metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.89D14, C14.472- 1+4, C28⋊2Q8⋊5C2, C4⋊C4.267D14, (C4×Dic14)⋊7C2, Dic7.Q8⋊4C2, C28.6Q8⋊3C2, (C2×C14).62C24, (C4×C28).22C22, C22⋊C4.90D14, C28.235(C4○D4), C4.119(C4○D28), (C2×C28).141C23, C42⋊C2.12D7, (C22×C4).186D14, C4⋊Dic7.31C22, C22.95(C23×D7), C23.83(C22×D7), C23.D7.3C22, C28.48D4.18C2, Dic7⋊C4.74C22, (C2×Dic7).21C23, C23.D14.1C2, C2.6(D4.10D14), (C22×C28).307C22, (C22×C14).132C23, C7⋊1(C22.35C24), (C4×Dic7).194C22, (C2×Dic14).229C22, C14.27(C2×C4○D4), C2.29(C2×C4○D28), (C7×C4⋊C4).303C22, (C2×C4).269(C22×D7), (C7×C42⋊C2).13C2, (C7×C22⋊C4).111C22, SmallGroup(448,971)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.89D14
G = < a,b,c,d | a4=b4=1, c14=a2, d2=b2, ab=ba, ac=ca, dad-1=a-1, cbc-1=dbd-1=a2b, dcd-1=b2c13 >
Subgroups: 692 in 192 conjugacy classes, 95 normal (23 characteristic)
C1, C2, C2, C2, C4, C4, 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, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C42⋊C2, C4×Q8, C22⋊Q8, C42.C2, C42⋊2C2, C4⋊Q8, Dic14, C2×Dic7, C2×C28, C2×C28, C2×C28, C22×C14, C22.35C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C22×C28, C4×Dic14, C28⋊2Q8, C28.6Q8, C23.D14, Dic7.Q8, C28.48D4, C7×C42⋊C2, C42.89D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2- 1+4, C22×D7, C22.35C24, C4○D28, C23×D7, C2×C4○D28, D4.10D14, C42.89D14
►On 224 points
Generators in S224
(1 8 15 22)(2 9 16 23)(3 10 17 24)(4 11 18 25)(5 12 19 26)(6 13 20 27)(7 14 21 28)(29 221 43 207)(30 222 44 208)(31 223 45 209)(32 224 46 210)(33 197 47 211)(34 198 48 212)(35 199 49 213)(36 200 50 214)(37 201 51 215)(38 202 52 216)(39 203 53 217)(40 204 54 218)(41 205 55 219)(42 206 56 220)(57 137 71 123)(58 138 72 124)(59 139 73 125)(60 140 74 126)(61 113 75 127)(62 114 76 128)(63 115 77 129)(64 116 78 130)(65 117 79 131)(66 118 80 132)(67 119 81 133)(68 120 82 134)(69 121 83 135)(70 122 84 136)(85 106 99 92)(86 107 100 93)(87 108 101 94)(88 109 102 95)(89 110 103 96)(90 111 104 97)(91 112 105 98)(141 162 155 148)(142 163 156 149)(143 164 157 150)(144 165 158 151)(145 166 159 152)(146 167 160 153)(147 168 161 154)(169 176 183 190)(170 177 184 191)(171 178 185 192)(172 179 186 193)(173 180 187 194)(174 181 188 195)(175 182 189 196)
(1 90 172 158)(2 105 173 145)(3 92 174 160)(4 107 175 147)(5 94 176 162)(6 109 177 149)(7 96 178 164)(8 111 179 151)(9 98 180 166)(10 85 181 153)(11 100 182 168)(12 87 183 155)(13 102 184 142)(14 89 185 157)(15 104 186 144)(16 91 187 159)(17 106 188 146)(18 93 189 161)(19 108 190 148)(20 95 191 163)(21 110 192 150)(22 97 193 165)(23 112 194 152)(24 99 195 167)(25 86 196 154)(26 101 169 141)(27 88 170 156)(28 103 171 143)(29 131 200 58)(30 118 201 73)(31 133 202 60)(32 120 203 75)(33 135 204 62)(34 122 205 77)(35 137 206 64)(36 124 207 79)(37 139 208 66)(38 126 209 81)(39 113 210 68)(40 128 211 83)(41 115 212 70)(42 130 213 57)(43 117 214 72)(44 132 215 59)(45 119 216 74)(46 134 217 61)(47 121 218 76)(48 136 219 63)(49 123 220 78)(50 138 221 65)(51 125 222 80)(52 140 223 67)(53 127 224 82)(54 114 197 69)(55 129 198 84)(56 116 199 71)
(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)
(1 215 172 44)(2 29 173 200)(3 213 174 42)(4 55 175 198)(5 211 176 40)(6 53 177 224)(7 209 178 38)(8 51 179 222)(9 207 180 36)(10 49 181 220)(11 205 182 34)(12 47 183 218)(13 203 184 32)(14 45 185 216)(15 201 186 30)(16 43 187 214)(17 199 188 56)(18 41 189 212)(19 197 190 54)(20 39 191 210)(21 223 192 52)(22 37 193 208)(23 221 194 50)(24 35 195 206)(25 219 196 48)(26 33 169 204)(27 217 170 46)(28 31 171 202)(57 146 130 106)(58 91 131 159)(59 144 132 104)(60 89 133 157)(61 142 134 102)(62 87 135 155)(63 168 136 100)(64 85 137 153)(65 166 138 98)(66 111 139 151)(67 164 140 96)(68 109 113 149)(69 162 114 94)(70 107 115 147)(71 160 116 92)(72 105 117 145)(73 158 118 90)(74 103 119 143)(75 156 120 88)(76 101 121 141)(77 154 122 86)(78 99 123 167)(79 152 124 112)(80 97 125 165)(81 150 126 110)(82 95 127 163)(83 148 128 108)(84 93 129 161)
G:=sub<Sym(224)| (1,8,15,22)(2,9,16,23)(3,10,17,24)(4,11,18,25)(5,12,19,26)(6,13,20,27)(7,14,21,28)(29,221,43,207)(30,222,44,208)(31,223,45,209)(32,224,46,210)(33,197,47,211)(34,198,48,212)(35,199,49,213)(36,200,50,214)(37,201,51,215)(38,202,52,216)(39,203,53,217)(40,204,54,218)(41,205,55,219)(42,206,56,220)(57,137,71,123)(58,138,72,124)(59,139,73,125)(60,140,74,126)(61,113,75,127)(62,114,76,128)(63,115,77,129)(64,116,78,130)(65,117,79,131)(66,118,80,132)(67,119,81,133)(68,120,82,134)(69,121,83,135)(70,122,84,136)(85,106,99,92)(86,107,100,93)(87,108,101,94)(88,109,102,95)(89,110,103,96)(90,111,104,97)(91,112,105,98)(141,162,155,148)(142,163,156,149)(143,164,157,150)(144,165,158,151)(145,166,159,152)(146,167,160,153)(147,168,161,154)(169,176,183,190)(170,177,184,191)(171,178,185,192)(172,179,186,193)(173,180,187,194)(174,181,188,195)(175,182,189,196), (1,90,172,158)(2,105,173,145)(3,92,174,160)(4,107,175,147)(5,94,176,162)(6,109,177,149)(7,96,178,164)(8,111,179,151)(9,98,180,166)(10,85,181,153)(11,100,182,168)(12,87,183,155)(13,102,184,142)(14,89,185,157)(15,104,186,144)(16,91,187,159)(17,106,188,146)(18,93,189,161)(19,108,190,148)(20,95,191,163)(21,110,192,150)(22,97,193,165)(23,112,194,152)(24,99,195,167)(25,86,196,154)(26,101,169,141)(27,88,170,156)(28,103,171,143)(29,131,200,58)(30,118,201,73)(31,133,202,60)(32,120,203,75)(33,135,204,62)(34,122,205,77)(35,137,206,64)(36,124,207,79)(37,139,208,66)(38,126,209,81)(39,113,210,68)(40,128,211,83)(41,115,212,70)(42,130,213,57)(43,117,214,72)(44,132,215,59)(45,119,216,74)(46,134,217,61)(47,121,218,76)(48,136,219,63)(49,123,220,78)(50,138,221,65)(51,125,222,80)(52,140,223,67)(53,127,224,82)(54,114,197,69)(55,129,198,84)(56,116,199,71), (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), (1,215,172,44)(2,29,173,200)(3,213,174,42)(4,55,175,198)(5,211,176,40)(6,53,177,224)(7,209,178,38)(8,51,179,222)(9,207,180,36)(10,49,181,220)(11,205,182,34)(12,47,183,218)(13,203,184,32)(14,45,185,216)(15,201,186,30)(16,43,187,214)(17,199,188,56)(18,41,189,212)(19,197,190,54)(20,39,191,210)(21,223,192,52)(22,37,193,208)(23,221,194,50)(24,35,195,206)(25,219,196,48)(26,33,169,204)(27,217,170,46)(28,31,171,202)(57,146,130,106)(58,91,131,159)(59,144,132,104)(60,89,133,157)(61,142,134,102)(62,87,135,155)(63,168,136,100)(64,85,137,153)(65,166,138,98)(66,111,139,151)(67,164,140,96)(68,109,113,149)(69,162,114,94)(70,107,115,147)(71,160,116,92)(72,105,117,145)(73,158,118,90)(74,103,119,143)(75,156,120,88)(76,101,121,141)(77,154,122,86)(78,99,123,167)(79,152,124,112)(80,97,125,165)(81,150,126,110)(82,95,127,163)(83,148,128,108)(84,93,129,161)>;
G:=Group( (1,8,15,22)(2,9,16,23)(3,10,17,24)(4,11,18,25)(5,12,19,26)(6,13,20,27)(7,14,21,28)(29,221,43,207)(30,222,44,208)(31,223,45,209)(32,224,46,210)(33,197,47,211)(34,198,48,212)(35,199,49,213)(36,200,50,214)(37,201,51,215)(38,202,52,216)(39,203,53,217)(40,204,54,218)(41,205,55,219)(42,206,56,220)(57,137,71,123)(58,138,72,124)(59,139,73,125)(60,140,74,126)(61,113,75,127)(62,114,76,128)(63,115,77,129)(64,116,78,130)(65,117,79,131)(66,118,80,132)(67,119,81,133)(68,120,82,134)(69,121,83,135)(70,122,84,136)(85,106,99,92)(86,107,100,93)(87,108,101,94)(88,109,102,95)(89,110,103,96)(90,111,104,97)(91,112,105,98)(141,162,155,148)(142,163,156,149)(143,164,157,150)(144,165,158,151)(145,166,159,152)(146,167,160,153)(147,168,161,154)(169,176,183,190)(170,177,184,191)(171,178,185,192)(172,179,186,193)(173,180,187,194)(174,181,188,195)(175,182,189,196), (1,90,172,158)(2,105,173,145)(3,92,174,160)(4,107,175,147)(5,94,176,162)(6,109,177,149)(7,96,178,164)(8,111,179,151)(9,98,180,166)(10,85,181,153)(11,100,182,168)(12,87,183,155)(13,102,184,142)(14,89,185,157)(15,104,186,144)(16,91,187,159)(17,106,188,146)(18,93,189,161)(19,108,190,148)(20,95,191,163)(21,110,192,150)(22,97,193,165)(23,112,194,152)(24,99,195,167)(25,86,196,154)(26,101,169,141)(27,88,170,156)(28,103,171,143)(29,131,200,58)(30,118,201,73)(31,133,202,60)(32,120,203,75)(33,135,204,62)(34,122,205,77)(35,137,206,64)(36,124,207,79)(37,139,208,66)(38,126,209,81)(39,113,210,68)(40,128,211,83)(41,115,212,70)(42,130,213,57)(43,117,214,72)(44,132,215,59)(45,119,216,74)(46,134,217,61)(47,121,218,76)(48,136,219,63)(49,123,220,78)(50,138,221,65)(51,125,222,80)(52,140,223,67)(53,127,224,82)(54,114,197,69)(55,129,198,84)(56,116,199,71), (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), (1,215,172,44)(2,29,173,200)(3,213,174,42)(4,55,175,198)(5,211,176,40)(6,53,177,224)(7,209,178,38)(8,51,179,222)(9,207,180,36)(10,49,181,220)(11,205,182,34)(12,47,183,218)(13,203,184,32)(14,45,185,216)(15,201,186,30)(16,43,187,214)(17,199,188,56)(18,41,189,212)(19,197,190,54)(20,39,191,210)(21,223,192,52)(22,37,193,208)(23,221,194,50)(24,35,195,206)(25,219,196,48)(26,33,169,204)(27,217,170,46)(28,31,171,202)(57,146,130,106)(58,91,131,159)(59,144,132,104)(60,89,133,157)(61,142,134,102)(62,87,135,155)(63,168,136,100)(64,85,137,153)(65,166,138,98)(66,111,139,151)(67,164,140,96)(68,109,113,149)(69,162,114,94)(70,107,115,147)(71,160,116,92)(72,105,117,145)(73,158,118,90)(74,103,119,143)(75,156,120,88)(76,101,121,141)(77,154,122,86)(78,99,123,167)(79,152,124,112)(80,97,125,165)(81,150,126,110)(82,95,127,163)(83,148,128,108)(84,93,129,161) );
G=PermutationGroup([[(1,8,15,22),(2,9,16,23),(3,10,17,24),(4,11,18,25),(5,12,19,26),(6,13,20,27),(7,14,21,28),(29,221,43,207),(30,222,44,208),(31,223,45,209),(32,224,46,210),(33,197,47,211),(34,198,48,212),(35,199,49,213),(36,200,50,214),(37,201,51,215),(38,202,52,216),(39,203,53,217),(40,204,54,218),(41,205,55,219),(42,206,56,220),(57,137,71,123),(58,138,72,124),(59,139,73,125),(60,140,74,126),(61,113,75,127),(62,114,76,128),(63,115,77,129),(64,116,78,130),(65,117,79,131),(66,118,80,132),(67,119,81,133),(68,120,82,134),(69,121,83,135),(70,122,84,136),(85,106,99,92),(86,107,100,93),(87,108,101,94),(88,109,102,95),(89,110,103,96),(90,111,104,97),(91,112,105,98),(141,162,155,148),(142,163,156,149),(143,164,157,150),(144,165,158,151),(145,166,159,152),(146,167,160,153),(147,168,161,154),(169,176,183,190),(170,177,184,191),(171,178,185,192),(172,179,186,193),(173,180,187,194),(174,181,188,195),(175,182,189,196)], [(1,90,172,158),(2,105,173,145),(3,92,174,160),(4,107,175,147),(5,94,176,162),(6,109,177,149),(7,96,178,164),(8,111,179,151),(9,98,180,166),(10,85,181,153),(11,100,182,168),(12,87,183,155),(13,102,184,142),(14,89,185,157),(15,104,186,144),(16,91,187,159),(17,106,188,146),(18,93,189,161),(19,108,190,148),(20,95,191,163),(21,110,192,150),(22,97,193,165),(23,112,194,152),(24,99,195,167),(25,86,196,154),(26,101,169,141),(27,88,170,156),(28,103,171,143),(29,131,200,58),(30,118,201,73),(31,133,202,60),(32,120,203,75),(33,135,204,62),(34,122,205,77),(35,137,206,64),(36,124,207,79),(37,139,208,66),(38,126,209,81),(39,113,210,68),(40,128,211,83),(41,115,212,70),(42,130,213,57),(43,117,214,72),(44,132,215,59),(45,119,216,74),(46,134,217,61),(47,121,218,76),(48,136,219,63),(49,123,220,78),(50,138,221,65),(51,125,222,80),(52,140,223,67),(53,127,224,82),(54,114,197,69),(55,129,198,84),(56,116,199,71)], [(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)], [(1,215,172,44),(2,29,173,200),(3,213,174,42),(4,55,175,198),(5,211,176,40),(6,53,177,224),(7,209,178,38),(8,51,179,222),(9,207,180,36),(10,49,181,220),(11,205,182,34),(12,47,183,218),(13,203,184,32),(14,45,185,216),(15,201,186,30),(16,43,187,214),(17,199,188,56),(18,41,189,212),(19,197,190,54),(20,39,191,210),(21,223,192,52),(22,37,193,208),(23,221,194,50),(24,35,195,206),(25,219,196,48),(26,33,169,204),(27,217,170,46),(28,31,171,202),(57,146,130,106),(58,91,131,159),(59,144,132,104),(60,89,133,157),(61,142,134,102),(62,87,135,155),(63,168,136,100),(64,85,137,153),(65,166,138,98),(66,111,139,151),(67,164,140,96),(68,109,113,149),(69,162,114,94),(70,107,115,147),(71,160,116,92),(72,105,117,145),(73,158,118,90),(74,103,119,143),(75,156,120,88),(76,101,121,141),(77,154,122,86),(78,99,123,167),(79,152,124,112),(80,97,125,165),(81,150,126,110),(82,95,127,163),(83,148,128,108),(84,93,129,161)]])
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | ··· | 4F | 4G | 4H | 4I | 4J | ··· | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| order | 1 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 2 | ··· | 2 | 4 | 4 | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | D14 | C4○D28 | 2- 1+4 | D4.10D14 |
| kernel | C42.89D14 | C4×Dic14 | C28⋊2Q8 | C28.6Q8 | C23.D14 | Dic7.Q8 | C28.48D4 | C7×C42⋊C2 | C42⋊C2 | C28 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C4 | C14 | C2 |
| # reps | 1 | 2 | 1 | 1 | 4 | 4 | 2 | 1 | 3 | 4 | 6 | 6 | 6 | 3 | 24 | 2 | 12 |
Matrix representation of C42.89D14 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 18 | 0 | 0 |
| 0 | 0 | 5 | 24 | 0 | 0 |
| 0 | 0 | 11 | 0 | 2 | 18 |
| 0 | 0 | 7 | 18 | 11 | 27 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 5 | 1 |
| 0 | 0 | 26 | 1 | 3 | 3 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 1 | 0 | 5 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 3 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 12 | 0 | 0 |
| 0 | 0 | 13 | 22 | 0 | 0 |
| 0 | 0 | 24 | 17 | 12 | 17 |
| 0 | 0 | 3 | 19 | 12 | 5 |
| 25 | 7 | 0 | 0 | 0 | 0 |
| 10 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 7 | 20 | 15 |
| 0 | 0 | 11 | 6 | 4 | 21 |
| 0 | 0 | 20 | 12 | 5 | 27 |
| 0 | 0 | 22 | 20 | 4 | 10 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,5,5,11,7,0,0,18,24,0,18,0,0,0,0,2,11,0,0,0,0,18,27],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,0,26,0,1,0,0,0,1,0,0,0,0,5,3,28,5,0,0,1,3,0,0],[28,3,0,0,0,0,0,1,0,0,0,0,0,0,19,13,24,3,0,0,12,22,17,19,0,0,0,0,12,12,0,0,0,0,17,5],[25,10,0,0,0,0,7,4,0,0,0,0,0,0,8,11,20,22,0,0,7,6,12,20,0,0,20,4,5,4,0,0,15,21,27,10] >;
C42.89D14 in GAP, Magma, Sage, TeX
C_4^2._{89}D_{14} % in TeX
G:=Group("C4^2.89D14"); // GroupNames label
G:=SmallGroup(448,971);
// by ID
G=gap.SmallGroup(448,971);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,477,232,100,675,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=a^2,d^2=b^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=b^2*c^13>;
// generators/relations