196)(5 169 131 38)(6 39 132 170)(7 171 133 40)(8 41 134 172)(9 173 135 42)(10 43 136 174)(11 175 137 44)(12 45 138 176)(13 177 139 46)(14 47 140 178)(15 179 113 48)(16 49 114 180)(17 181 115 50)(18 51 116 182)(19 183 117 52)(20 53 118 184)(21 185 119 54)(22 55 120 186)(23 187 121 56)(24 29 122 188)(25 189 123 30)(26 31 124 190)(27 191 125 32)(28 33 126 192)(57 86 203 149)(58 150 204 87)(59 88 205 151)(60 152 206 89)(61 90 207 153)(62 154 208 91)(63 92 209 155)(64 156 210 93)(65 94 211 157)(66 158 212 95)(67 96 213 159)(68 160 214 97)(69 98 215 161)(70 162 216 99)(71 100 217 163)(72 164 218 101)(73 102 219 165)(74 166 220 103)(75 104 221 167)(76 168 222 105)(77 106 223 141)(78 142 224 107)(79 108 197 143)(80 144 198 109)(81 110 199 145)(82 146 200 111)(83 112 201 147)(84 148 202 85)
(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 52 43 38)(30 37 44 51)(31 50 45 36)(32 35 46 49)(33 48 47 34)(39 42 53 56)(40 55 54 41)(57 70 71 84)(58 83 72 69)(59 68 73 82)(60 81 74 67)(61 66 75 80)(62 79 76 65)(63 64 77 78)(85 100 99 86)(87 98 101 112)(88 111 102 97)(89 96 103 110)(90 109 104 95)(91 94 105 108)(92 107 106 93)(113 126 127 140)(114 139 128 125)(115 124 129 138)(116 137 130 123)(117 122 131 136)(118 135 132 121)(119 120 133 134)(141 156 155 142)(143 154 157 168)(144 167 158 153)(145 152 159 166)(146 165 160 151)(147 150 161 164)(148 163 162 149)(169 188 183 174)(170 173 184 187)(171 186 185 172)(175 182 189 196)(176 195 190 181)(177 180 191 194)(178 193 192 179)(197 222 211 208)(198 207 212 221)(199 220 213 206)(200 205 214 219)(201 218 215 204)(202 203 216 217)(209 210 223 224)
G:=sub<Sym(224)| (1,57,15,71)(2,72,16,58)(3,59,17,73)(4,74,18,60)(5,61,19,75)(6,76,20,62)(7,63,21,77)(8,78,22,64)(9,65,23,79)(10,80,24,66)(11,67,25,81)(12,82,26,68)(13,69,27,83)(14,84,28,70)(29,158,43,144)(30,145,44,159)(31,160,45,146)(32,147,46,161)(33,162,47,148)(34,149,48,163)(35,164,49,150)(36,151,50,165)(37,166,51,152)(38,153,52,167)(39,168,53,154)(40,155,54,141)(41,142,55,156)(42,157,56,143)(85,192,99,178)(86,179,100,193)(87,194,101,180)(88,181,102,195)(89,196,103,182)(90,183,104,169)(91,170,105,184)(92,185,106,171)(93,172,107,186)(94,187,108,173)(95,174,109,188)(96,189,110,175)(97,176,111,190)(98,191,112,177)(113,217,127,203)(114,204,128,218)(115,219,129,205)(116,206,130,220)(117,221,131,207)(118,208,132,222)(119,223,133,209)(120,210,134,224)(121,197,135,211)(122,212,136,198)(123,199,137,213)(124,214,138,200)(125,201,139,215)(126,216,140,202), (1,193,127,34)(2,35,128,194)(3,195,129,36)(4,37,130,196)(5,169,131,38)(6,39,132,170)(7,171,133,40)(8,41,134,172)(9,173,135,42)(10,43,136,174)(11,175,137,44)(12,45,138,176)(13,177,139,46)(14,47,140,178)(15,179,113,48)(16,49,114,180)(17,181,115,50)(18,51,116,182)(19,183,117,52)(20,53,118,184)(21,185,119,54)(22,55,120,186)(23,187,121,56)(24,29,122,188)(25,189,123,30)(26,31,124,190)(27,191,125,32)(28,33,126,192)(57,86,203,149)(58,150,204,87)(59,88,205,151)(60,152,206,89)(61,90,207,153)(62,154,208,91)(63,92,209,155)(64,156,210,93)(65,94,211,157)(66,158,212,95)(67,96,213,159)(68,160,214,97)(69,98,215,161)(70,162,216,99)(71,100,217,163)(72,164,218,101)(73,102,219,165)(74,166,220,103)(75,104,221,167)(76,168,222,105)(77,106,223,141)(78,142,224,107)(79,108,197,143)(80,144,198,109)(81,110,199,145)(82,146,200,111)(83,112,201,147)(84,148,202,85), (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)(29,52,43,38)(30,37,44,51)(31,50,45,36)(32,35,46,49)(33,48,47,34)(39,42,53,56)(40,55,54,41)(57,70,71,84)(58,83,72,69)(59,68,73,82)(60,81,74,67)(61,66,75,80)(62,79,76,65)(63,64,77,78)(85,100,99,86)(87,98,101,112)(88,111,102,97)(89,96,103,110)(90,109,104,95)(91,94,105,108)(92,107,106,93)(113,126,127,140)(114,139,128,125)(115,124,129,138)(116,137,130,123)(117,122,131,136)(118,135,132,121)(119,120,133,134)(141,156,155,142)(143,154,157,168)(144,167,158,153)(145,152,159,166)(146,165,160,151)(147,150,161,164)(148,163,162,149)(169,188,183,174)(170,173,184,187)(171,186,185,172)(175,182,189,196)(176,195,190,181)(177,180,191,194)(178,193,192,179)(197,222,211,208)(198,207,212,221)(199,220,213,206)(200,205,214,219)(201,218,215,204)(202,203,216,217)(209,210,223,224)>;
G:=Group( (1,57,15,71)(2,72,16,58)(3,59,17,73)(4,74,18,60)(5,61,19,75)(6,76,20,62)(7,63,21,77)(8,78,22,64)(9,65,23,79)(10,80,24,66)(11,67,25,81)(12,82,26,68)(13,69,27,83)(14,84,28,70)(29,158,43,144)(30,145,44,159)(31,160,45,146)(32,147,46,161)(33,162,47,148)(34,149,48,163)(35,164,49,150)(36,151,50,165)(37,166,51,152)(38,153,52,167)(39,168,53,154)(40,155,54,141)(41,142,55,156)(42,157,56,143)(85,192,99,178)(86,179,100,193)(87,194,101,180)(88,181,102,195)(89,196,103,182)(90,183,104,169)(91,170,105,184)(92,185,106,171)(93,172,107,186)(94,187,108,173)(95,174,109,188)(96,189,110,175)(97,176,111,190)(98,191,112,177)(113,217,127,203)(114,204,128,218)(115,219,129,205)(116,206,130,220)(117,221,131,207)(118,208,132,222)(119,223,133,209)(120,210,134,224)(121,197,135,211)(122,212,136,198)(123,199,137,213)(124,214,138,200)(125,201,139,215)(126,216,140,202), (1,193,127,34)(2,35,128,194)(3,195,129,36)(4,37,130,196)(5,169,131,38)(6,39,132,170)(7,171,133,40)(8,41,134,172)(9,173,135,42)(10,43,136,174)(11,175,137,44)(12,45,138,176)(13,177,139,46)(14,47,140,178)(15,179,113,48)(16,49,114,180)(17,181,115,50)(18,51,116,182)(19,183,117,52)(20,53,118,184)(21,185,119,54)(22,55,120,186)(23,187,121,56)(24,29,122,188)(25,189,123,30)(26,31,124,190)(27,191,125,32)(28,33,126,192)(57,86,203,149)(58,150,204,87)(59,88,205,151)(60,152,206,89)(61,90,207,153)(62,154,208,91)(63,92,209,155)(64,156,210,93)(65,94,211,157)(66,158,212,95)(67,96,213,159)(68,160,214,97)(69,98,215,161)(70,162,216,99)(71,100,217,163)(72,164,218,101)(73,102,219,165)(74,166,220,103)(75,104,221,167)(76,168,222,105)(77,106,223,141)(78,142,224,107)(79,108,197,143)(80,144,198,109)(81,110,199,145)(82,146,200,111)(83,112,201,147)(84,148,202,85), (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)(29,52,43,38)(30,37,44,51)(31,50,45,36)(32,35,46,49)(33,48,47,34)(39,42,53,56)(40,55,54,41)(57,70,71,84)(58,83,72,69)(59,68,73,82)(60,81,74,67)(61,66,75,80)(62,79,76,65)(63,64,77,78)(85,100,99,86)(87,98,101,112)(88,111,102,97)(89,96,103,110)(90,109,104,95)(91,94,105,108)(92,107,106,93)(113,126,127,140)(114,139,128,125)(115,124,129,138)(116,137,130,123)(117,122,131,136)(118,135,132,121)(119,120,133,134)(141,156,155,142)(143,154,157,168)(144,167,158,153)(145,152,159,166)(146,165,160,151)(147,150,161,164)(148,163,162,149)(169,188,183,174)(170,173,184,187)(171,186,185,172)(175,182,189,196)(176,195,190,181)(177,180,191,194)(178,193,192,179)(197,222,211,208)(198,207,212,221)(199,220,213,206)(200,205,214,219)(201,218,215,204)(202,203,216,217)(209,210,223,224) );
G=PermutationGroup([[(1,57,15,71),(2,72,16,58),(3,59,17,73),(4,74,18,60),(5,61,19,75),(6,76,20,62),(7,63,21,77),(8,78,22,64),(9,65,23,79),(10,80,24,66),(11,67,25,81),(12,82,26,68),(13,69,27,83),(14,84,28,70),(29,158,43,144),(30,145,44,159),(31,160,45,146),(32,147,46,161),(33,162,47,148),(34,149,48,163),(35,164,49,150),(36,151,50,165),(37,166,51,152),(38,153,52,167),(39,168,53,154),(40,155,54,141),(41,142,55,156),(42,157,56,143),(85,192,99,178),(86,179,100,193),(87,194,101,180),(88,181,102,195),(89,196,103,182),(90,183,104,169),(91,170,105,184),(92,185,106,171),(93,172,107,186),(94,187,108,173),(95,174,109,188),(96,189,110,175),(97,176,111,190),(98,191,112,177),(113,217,127,203),(114,204,128,218),(115,219,129,205),(116,206,130,220),(117,221,131,207),(118,208,132,222),(119,223,133,209),(120,210,134,224),(121,197,135,211),(122,212,136,198),(123,199,137,213),(124,214,138,200),(125,201,139,215),(126,216,140,202)], [(1,193,127,34),(2,35,128,194),(3,195,129,36),(4,37,130,196),(5,169,131,38),(6,39,132,170),(7,171,133,40),(8,41,134,172),(9,173,135,42),(10,43,136,174),(11,175,137,44),(12,45,138,176),(13,177,139,46),(14,47,140,178),(15,179,113,48),(16,49,114,180),(17,181,115,50),(18,51,116,182),(19,183,117,52),(20,53,118,184),(21,185,119,54),(22,55,120,186),(23,187,121,56),(24,29,122,188),(25,189,123,30),(26,31,124,190),(27,191,125,32),(28,33,126,192),(57,86,203,149),(58,150,204,87),(59,88,205,151),(60,152,206,89),(61,90,207,153),(62,154,208,91),(63,92,209,155),(64,156,210,93),(65,94,211,157),(66,158,212,95),(67,96,213,159),(68,160,214,97),(69,98,215,161),(70,162,216,99),(71,100,217,163),(72,164,218,101),(73,102,219,165),(74,166,220,103),(75,104,221,167),(76,168,222,105),(77,106,223,141),(78,142,224,107),(79,108,197,143),(80,144,198,109),(81,110,199,145),(82,146,200,111),(83,112,201,147),(84,148,202,85)], [(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),(29,52,43,38),(30,37,44,51),(31,50,45,36),(32,35,46,49),(33,48,47,34),(39,42,53,56),(40,55,54,41),(57,70,71,84),(58,83,72,69),(59,68,73,82),(60,81,74,67),(61,66,75,80),(62,79,76,65),(63,64,77,78),(85,100,99,86),(87,98,101,112),(88,111,102,97),(89,96,103,110),(90,109,104,95),(91,94,105,108),(92,107,106,93),(113,126,127,140),(114,139,128,125),(115,124,129,138),(116,137,130,123),(117,122,131,136),(118,135,132,121),(119,120,133,134),(141,156,155,142),(143,154,157,168),(144,167,158,153),(145,152,159,166),(146,165,160,151),(147,150,161,164),(148,163,162,149),(169,188,183,174),(170,173,184,187),(171,186,185,172),(175,182,189,196),(176,195,190,181),(177,180,191,194),(178,193,192,179),(197,222,211,208),(198,207,212,221),(199,220,213,206),(200,205,214,219),(201,218,215,204),(202,203,216,217),(209,210,223,224)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 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 | 14 | 14 | 28 | 28 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | D14 | D14 | D14 | 2- 1+4 | D4×D7 | Q8.10D14 |
| kernel | C42.171D14 | C42⋊D7 | C4.D28 | D14.5D4 | D14⋊Q8 | Dic7⋊Q8 | C28.23D4 | C7×C4⋊Q8 | C2×Q8×D7 | C2×Q8⋊2D7 | C4×D7 | C4⋊Q8 | C42 | C4⋊C4 | C2×Q8 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 4 | 4 | 1 | 1 | 1 | 1 | 1 | 4 | 3 | 3 | 12 | 6 | 2 | 6 | 12 |
Matrix representation of C42.171D14 ►in GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 13 | 2 | 22 |
| 0 | 0 | 18 | 9 | 13 | 19 |
| 0 | 0 | 20 | 2 | 5 | 16 |
| 0 | 0 | 8 | 11 | 16 | 5 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 16 | 0 | 4 |
| 0 | 0 | 24 | 20 | 25 | 11 |
| 0 | 0 | 24 | 15 | 24 | 13 |
| 0 | 0 | 14 | 0 | 16 | 5 |
| 5 | 18 | 0 | 0 | 0 | 0 |
| 18 | 24 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 5 | 13 | 9 |
| 0 | 0 | 24 | 2 | 1 | 16 |
| 0 | 0 | 21 | 25 | 19 | 24 |
| 0 | 0 | 0 | 10 | 10 | 12 |
| 24 | 11 | 0 | 0 | 0 | 0 |
| 11 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 20 | 12 | 20 | 16 |
| 0 | 0 | 3 | 14 | 13 | 28 |
| 0 | 0 | 17 | 19 | 5 | 10 |
| 0 | 0 | 4 | 16 | 17 | 19 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,10,18,20,8,0,0,13,9,2,11,0,0,2,13,5,16,0,0,22,19,16,5],[0,1,0,0,0,0,28,0,0,0,0,0,0,0,9,24,24,14,0,0,16,20,15,0,0,0,0,25,24,16,0,0,4,11,13,5],[5,18,0,0,0,0,18,24,0,0,0,0,0,0,25,24,21,0,0,0,5,2,25,10,0,0,13,1,19,10,0,0,9,16,24,12],[24,11,0,0,0,0,11,5,0,0,0,0,0,0,20,3,17,4,0,0,12,14,19,16,0,0,20,13,5,17,0,0,16,28,10,19] >;
C42.171D14 in GAP, Magma, Sage, TeX
C_4^2._{171}D_{14} % in TeX
G:=Group("C4^2.171D14"); // GroupNames label
G:=SmallGroup(448,1177);
// by ID
G=gap.SmallGroup(448,1177);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,100,675,297,136,18822]);
// 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=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