metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.87D14, C14.462- 1+4, C4⋊C4.308D14, (C4×Dic14)⋊5C2, (C2×Dic14)⋊18C4, C14.15(C23×C4), (C2×C14).60C24, (C4×C28).20C22, Dic7⋊3Q8⋊11C2, (C2×C28).581C23, C28.119(C22×C4), C22⋊C4.123D14, Dic14.31(C2×C4), C42⋊C2.10D7, (C22×C4).185D14, Dic7.6(C22×C4), C22.25(C23×D7), C4⋊Dic7.396C22, (C4×Dic7).67C22, C23.149(C22×D7), C2.1(D4.10D14), C23.D7.90C22, Dic7⋊C4.130C22, (C22×C28).221C22, (C22×C14).130C23, C7⋊1(C23.32C23), (C2×Dic7).192C23, (C22×Dic14).17C2, C23.11D14.4C2, (C2×Dic14).283C22, C23.21D14.21C2, (C22×Dic7).84C22, C4.57(C2×C4×D7), (C2×C4).57(C4×D7), C2.17(D7×C22×C4), C22.25(C2×C4×D7), (C2×C28).129(C2×C4), (C7×C4⋊C4).301C22, (C2×C14).19(C22×C4), (C2×Dic7).36(C2×C4), (C2×C4).268(C22×D7), (C7×C42⋊C2).11C2, (C7×C22⋊C4).133C22, SmallGroup(448,969)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.87D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2, ab=ba, ac=ca, dad-1=a-1, cbc-1=dbd-1=a2b, dcd-1=c-1 >
Subgroups: 884 in 266 conjugacy classes, 151 normal (19 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, Q8, C23, C14, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×Q8, Dic7, Dic7, C28, C28, C2×C14, C2×C14, C2×C14, C42⋊C2, C42⋊C2, C4×Q8, C22×Q8, Dic14, C2×Dic7, C2×C28, C2×C28, C22×C14, C23.32C23, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C22×Dic7, C22×C28, C4×Dic14, C23.11D14, Dic7⋊3Q8, C23.21D14, C7×C42⋊C2, C22×Dic14, C42.87D14
Quotients: C1, C2, C4, C22, C2×C4, C23, D7, C22×C4, C24, D14, C23×C4, 2- 1+4, C4×D7, C22×D7, C23.32C23, C2×C4×D7, C23×D7, D7×C22×C4, D4.10D14, C42.87D14
►On 224 points
Generators in S224
(1 88 28 31)(2 89 22 32)(3 90 23 33)(4 91 24 34)(5 85 25 35)(6 86 26 29)(7 87 27 30)(8 62 110 69)(9 63 111 70)(10 57 112 64)(11 58 106 65)(12 59 107 66)(13 60 108 67)(14 61 109 68)(15 78 42 71)(16 79 36 72)(17 80 37 73)(18 81 38 74)(19 82 39 75)(20 83 40 76)(21 84 41 77)(43 103 53 97)(44 104 54 98)(45 105 55 92)(46 99 56 93)(47 100 50 94)(48 101 51 95)(49 102 52 96)(113 164 120 157)(114 165 121 158)(115 166 122 159)(116 167 123 160)(117 168 124 161)(118 155 125 162)(119 156 126 163)(127 185 134 192)(128 186 135 193)(129 187 136 194)(130 188 137 195)(131 189 138 196)(132 190 139 183)(133 191 140 184)(141 220 148 213)(142 221 149 214)(143 222 150 215)(144 223 151 216)(145 224 152 217)(146 211 153 218)(147 212 154 219)(169 201 176 208)(170 202 177 209)(171 203 178 210)(172 204 179 197)(173 205 180 198)(174 206 181 199)(175 207 182 200)
(1 215 45 172)(2 223 46 180)(3 217 47 174)(4 211 48 182)(5 219 49 176)(6 213 43 170)(7 221 44 178)(8 115 40 139)(9 123 41 133)(10 117 42 127)(11 125 36 135)(12 119 37 129)(13 113 38 137)(14 121 39 131)(15 134 112 124)(16 128 106 118)(17 136 107 126)(18 130 108 120)(19 138 109 114)(20 132 110 122)(21 140 111 116)(22 216 56 173)(23 224 50 181)(24 218 51 175)(25 212 52 169)(26 220 53 177)(27 214 54 171)(28 222 55 179)(29 148 97 209)(30 142 98 203)(31 150 92 197)(32 144 93 205)(33 152 94 199)(34 146 95 207)(35 154 96 201)(57 168 71 185)(58 162 72 193)(59 156 73 187)(60 164 74 195)(61 158 75 189)(62 166 76 183)(63 160 77 191)(64 161 78 192)(65 155 79 186)(66 163 80 194)(67 157 81 188)(68 165 82 196)(69 159 83 190)(70 167 84 184)(85 147 102 208)(86 141 103 202)(87 149 104 210)(88 143 105 204)(89 151 99 198)(90 145 100 206)(91 153 101 200)
(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 10 28 112)(2 9 22 111)(3 8 23 110)(4 14 24 109)(5 13 25 108)(6 12 26 107)(7 11 27 106)(15 45 42 55)(16 44 36 54)(17 43 37 53)(18 49 38 52)(19 48 39 51)(20 47 40 50)(21 46 41 56)(29 59 86 66)(30 58 87 65)(31 57 88 64)(32 63 89 70)(33 62 90 69)(34 61 91 68)(35 60 85 67)(71 105 78 92)(72 104 79 98)(73 103 80 97)(74 102 81 96)(75 101 82 95)(76 100 83 94)(77 99 84 93)(113 219 120 212)(114 218 121 211)(115 217 122 224)(116 216 123 223)(117 215 124 222)(118 214 125 221)(119 213 126 220)(127 172 134 179)(128 171 135 178)(129 170 136 177)(130 169 137 176)(131 182 138 175)(132 181 139 174)(133 180 140 173)(141 156 148 163)(142 155 149 162)(143 168 150 161)(144 167 151 160)(145 166 152 159)(146 165 153 158)(147 164 154 157)(183 199 190 206)(184 198 191 205)(185 197 192 204)(186 210 193 203)(187 209 194 202)(188 208 195 201)(189 207 196 200)
G:=sub<Sym(224)| (1,88,28,31)(2,89,22,32)(3,90,23,33)(4,91,24,34)(5,85,25,35)(6,86,26,29)(7,87,27,30)(8,62,110,69)(9,63,111,70)(10,57,112,64)(11,58,106,65)(12,59,107,66)(13,60,108,67)(14,61,109,68)(15,78,42,71)(16,79,36,72)(17,80,37,73)(18,81,38,74)(19,82,39,75)(20,83,40,76)(21,84,41,77)(43,103,53,97)(44,104,54,98)(45,105,55,92)(46,99,56,93)(47,100,50,94)(48,101,51,95)(49,102,52,96)(113,164,120,157)(114,165,121,158)(115,166,122,159)(116,167,123,160)(117,168,124,161)(118,155,125,162)(119,156,126,163)(127,185,134,192)(128,186,135,193)(129,187,136,194)(130,188,137,195)(131,189,138,196)(132,190,139,183)(133,191,140,184)(141,220,148,213)(142,221,149,214)(143,222,150,215)(144,223,151,216)(145,224,152,217)(146,211,153,218)(147,212,154,219)(169,201,176,208)(170,202,177,209)(171,203,178,210)(172,204,179,197)(173,205,180,198)(174,206,181,199)(175,207,182,200), (1,215,45,172)(2,223,46,180)(3,217,47,174)(4,211,48,182)(5,219,49,176)(6,213,43,170)(7,221,44,178)(8,115,40,139)(9,123,41,133)(10,117,42,127)(11,125,36,135)(12,119,37,129)(13,113,38,137)(14,121,39,131)(15,134,112,124)(16,128,106,118)(17,136,107,126)(18,130,108,120)(19,138,109,114)(20,132,110,122)(21,140,111,116)(22,216,56,173)(23,224,50,181)(24,218,51,175)(25,212,52,169)(26,220,53,177)(27,214,54,171)(28,222,55,179)(29,148,97,209)(30,142,98,203)(31,150,92,197)(32,144,93,205)(33,152,94,199)(34,146,95,207)(35,154,96,201)(57,168,71,185)(58,162,72,193)(59,156,73,187)(60,164,74,195)(61,158,75,189)(62,166,76,183)(63,160,77,191)(64,161,78,192)(65,155,79,186)(66,163,80,194)(67,157,81,188)(68,165,82,196)(69,159,83,190)(70,167,84,184)(85,147,102,208)(86,141,103,202)(87,149,104,210)(88,143,105,204)(89,151,99,198)(90,145,100,206)(91,153,101,200), (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), (1,10,28,112)(2,9,22,111)(3,8,23,110)(4,14,24,109)(5,13,25,108)(6,12,26,107)(7,11,27,106)(15,45,42,55)(16,44,36,54)(17,43,37,53)(18,49,38,52)(19,48,39,51)(20,47,40,50)(21,46,41,56)(29,59,86,66)(30,58,87,65)(31,57,88,64)(32,63,89,70)(33,62,90,69)(34,61,91,68)(35,60,85,67)(71,105,78,92)(72,104,79,98)(73,103,80,97)(74,102,81,96)(75,101,82,95)(76,100,83,94)(77,99,84,93)(113,219,120,212)(114,218,121,211)(115,217,122,224)(116,216,123,223)(117,215,124,222)(118,214,125,221)(119,213,126,220)(127,172,134,179)(128,171,135,178)(129,170,136,177)(130,169,137,176)(131,182,138,175)(132,181,139,174)(133,180,140,173)(141,156,148,163)(142,155,149,162)(143,168,150,161)(144,167,151,160)(145,166,152,159)(146,165,153,158)(147,164,154,157)(183,199,190,206)(184,198,191,205)(185,197,192,204)(186,210,193,203)(187,209,194,202)(188,208,195,201)(189,207,196,200)>;
G:=Group( (1,88,28,31)(2,89,22,32)(3,90,23,33)(4,91,24,34)(5,85,25,35)(6,86,26,29)(7,87,27,30)(8,62,110,69)(9,63,111,70)(10,57,112,64)(11,58,106,65)(12,59,107,66)(13,60,108,67)(14,61,109,68)(15,78,42,71)(16,79,36,72)(17,80,37,73)(18,81,38,74)(19,82,39,75)(20,83,40,76)(21,84,41,77)(43,103,53,97)(44,104,54,98)(45,105,55,92)(46,99,56,93)(47,100,50,94)(48,101,51,95)(49,102,52,96)(113,164,120,157)(114,165,121,158)(115,166,122,159)(116,167,123,160)(117,168,124,161)(118,155,125,162)(119,156,126,163)(127,185,134,192)(128,186,135,193)(129,187,136,194)(130,188,137,195)(131,189,138,196)(132,190,139,183)(133,191,140,184)(141,220,148,213)(142,221,149,214)(143,222,150,215)(144,223,151,216)(145,224,152,217)(146,211,153,218)(147,212,154,219)(169,201,176,208)(170,202,177,209)(171,203,178,210)(172,204,179,197)(173,205,180,198)(174,206,181,199)(175,207,182,200), (1,215,45,172)(2,223,46,180)(3,217,47,174)(4,211,48,182)(5,219,49,176)(6,213,43,170)(7,221,44,178)(8,115,40,139)(9,123,41,133)(10,117,42,127)(11,125,36,135)(12,119,37,129)(13,113,38,137)(14,121,39,131)(15,134,112,124)(16,128,106,118)(17,136,107,126)(18,130,108,120)(19,138,109,114)(20,132,110,122)(21,140,111,116)(22,216,56,173)(23,224,50,181)(24,218,51,175)(25,212,52,169)(26,220,53,177)(27,214,54,171)(28,222,55,179)(29,148,97,209)(30,142,98,203)(31,150,92,197)(32,144,93,205)(33,152,94,199)(34,146,95,207)(35,154,96,201)(57,168,71,185)(58,162,72,193)(59,156,73,187)(60,164,74,195)(61,158,75,189)(62,166,76,183)(63,160,77,191)(64,161,78,192)(65,155,79,186)(66,163,80,194)(67,157,81,188)(68,165,82,196)(69,159,83,190)(70,167,84,184)(85,147,102,208)(86,141,103,202)(87,149,104,210)(88,143,105,204)(89,151,99,198)(90,145,100,206)(91,153,101,200), (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), (1,10,28,112)(2,9,22,111)(3,8,23,110)(4,14,24,109)(5,13,25,108)(6,12,26,107)(7,11,27,106)(15,45,42,55)(16,44,36,54)(17,43,37,53)(18,49,38,52)(19,48,39,51)(20,47,40,50)(21,46,41,56)(29,59,86,66)(30,58,87,65)(31,57,88,64)(32,63,89,70)(33,62,90,69)(34,61,91,68)(35,60,85,67)(71,105,78,92)(72,104,79,98)(73,103,80,97)(74,102,81,96)(75,101,82,95)(76,100,83,94)(77,99,84,93)(113,219,120,212)(114,218,121,211)(115,217,122,224)(116,216,123,223)(117,215,124,222)(118,214,125,221)(119,213,126,220)(127,172,134,179)(128,171,135,178)(129,170,136,177)(130,169,137,176)(131,182,138,175)(132,181,139,174)(133,180,140,173)(141,156,148,163)(142,155,149,162)(143,168,150,161)(144,167,151,160)(145,166,152,159)(146,165,153,158)(147,164,154,157)(183,199,190,206)(184,198,191,205)(185,197,192,204)(186,210,193,203)(187,209,194,202)(188,208,195,201)(189,207,196,200) );
G=PermutationGroup([[(1,88,28,31),(2,89,22,32),(3,90,23,33),(4,91,24,34),(5,85,25,35),(6,86,26,29),(7,87,27,30),(8,62,110,69),(9,63,111,70),(10,57,112,64),(11,58,106,65),(12,59,107,66),(13,60,108,67),(14,61,109,68),(15,78,42,71),(16,79,36,72),(17,80,37,73),(18,81,38,74),(19,82,39,75),(20,83,40,76),(21,84,41,77),(43,103,53,97),(44,104,54,98),(45,105,55,92),(46,99,56,93),(47,100,50,94),(48,101,51,95),(49,102,52,96),(113,164,120,157),(114,165,121,158),(115,166,122,159),(116,167,123,160),(117,168,124,161),(118,155,125,162),(119,156,126,163),(127,185,134,192),(128,186,135,193),(129,187,136,194),(130,188,137,195),(131,189,138,196),(132,190,139,183),(133,191,140,184),(141,220,148,213),(142,221,149,214),(143,222,150,215),(144,223,151,216),(145,224,152,217),(146,211,153,218),(147,212,154,219),(169,201,176,208),(170,202,177,209),(171,203,178,210),(172,204,179,197),(173,205,180,198),(174,206,181,199),(175,207,182,200)], [(1,215,45,172),(2,223,46,180),(3,217,47,174),(4,211,48,182),(5,219,49,176),(6,213,43,170),(7,221,44,178),(8,115,40,139),(9,123,41,133),(10,117,42,127),(11,125,36,135),(12,119,37,129),(13,113,38,137),(14,121,39,131),(15,134,112,124),(16,128,106,118),(17,136,107,126),(18,130,108,120),(19,138,109,114),(20,132,110,122),(21,140,111,116),(22,216,56,173),(23,224,50,181),(24,218,51,175),(25,212,52,169),(26,220,53,177),(27,214,54,171),(28,222,55,179),(29,148,97,209),(30,142,98,203),(31,150,92,197),(32,144,93,205),(33,152,94,199),(34,146,95,207),(35,154,96,201),(57,168,71,185),(58,162,72,193),(59,156,73,187),(60,164,74,195),(61,158,75,189),(62,166,76,183),(63,160,77,191),(64,161,78,192),(65,155,79,186),(66,163,80,194),(67,157,81,188),(68,165,82,196),(69,159,83,190),(70,167,84,184),(85,147,102,208),(86,141,103,202),(87,149,104,210),(88,143,105,204),(89,151,99,198),(90,145,100,206),(91,153,101,200)], [(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)], [(1,10,28,112),(2,9,22,111),(3,8,23,110),(4,14,24,109),(5,13,25,108),(6,12,26,107),(7,11,27,106),(15,45,42,55),(16,44,36,54),(17,43,37,53),(18,49,38,52),(19,48,39,51),(20,47,40,50),(21,46,41,56),(29,59,86,66),(30,58,87,65),(31,57,88,64),(32,63,89,70),(33,62,90,69),(34,61,91,68),(35,60,85,67),(71,105,78,92),(72,104,79,98),(73,103,80,97),(74,102,81,96),(75,101,82,95),(76,100,83,94),(77,99,84,93),(113,219,120,212),(114,218,121,211),(115,217,122,224),(116,216,123,223),(117,215,124,222),(118,214,125,221),(119,213,126,220),(127,172,134,179),(128,171,135,178),(129,170,136,177),(130,169,137,176),(131,182,138,175),(132,181,139,174),(133,180,140,173),(141,156,148,163),(142,155,149,162),(143,168,150,161),(144,167,151,160),(145,166,152,159),(146,165,153,158),(147,164,154,157),(183,199,190,206),(184,198,191,205),(185,197,192,204),(186,210,193,203),(187,209,194,202),(188,208,195,201),(189,207,196,200)]])
94 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4L | 4M | ··· | 4AB | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | ··· | 2 | 14 | ··· | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
94 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | D7 | D14 | D14 | D14 | D14 | C4×D7 | 2- 1+4 | D4.10D14 |
| kernel | C42.87D14 | C4×Dic14 | C23.11D14 | Dic7⋊3Q8 | C23.21D14 | C7×C42⋊C2 | C22×Dic14 | C2×Dic14 | C42⋊C2 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×C4 | C14 | C2 |
| # reps | 1 | 4 | 4 | 4 | 1 | 1 | 1 | 16 | 3 | 6 | 6 | 6 | 3 | 24 | 2 | 12 |
Matrix representation of C42.87D14 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 13 | 24 | 0 | 0 |
| 0 | 0 | 5 | 16 | 0 | 0 |
| 0 | 0 | 9 | 0 | 16 | 24 |
| 0 | 0 | 0 | 20 | 5 | 13 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 4 | 14 | 8 | 10 |
| 0 | 0 | 18 | 2 | 20 | 8 |
| 0 | 0 | 18 | 25 | 27 | 15 |
| 0 | 0 | 14 | 18 | 11 | 25 |
| 8 | 8 | 0 | 0 | 0 | 0 |
| 21 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 25 | 0 | 0 |
| 0 | 0 | 4 | 25 | 0 | 0 |
| 0 | 0 | 6 | 5 | 4 | 4 |
| 0 | 0 | 17 | 6 | 25 | 18 |
| 26 | 1 | 0 | 0 | 0 | 0 |
| 21 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 19 | 0 | 0 |
| 0 | 0 | 13 | 19 | 0 | 0 |
| 0 | 0 | 17 | 24 | 0 | 12 |
| 0 | 0 | 13 | 10 | 12 | 0 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,13,5,9,0,0,0,24,16,0,20,0,0,0,0,16,5,0,0,0,0,24,13],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,4,18,18,14,0,0,14,2,25,18,0,0,8,20,27,11,0,0,10,8,15,25],[8,21,0,0,0,0,8,3,0,0,0,0,0,0,11,4,6,17,0,0,25,25,5,6,0,0,0,0,4,25,0,0,0,0,4,18],[26,21,0,0,0,0,1,3,0,0,0,0,0,0,10,13,17,13,0,0,19,19,24,10,0,0,0,0,0,12,0,0,0,0,12,0] >;
C42.87D14 in GAP, Magma, Sage, TeX
C_4^2._{87}D_{14} % in TeX
G:=Group("C4^2.87D14"); // GroupNames label
G:=SmallGroup(448,969);
// by ID
G=gap.SmallGroup(448,969);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,758,184,570,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,c*b*c^-1=d*b*d^-1=a^2*b,d*c*d^-1=c^-1>;
// generators/relations