metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.16D14, C8⋊1(C4×D7), C56⋊1(C2×C4), C8⋊C4⋊1D7, C56⋊C2⋊1C4, (C4×D28).5C2, C56⋊1C4⋊16C2, (C2×C8).53D14, C2.14(C4×D28), C14.11(C4×D4), (C4×Dic14)⋊2C2, Dic14⋊9(C2×C4), D28.14(C2×C4), (C2×C28).236D4, (C2×C4).114D28, C7⋊1(SD16⋊C4), C2.1(C8⋊D14), C14.2(C8⋊C22), (C4×C28).14C22, (C2×C56).54C22, C22.30(C2×D28), C2.D56.15C2, C28.222(C4○D4), C4.106(C4○D28), C28.44D4⋊37C2, C28.105(C22×C4), (C2×C28).731C23, C2.1(C8.D14), C14.3(C8.C22), (C2×D28).189C22, C4⋊Dic7.265C22, (C2×Dic14).208C22, C4.63(C2×C4×D7), (C7×C8⋊C4)⋊2C2, (C2×C56⋊C2).1C2, (C2×C14).114(C2×D4), (C2×C4).675(C22×D7), SmallGroup(448,244)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.16D14
G = < a,b,c,d | a4=b4=1, c14=dbd-1=b-1, d2=b2, ab=ba, cac-1=dad-1=ab2, bc=cb, dcd-1=b-1c13 >
Subgroups: 676 in 120 conjugacy classes, 51 normal (39 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C8, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C42, C22⋊C4, C4⋊C4, C2×C8, SD16, C22×C4, C2×D4, C2×Q8, Dic7, C28, C28, D14, C2×C14, C8⋊C4, D4⋊C4, Q8⋊C4, C2.D8, C4×D4, C4×Q8, C2×SD16, C56, C56, Dic14, Dic14, C4×D7, D28, D28, C2×Dic7, C2×C28, C22×D7, SD16⋊C4, C56⋊C2, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C4×C28, C2×C56, C2×Dic14, C2×C4×D7, C2×D28, C28.44D4, C56⋊1C4, C2.D56, C7×C8⋊C4, C4×Dic14, C4×D28, C2×C56⋊C2, C42.16D14
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22×C4, C2×D4, C4○D4, D14, C4×D4, C8⋊C22, C8.C22, C4×D7, D28, C22×D7, SD16⋊C4, C2×C4×D7, C2×D28, C4○D28, C4×D28, C8⋊D14, C8.D14, C42.16D14
►On 224 points
Generators in S224
(1 59 116 184)(2 88 117 213)(3 61 118 186)(4 90 119 215)(5 63 120 188)(6 92 121 217)(7 65 122 190)(8 94 123 219)(9 67 124 192)(10 96 125 221)(11 69 126 194)(12 98 127 223)(13 71 128 196)(14 100 129 169)(15 73 130 198)(16 102 131 171)(17 75 132 200)(18 104 133 173)(19 77 134 202)(20 106 135 175)(21 79 136 204)(22 108 137 177)(23 81 138 206)(24 110 139 179)(25 83 140 208)(26 112 141 181)(27 85 142 210)(28 58 143 183)(29 87 144 212)(30 60 145 185)(31 89 146 214)(32 62 147 187)(33 91 148 216)(34 64 149 189)(35 93 150 218)(36 66 151 191)(37 95 152 220)(38 68 153 193)(39 97 154 222)(40 70 155 195)(41 99 156 224)(42 72 157 197)(43 101 158 170)(44 74 159 199)(45 103 160 172)(46 76 161 201)(47 105 162 174)(48 78 163 203)(49 107 164 176)(50 80 165 205)(51 109 166 178)(52 82 167 207)(53 111 168 180)(54 84 113 209)(55 57 114 182)(56 86 115 211)
(1 43 29 15)(2 44 30 16)(3 45 31 17)(4 46 32 18)(5 47 33 19)(6 48 34 20)(7 49 35 21)(8 50 36 22)(9 51 37 23)(10 52 38 24)(11 53 39 25)(12 54 40 26)(13 55 41 27)(14 56 42 28)(57 99 85 71)(58 100 86 72)(59 101 87 73)(60 102 88 74)(61 103 89 75)(62 104 90 76)(63 105 91 77)(64 106 92 78)(65 107 93 79)(66 108 94 80)(67 109 95 81)(68 110 96 82)(69 111 97 83)(70 112 98 84)(113 155 141 127)(114 156 142 128)(115 157 143 129)(116 158 144 130)(117 159 145 131)(118 160 146 132)(119 161 147 133)(120 162 148 134)(121 163 149 135)(122 164 150 136)(123 165 151 137)(124 166 152 138)(125 167 153 139)(126 168 154 140)(169 211 197 183)(170 212 198 184)(171 213 199 185)(172 214 200 186)(173 215 201 187)(174 216 202 188)(175 217 203 189)(176 218 204 190)(177 219 205 191)(178 220 206 192)(179 221 207 193)(180 222 208 194)(181 223 209 195)(182 224 210 196)
(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)
(1 157 29 129)(2 128 30 156)(3 155 31 127)(4 126 32 154)(5 153 33 125)(6 124 34 152)(7 151 35 123)(8 122 36 150)(9 149 37 121)(10 120 38 148)(11 147 39 119)(12 118 40 146)(13 145 41 117)(14 116 42 144)(15 143 43 115)(16 114 44 142)(17 141 45 113)(18 168 46 140)(19 139 47 167)(20 166 48 138)(21 137 49 165)(22 164 50 136)(23 135 51 163)(24 162 52 134)(25 133 53 161)(26 160 54 132)(27 131 55 159)(28 158 56 130)(57 171 85 199)(58 198 86 170)(59 169 87 197)(60 196 88 224)(61 223 89 195)(62 194 90 222)(63 221 91 193)(64 192 92 220)(65 219 93 191)(66 190 94 218)(67 217 95 189)(68 188 96 216)(69 215 97 187)(70 186 98 214)(71 213 99 185)(72 184 100 212)(73 211 101 183)(74 182 102 210)(75 209 103 181)(76 180 104 208)(77 207 105 179)(78 178 106 206)(79 205 107 177)(80 176 108 204)(81 203 109 175)(82 174 110 202)(83 201 111 173)(84 172 112 200)
G:=sub<Sym(224)| (1,59,116,184)(2,88,117,213)(3,61,118,186)(4,90,119,215)(5,63,120,188)(6,92,121,217)(7,65,122,190)(8,94,123,219)(9,67,124,192)(10,96,125,221)(11,69,126,194)(12,98,127,223)(13,71,128,196)(14,100,129,169)(15,73,130,198)(16,102,131,171)(17,75,132,200)(18,104,133,173)(19,77,134,202)(20,106,135,175)(21,79,136,204)(22,108,137,177)(23,81,138,206)(24,110,139,179)(25,83,140,208)(26,112,141,181)(27,85,142,210)(28,58,143,183)(29,87,144,212)(30,60,145,185)(31,89,146,214)(32,62,147,187)(33,91,148,216)(34,64,149,189)(35,93,150,218)(36,66,151,191)(37,95,152,220)(38,68,153,193)(39,97,154,222)(40,70,155,195)(41,99,156,224)(42,72,157,197)(43,101,158,170)(44,74,159,199)(45,103,160,172)(46,76,161,201)(47,105,162,174)(48,78,163,203)(49,107,164,176)(50,80,165,205)(51,109,166,178)(52,82,167,207)(53,111,168,180)(54,84,113,209)(55,57,114,182)(56,86,115,211), (1,43,29,15)(2,44,30,16)(3,45,31,17)(4,46,32,18)(5,47,33,19)(6,48,34,20)(7,49,35,21)(8,50,36,22)(9,51,37,23)(10,52,38,24)(11,53,39,25)(12,54,40,26)(13,55,41,27)(14,56,42,28)(57,99,85,71)(58,100,86,72)(59,101,87,73)(60,102,88,74)(61,103,89,75)(62,104,90,76)(63,105,91,77)(64,106,92,78)(65,107,93,79)(66,108,94,80)(67,109,95,81)(68,110,96,82)(69,111,97,83)(70,112,98,84)(113,155,141,127)(114,156,142,128)(115,157,143,129)(116,158,144,130)(117,159,145,131)(118,160,146,132)(119,161,147,133)(120,162,148,134)(121,163,149,135)(122,164,150,136)(123,165,151,137)(124,166,152,138)(125,167,153,139)(126,168,154,140)(169,211,197,183)(170,212,198,184)(171,213,199,185)(172,214,200,186)(173,215,201,187)(174,216,202,188)(175,217,203,189)(176,218,204,190)(177,219,205,191)(178,220,206,192)(179,221,207,193)(180,222,208,194)(181,223,209,195)(182,224,210,196), (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), (1,157,29,129)(2,128,30,156)(3,155,31,127)(4,126,32,154)(5,153,33,125)(6,124,34,152)(7,151,35,123)(8,122,36,150)(9,149,37,121)(10,120,38,148)(11,147,39,119)(12,118,40,146)(13,145,41,117)(14,116,42,144)(15,143,43,115)(16,114,44,142)(17,141,45,113)(18,168,46,140)(19,139,47,167)(20,166,48,138)(21,137,49,165)(22,164,50,136)(23,135,51,163)(24,162,52,134)(25,133,53,161)(26,160,54,132)(27,131,55,159)(28,158,56,130)(57,171,85,199)(58,198,86,170)(59,169,87,197)(60,196,88,224)(61,223,89,195)(62,194,90,222)(63,221,91,193)(64,192,92,220)(65,219,93,191)(66,190,94,218)(67,217,95,189)(68,188,96,216)(69,215,97,187)(70,186,98,214)(71,213,99,185)(72,184,100,212)(73,211,101,183)(74,182,102,210)(75,209,103,181)(76,180,104,208)(77,207,105,179)(78,178,106,206)(79,205,107,177)(80,176,108,204)(81,203,109,175)(82,174,110,202)(83,201,111,173)(84,172,112,200)>;
G:=Group( (1,59,116,184)(2,88,117,213)(3,61,118,186)(4,90,119,215)(5,63,120,188)(6,92,121,217)(7,65,122,190)(8,94,123,219)(9,67,124,192)(10,96,125,221)(11,69,126,194)(12,98,127,223)(13,71,128,196)(14,100,129,169)(15,73,130,198)(16,102,131,171)(17,75,132,200)(18,104,133,173)(19,77,134,202)(20,106,135,175)(21,79,136,204)(22,108,137,177)(23,81,138,206)(24,110,139,179)(25,83,140,208)(26,112,141,181)(27,85,142,210)(28,58,143,183)(29,87,144,212)(30,60,145,185)(31,89,146,214)(32,62,147,187)(33,91,148,216)(34,64,149,189)(35,93,150,218)(36,66,151,191)(37,95,152,220)(38,68,153,193)(39,97,154,222)(40,70,155,195)(41,99,156,224)(42,72,157,197)(43,101,158,170)(44,74,159,199)(45,103,160,172)(46,76,161,201)(47,105,162,174)(48,78,163,203)(49,107,164,176)(50,80,165,205)(51,109,166,178)(52,82,167,207)(53,111,168,180)(54,84,113,209)(55,57,114,182)(56,86,115,211), (1,43,29,15)(2,44,30,16)(3,45,31,17)(4,46,32,18)(5,47,33,19)(6,48,34,20)(7,49,35,21)(8,50,36,22)(9,51,37,23)(10,52,38,24)(11,53,39,25)(12,54,40,26)(13,55,41,27)(14,56,42,28)(57,99,85,71)(58,100,86,72)(59,101,87,73)(60,102,88,74)(61,103,89,75)(62,104,90,76)(63,105,91,77)(64,106,92,78)(65,107,93,79)(66,108,94,80)(67,109,95,81)(68,110,96,82)(69,111,97,83)(70,112,98,84)(113,155,141,127)(114,156,142,128)(115,157,143,129)(116,158,144,130)(117,159,145,131)(118,160,146,132)(119,161,147,133)(120,162,148,134)(121,163,149,135)(122,164,150,136)(123,165,151,137)(124,166,152,138)(125,167,153,139)(126,168,154,140)(169,211,197,183)(170,212,198,184)(171,213,199,185)(172,214,200,186)(173,215,201,187)(174,216,202,188)(175,217,203,189)(176,218,204,190)(177,219,205,191)(178,220,206,192)(179,221,207,193)(180,222,208,194)(181,223,209,195)(182,224,210,196), (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), (1,157,29,129)(2,128,30,156)(3,155,31,127)(4,126,32,154)(5,153,33,125)(6,124,34,152)(7,151,35,123)(8,122,36,150)(9,149,37,121)(10,120,38,148)(11,147,39,119)(12,118,40,146)(13,145,41,117)(14,116,42,144)(15,143,43,115)(16,114,44,142)(17,141,45,113)(18,168,46,140)(19,139,47,167)(20,166,48,138)(21,137,49,165)(22,164,50,136)(23,135,51,163)(24,162,52,134)(25,133,53,161)(26,160,54,132)(27,131,55,159)(28,158,56,130)(57,171,85,199)(58,198,86,170)(59,169,87,197)(60,196,88,224)(61,223,89,195)(62,194,90,222)(63,221,91,193)(64,192,92,220)(65,219,93,191)(66,190,94,218)(67,217,95,189)(68,188,96,216)(69,215,97,187)(70,186,98,214)(71,213,99,185)(72,184,100,212)(73,211,101,183)(74,182,102,210)(75,209,103,181)(76,180,104,208)(77,207,105,179)(78,178,106,206)(79,205,107,177)(80,176,108,204)(81,203,109,175)(82,174,110,202)(83,201,111,173)(84,172,112,200) );
G=PermutationGroup([[(1,59,116,184),(2,88,117,213),(3,61,118,186),(4,90,119,215),(5,63,120,188),(6,92,121,217),(7,65,122,190),(8,94,123,219),(9,67,124,192),(10,96,125,221),(11,69,126,194),(12,98,127,223),(13,71,128,196),(14,100,129,169),(15,73,130,198),(16,102,131,171),(17,75,132,200),(18,104,133,173),(19,77,134,202),(20,106,135,175),(21,79,136,204),(22,108,137,177),(23,81,138,206),(24,110,139,179),(25,83,140,208),(26,112,141,181),(27,85,142,210),(28,58,143,183),(29,87,144,212),(30,60,145,185),(31,89,146,214),(32,62,147,187),(33,91,148,216),(34,64,149,189),(35,93,150,218),(36,66,151,191),(37,95,152,220),(38,68,153,193),(39,97,154,222),(40,70,155,195),(41,99,156,224),(42,72,157,197),(43,101,158,170),(44,74,159,199),(45,103,160,172),(46,76,161,201),(47,105,162,174),(48,78,163,203),(49,107,164,176),(50,80,165,205),(51,109,166,178),(52,82,167,207),(53,111,168,180),(54,84,113,209),(55,57,114,182),(56,86,115,211)], [(1,43,29,15),(2,44,30,16),(3,45,31,17),(4,46,32,18),(5,47,33,19),(6,48,34,20),(7,49,35,21),(8,50,36,22),(9,51,37,23),(10,52,38,24),(11,53,39,25),(12,54,40,26),(13,55,41,27),(14,56,42,28),(57,99,85,71),(58,100,86,72),(59,101,87,73),(60,102,88,74),(61,103,89,75),(62,104,90,76),(63,105,91,77),(64,106,92,78),(65,107,93,79),(66,108,94,80),(67,109,95,81),(68,110,96,82),(69,111,97,83),(70,112,98,84),(113,155,141,127),(114,156,142,128),(115,157,143,129),(116,158,144,130),(117,159,145,131),(118,160,146,132),(119,161,147,133),(120,162,148,134),(121,163,149,135),(122,164,150,136),(123,165,151,137),(124,166,152,138),(125,167,153,139),(126,168,154,140),(169,211,197,183),(170,212,198,184),(171,213,199,185),(172,214,200,186),(173,215,201,187),(174,216,202,188),(175,217,203,189),(176,218,204,190),(177,219,205,191),(178,220,206,192),(179,221,207,193),(180,222,208,194),(181,223,209,195),(182,224,210,196)], [(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)], [(1,157,29,129),(2,128,30,156),(3,155,31,127),(4,126,32,154),(5,153,33,125),(6,124,34,152),(7,151,35,123),(8,122,36,150),(9,149,37,121),(10,120,38,148),(11,147,39,119),(12,118,40,146),(13,145,41,117),(14,116,42,144),(15,143,43,115),(16,114,44,142),(17,141,45,113),(18,168,46,140),(19,139,47,167),(20,166,48,138),(21,137,49,165),(22,164,50,136),(23,135,51,163),(24,162,52,134),(25,133,53,161),(26,160,54,132),(27,131,55,159),(28,158,56,130),(57,171,85,199),(58,198,86,170),(59,169,87,197),(60,196,88,224),(61,223,89,195),(62,194,90,222),(63,221,91,193),(64,192,92,220),(65,219,93,191),(66,190,94,218),(67,217,95,189),(68,188,96,216),(69,215,97,187),(70,186,98,214),(71,213,99,185),(72,184,100,212),(73,211,101,183),(74,182,102,210),(75,209,103,181),(76,180,104,208),(77,207,105,179),(78,178,106,206),(79,205,107,177),(80,176,108,204),(81,203,109,175),(82,174,110,202),(83,201,111,173),(84,172,112,200)]])
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4F | 4G | ··· | 4L | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28X | 56A | ··· | 56X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 2 | ··· | 2 | 28 | ··· | 28 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D7 | C4○D4 | D14 | D14 | C4×D7 | D28 | C4○D28 | C8⋊C22 | C8.C22 | C8⋊D14 | C8.D14 |
| kernel | C42.16D14 | C28.44D4 | C56⋊1C4 | C2.D56 | C7×C8⋊C4 | C4×Dic14 | C4×D28 | C2×C56⋊C2 | C56⋊C2 | C2×C28 | C8⋊C4 | C28 | C42 | C2×C8 | C8 | C2×C4 | C4 | C14 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8 | 2 | 3 | 2 | 3 | 6 | 12 | 12 | 12 | 1 | 1 | 6 | 6 |
Matrix representation of C42.16D14 ►in GL6(𝔽113)
| 98 | 0 | 0 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 | 0 | 0 |
| 0 | 0 | 98 | 0 | 83 | 36 |
| 0 | 0 | 0 | 98 | 55 | 43 |
| 0 | 0 | 0 | 0 | 15 | 0 |
| 0 | 0 | 0 | 0 | 0 | 15 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 46 | 0 | 0 |
| 0 | 0 | 67 | 104 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 46 |
| 0 | 0 | 0 | 0 | 33 | 96 |
| 33 | 10 | 0 | 0 | 0 | 0 |
| 71 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 38 | 24 | 15 | 87 |
| 0 | 0 | 89 | 63 | 38 | 69 |
| 0 | 0 | 3 | 30 | 61 | 89 |
| 0 | 0 | 53 | 45 | 27 | 64 |
| 9 | 24 | 0 | 0 | 0 | 0 |
| 72 | 104 | 0 | 0 | 0 | 0 |
| 0 | 0 | 42 | 81 | 12 | 49 |
| 0 | 0 | 40 | 71 | 103 | 26 |
| 0 | 0 | 35 | 34 | 48 | 75 |
| 0 | 0 | 83 | 77 | 36 | 65 |
G:=sub<GL(6,GF(113))| [98,0,0,0,0,0,0,98,0,0,0,0,0,0,98,0,0,0,0,0,0,98,0,0,0,0,83,55,15,0,0,0,36,43,0,15],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,9,67,0,0,0,0,46,104,0,0,0,0,0,0,17,33,0,0,0,0,46,96],[33,71,0,0,0,0,10,1,0,0,0,0,0,0,38,89,3,53,0,0,24,63,30,45,0,0,15,38,61,27,0,0,87,69,89,64],[9,72,0,0,0,0,24,104,0,0,0,0,0,0,42,40,35,83,0,0,81,71,34,77,0,0,12,103,48,36,0,0,49,26,75,65] >;
C42.16D14 in GAP, Magma, Sage, TeX
C_4^2._{16}D_{14} % in TeX
G:=Group("C4^2.16D14"); // GroupNames label
G:=SmallGroup(448,244);
// by ID
G=gap.SmallGroup(448,244);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,120,387,58,1684,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d*b*d^-1=b^-1,d^2=b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a*b^2,b*c=c*b,d*c*d^-1=b^-1*c^13>;
// generators/relations