metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14⋊1Q16, C7⋊C8.28D4, C4⋊C4.29D14, Q8⋊C4⋊3D7, C4.168(D4×D7), C2.11(D7×Q16), (C2×C8).211D14, C28.126(C2×D4), C7⋊1(C8.18D4), (C2×Q8).19D14, C14.19(C2×Q16), C14.49(C4○D8), C28.21(C4○D4), C4.34(C4○D28), C28.Q8⋊11C2, D14⋊2Q8.2C2, D14⋊3Q8.3C2, (C2×Dic7).95D4, (C22×D7).51D4, C22.203(D4×D7), C28.44D4⋊24C2, C14.25(C4⋊D4), (C2×C28).253C23, (C2×C56).202C22, C4⋊Dic7.97C22, (Q8×C14).36C22, C2.28(D14⋊D4), C2.18(SD16⋊3D7), (C2×Dic14).73C22, (D7×C2×C8).12C2, (C2×C7⋊Q16)⋊5C2, (C7×Q8⋊C4)⋊24C2, (C2×C14).266(C2×D4), (C7×C4⋊C4).54C22, (C2×C7⋊C8).221C22, (C2×C4×D7).229C22, (C2×C4).360(C22×D7), SmallGroup(448,347)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14⋊Q16
G = < a,b,c,d | a14=b2=c8=1, d2=c4, bab=cac-1=a-1, ad=da, cbc-1=a12b, dbd-1=a7b, dcd-1=c-1 >
Subgroups: 564 in 114 conjugacy classes, 41 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, Q8, C23, D7, C14, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, Q16, C22×C4, C2×Q8, C2×Q8, Dic7, C28, C28, D14, D14, C2×C14, Q8⋊C4, Q8⋊C4, C2.D8, C22⋊Q8, C22×C8, C2×Q16, C7⋊C8, C56, Dic14, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C8.18D4, C8×D7, C2×C7⋊C8, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C7⋊Q16, C7×C4⋊C4, C2×C56, C2×Dic14, C2×C4×D7, Q8×C14, C28.Q8, C28.44D4, C7×Q8⋊C4, D14⋊2Q8, D7×C2×C8, C2×C7⋊Q16, D14⋊3Q8, D14⋊Q16
Quotients: C1, C2, C22, D4, C23, D7, Q16, C2×D4, C4○D4, D14, C4⋊D4, C2×Q16, C4○D8, C22×D7, C8.18D4, C4○D28, D4×D7, D14⋊D4, SD16⋊3D7, D7×Q16, D14⋊Q16
►On 224 points
Generators in S224
(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 39)(2 38)(3 37)(4 36)(5 35)(6 34)(7 33)(8 32)(9 31)(10 30)(11 29)(12 42)(13 41)(14 40)(15 72)(16 71)(17 84)(18 83)(19 82)(20 81)(21 80)(22 79)(23 78)(24 77)(25 76)(26 75)(27 74)(28 73)(43 121)(44 120)(45 119)(46 118)(47 117)(48 116)(49 115)(50 114)(51 113)(52 126)(53 125)(54 124)(55 123)(56 122)(57 153)(58 152)(59 151)(60 150)(61 149)(62 148)(63 147)(64 146)(65 145)(66 144)(67 143)(68 142)(69 141)(70 154)(85 185)(86 184)(87 183)(88 196)(89 195)(90 194)(91 193)(92 192)(93 191)(94 190)(95 189)(96 188)(97 187)(98 186)(99 172)(100 171)(101 170)(102 169)(103 182)(104 181)(105 180)(106 179)(107 178)(108 177)(109 176)(110 175)(111 174)(112 173)(127 166)(128 165)(129 164)(130 163)(131 162)(132 161)(133 160)(134 159)(135 158)(136 157)(137 156)(138 155)(139 168)(140 167)(197 219)(198 218)(199 217)(200 216)(201 215)(202 214)(203 213)(204 212)(205 211)(206 224)(207 223)(208 222)(209 221)(210 220)
(1 128 113 78 40 166 52 24)(2 127 114 77 41 165 53 23)(3 140 115 76 42 164 54 22)(4 139 116 75 29 163 55 21)(5 138 117 74 30 162 56 20)(6 137 118 73 31 161 43 19)(7 136 119 72 32 160 44 18)(8 135 120 71 33 159 45 17)(9 134 121 84 34 158 46 16)(10 133 122 83 35 157 47 15)(11 132 123 82 36 156 48 28)(12 131 124 81 37 155 49 27)(13 130 125 80 38 168 50 26)(14 129 126 79 39 167 51 25)(57 107 220 98 141 178 198 186)(58 106 221 97 142 177 199 185)(59 105 222 96 143 176 200 184)(60 104 223 95 144 175 201 183)(61 103 224 94 145 174 202 196)(62 102 211 93 146 173 203 195)(63 101 212 92 147 172 204 194)(64 100 213 91 148 171 205 193)(65 99 214 90 149 170 206 192)(66 112 215 89 150 169 207 191)(67 111 216 88 151 182 208 190)(68 110 217 87 152 181 209 189)(69 109 218 86 153 180 210 188)(70 108 219 85 154 179 197 187)
(1 104 40 175)(2 105 41 176)(3 106 42 177)(4 107 29 178)(5 108 30 179)(6 109 31 180)(7 110 32 181)(8 111 33 182)(9 112 34 169)(10 99 35 170)(11 100 36 171)(12 101 37 172)(13 102 38 173)(14 103 39 174)(15 214 83 206)(16 215 84 207)(17 216 71 208)(18 217 72 209)(19 218 73 210)(20 219 74 197)(21 220 75 198)(22 221 76 199)(23 222 77 200)(24 223 78 201)(25 224 79 202)(26 211 80 203)(27 212 81 204)(28 213 82 205)(43 86 118 188)(44 87 119 189)(45 88 120 190)(46 89 121 191)(47 90 122 192)(48 91 123 193)(49 92 124 194)(50 93 125 195)(51 94 126 196)(52 95 113 183)(53 96 114 184)(54 97 115 185)(55 98 116 186)(56 85 117 187)(57 163 141 139)(58 164 142 140)(59 165 143 127)(60 166 144 128)(61 167 145 129)(62 168 146 130)(63 155 147 131)(64 156 148 132)(65 157 149 133)(66 158 150 134)(67 159 151 135)(68 160 152 136)(69 161 153 137)(70 162 154 138)
G:=sub<Sym(224)| (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), (1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,42)(13,41)(14,40)(15,72)(16,71)(17,84)(18,83)(19,82)(20,81)(21,80)(22,79)(23,78)(24,77)(25,76)(26,75)(27,74)(28,73)(43,121)(44,120)(45,119)(46,118)(47,117)(48,116)(49,115)(50,114)(51,113)(52,126)(53,125)(54,124)(55,123)(56,122)(57,153)(58,152)(59,151)(60,150)(61,149)(62,148)(63,147)(64,146)(65,145)(66,144)(67,143)(68,142)(69,141)(70,154)(85,185)(86,184)(87,183)(88,196)(89,195)(90,194)(91,193)(92,192)(93,191)(94,190)(95,189)(96,188)(97,187)(98,186)(99,172)(100,171)(101,170)(102,169)(103,182)(104,181)(105,180)(106,179)(107,178)(108,177)(109,176)(110,175)(111,174)(112,173)(127,166)(128,165)(129,164)(130,163)(131,162)(132,161)(133,160)(134,159)(135,158)(136,157)(137,156)(138,155)(139,168)(140,167)(197,219)(198,218)(199,217)(200,216)(201,215)(202,214)(203,213)(204,212)(205,211)(206,224)(207,223)(208,222)(209,221)(210,220), (1,128,113,78,40,166,52,24)(2,127,114,77,41,165,53,23)(3,140,115,76,42,164,54,22)(4,139,116,75,29,163,55,21)(5,138,117,74,30,162,56,20)(6,137,118,73,31,161,43,19)(7,136,119,72,32,160,44,18)(8,135,120,71,33,159,45,17)(9,134,121,84,34,158,46,16)(10,133,122,83,35,157,47,15)(11,132,123,82,36,156,48,28)(12,131,124,81,37,155,49,27)(13,130,125,80,38,168,50,26)(14,129,126,79,39,167,51,25)(57,107,220,98,141,178,198,186)(58,106,221,97,142,177,199,185)(59,105,222,96,143,176,200,184)(60,104,223,95,144,175,201,183)(61,103,224,94,145,174,202,196)(62,102,211,93,146,173,203,195)(63,101,212,92,147,172,204,194)(64,100,213,91,148,171,205,193)(65,99,214,90,149,170,206,192)(66,112,215,89,150,169,207,191)(67,111,216,88,151,182,208,190)(68,110,217,87,152,181,209,189)(69,109,218,86,153,180,210,188)(70,108,219,85,154,179,197,187), (1,104,40,175)(2,105,41,176)(3,106,42,177)(4,107,29,178)(5,108,30,179)(6,109,31,180)(7,110,32,181)(8,111,33,182)(9,112,34,169)(10,99,35,170)(11,100,36,171)(12,101,37,172)(13,102,38,173)(14,103,39,174)(15,214,83,206)(16,215,84,207)(17,216,71,208)(18,217,72,209)(19,218,73,210)(20,219,74,197)(21,220,75,198)(22,221,76,199)(23,222,77,200)(24,223,78,201)(25,224,79,202)(26,211,80,203)(27,212,81,204)(28,213,82,205)(43,86,118,188)(44,87,119,189)(45,88,120,190)(46,89,121,191)(47,90,122,192)(48,91,123,193)(49,92,124,194)(50,93,125,195)(51,94,126,196)(52,95,113,183)(53,96,114,184)(54,97,115,185)(55,98,116,186)(56,85,117,187)(57,163,141,139)(58,164,142,140)(59,165,143,127)(60,166,144,128)(61,167,145,129)(62,168,146,130)(63,155,147,131)(64,156,148,132)(65,157,149,133)(66,158,150,134)(67,159,151,135)(68,160,152,136)(69,161,153,137)(70,162,154,138)>;
G:=Group( (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), (1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,42)(13,41)(14,40)(15,72)(16,71)(17,84)(18,83)(19,82)(20,81)(21,80)(22,79)(23,78)(24,77)(25,76)(26,75)(27,74)(28,73)(43,121)(44,120)(45,119)(46,118)(47,117)(48,116)(49,115)(50,114)(51,113)(52,126)(53,125)(54,124)(55,123)(56,122)(57,153)(58,152)(59,151)(60,150)(61,149)(62,148)(63,147)(64,146)(65,145)(66,144)(67,143)(68,142)(69,141)(70,154)(85,185)(86,184)(87,183)(88,196)(89,195)(90,194)(91,193)(92,192)(93,191)(94,190)(95,189)(96,188)(97,187)(98,186)(99,172)(100,171)(101,170)(102,169)(103,182)(104,181)(105,180)(106,179)(107,178)(108,177)(109,176)(110,175)(111,174)(112,173)(127,166)(128,165)(129,164)(130,163)(131,162)(132,161)(133,160)(134,159)(135,158)(136,157)(137,156)(138,155)(139,168)(140,167)(197,219)(198,218)(199,217)(200,216)(201,215)(202,214)(203,213)(204,212)(205,211)(206,224)(207,223)(208,222)(209,221)(210,220), (1,128,113,78,40,166,52,24)(2,127,114,77,41,165,53,23)(3,140,115,76,42,164,54,22)(4,139,116,75,29,163,55,21)(5,138,117,74,30,162,56,20)(6,137,118,73,31,161,43,19)(7,136,119,72,32,160,44,18)(8,135,120,71,33,159,45,17)(9,134,121,84,34,158,46,16)(10,133,122,83,35,157,47,15)(11,132,123,82,36,156,48,28)(12,131,124,81,37,155,49,27)(13,130,125,80,38,168,50,26)(14,129,126,79,39,167,51,25)(57,107,220,98,141,178,198,186)(58,106,221,97,142,177,199,185)(59,105,222,96,143,176,200,184)(60,104,223,95,144,175,201,183)(61,103,224,94,145,174,202,196)(62,102,211,93,146,173,203,195)(63,101,212,92,147,172,204,194)(64,100,213,91,148,171,205,193)(65,99,214,90,149,170,206,192)(66,112,215,89,150,169,207,191)(67,111,216,88,151,182,208,190)(68,110,217,87,152,181,209,189)(69,109,218,86,153,180,210,188)(70,108,219,85,154,179,197,187), (1,104,40,175)(2,105,41,176)(3,106,42,177)(4,107,29,178)(5,108,30,179)(6,109,31,180)(7,110,32,181)(8,111,33,182)(9,112,34,169)(10,99,35,170)(11,100,36,171)(12,101,37,172)(13,102,38,173)(14,103,39,174)(15,214,83,206)(16,215,84,207)(17,216,71,208)(18,217,72,209)(19,218,73,210)(20,219,74,197)(21,220,75,198)(22,221,76,199)(23,222,77,200)(24,223,78,201)(25,224,79,202)(26,211,80,203)(27,212,81,204)(28,213,82,205)(43,86,118,188)(44,87,119,189)(45,88,120,190)(46,89,121,191)(47,90,122,192)(48,91,123,193)(49,92,124,194)(50,93,125,195)(51,94,126,196)(52,95,113,183)(53,96,114,184)(54,97,115,185)(55,98,116,186)(56,85,117,187)(57,163,141,139)(58,164,142,140)(59,165,143,127)(60,166,144,128)(61,167,145,129)(62,168,146,130)(63,155,147,131)(64,156,148,132)(65,157,149,133)(66,158,150,134)(67,159,151,135)(68,160,152,136)(69,161,153,137)(70,162,154,138) );
G=PermutationGroup([[(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)], [(1,39),(2,38),(3,37),(4,36),(5,35),(6,34),(7,33),(8,32),(9,31),(10,30),(11,29),(12,42),(13,41),(14,40),(15,72),(16,71),(17,84),(18,83),(19,82),(20,81),(21,80),(22,79),(23,78),(24,77),(25,76),(26,75),(27,74),(28,73),(43,121),(44,120),(45,119),(46,118),(47,117),(48,116),(49,115),(50,114),(51,113),(52,126),(53,125),(54,124),(55,123),(56,122),(57,153),(58,152),(59,151),(60,150),(61,149),(62,148),(63,147),(64,146),(65,145),(66,144),(67,143),(68,142),(69,141),(70,154),(85,185),(86,184),(87,183),(88,196),(89,195),(90,194),(91,193),(92,192),(93,191),(94,190),(95,189),(96,188),(97,187),(98,186),(99,172),(100,171),(101,170),(102,169),(103,182),(104,181),(105,180),(106,179),(107,178),(108,177),(109,176),(110,175),(111,174),(112,173),(127,166),(128,165),(129,164),(130,163),(131,162),(132,161),(133,160),(134,159),(135,158),(136,157),(137,156),(138,155),(139,168),(140,167),(197,219),(198,218),(199,217),(200,216),(201,215),(202,214),(203,213),(204,212),(205,211),(206,224),(207,223),(208,222),(209,221),(210,220)], [(1,128,113,78,40,166,52,24),(2,127,114,77,41,165,53,23),(3,140,115,76,42,164,54,22),(4,139,116,75,29,163,55,21),(5,138,117,74,30,162,56,20),(6,137,118,73,31,161,43,19),(7,136,119,72,32,160,44,18),(8,135,120,71,33,159,45,17),(9,134,121,84,34,158,46,16),(10,133,122,83,35,157,47,15),(11,132,123,82,36,156,48,28),(12,131,124,81,37,155,49,27),(13,130,125,80,38,168,50,26),(14,129,126,79,39,167,51,25),(57,107,220,98,141,178,198,186),(58,106,221,97,142,177,199,185),(59,105,222,96,143,176,200,184),(60,104,223,95,144,175,201,183),(61,103,224,94,145,174,202,196),(62,102,211,93,146,173,203,195),(63,101,212,92,147,172,204,194),(64,100,213,91,148,171,205,193),(65,99,214,90,149,170,206,192),(66,112,215,89,150,169,207,191),(67,111,216,88,151,182,208,190),(68,110,217,87,152,181,209,189),(69,109,218,86,153,180,210,188),(70,108,219,85,154,179,197,187)], [(1,104,40,175),(2,105,41,176),(3,106,42,177),(4,107,29,178),(5,108,30,179),(6,109,31,180),(7,110,32,181),(8,111,33,182),(9,112,34,169),(10,99,35,170),(11,100,36,171),(12,101,37,172),(13,102,38,173),(14,103,39,174),(15,214,83,206),(16,215,84,207),(17,216,71,208),(18,217,72,209),(19,218,73,210),(20,219,74,197),(21,220,75,198),(22,221,76,199),(23,222,77,200),(24,223,78,201),(25,224,79,202),(26,211,80,203),(27,212,81,204),(28,213,82,205),(43,86,118,188),(44,87,119,189),(45,88,120,190),(46,89,121,191),(47,90,122,192),(48,91,123,193),(49,92,124,194),(50,93,125,195),(51,94,126,196),(52,95,113,183),(53,96,114,184),(54,97,115,185),(55,98,116,186),(56,85,117,187),(57,163,141,139),(58,164,142,140),(59,165,143,127),(60,166,144,128),(61,167,145,129),(62,168,146,130),(63,155,147,131),(64,156,148,132),(65,157,149,133),(66,158,150,134),(67,159,151,135),(68,160,152,136),(69,161,153,137),(70,162,154,138)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 14A | ··· | 14I | 28A | ··· | 28F | 28G | ··· | 28R | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 2 | 2 | 8 | 8 | 14 | 14 | 56 | 56 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 14 | 14 | 14 | 14 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | + | + | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D7 | C4○D4 | Q16 | D14 | D14 | D14 | C4○D8 | C4○D28 | D4×D7 | D4×D7 | SD16⋊3D7 | D7×Q16 |
| kernel | D14⋊Q16 | C28.Q8 | C28.44D4 | C7×Q8⋊C4 | D14⋊2Q8 | D7×C2×C8 | C2×C7⋊Q16 | D14⋊3Q8 | C7⋊C8 | C2×Dic7 | C22×D7 | Q8⋊C4 | C28 | D14 | C4⋊C4 | C2×C8 | C2×Q8 | C14 | C4 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 3 | 2 | 4 | 3 | 3 | 3 | 4 | 12 | 3 | 3 | 6 | 6 |
Matrix representation of D14⋊Q16 ►in GL4(𝔽113) generated by
| 9 | 80 | 0 | 0 |
| 33 | 80 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 80 | 9 | 0 | 0 |
| 80 | 33 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 98 | 91 | 0 | 0 |
| 0 | 15 | 0 | 0 |
| 0 | 0 | 51 | 85 |
| 0 | 0 | 109 | 0 |
| 79 | 5 | 0 | 0 |
| 108 | 34 | 0 | 0 |
| 0 | 0 | 10 | 19 |
| 0 | 0 | 72 | 103 |
G:=sub<GL(4,GF(113))| [9,33,0,0,80,80,0,0,0,0,1,0,0,0,0,1],[80,80,0,0,9,33,0,0,0,0,112,0,0,0,0,112],[98,0,0,0,91,15,0,0,0,0,51,109,0,0,85,0],[79,108,0,0,5,34,0,0,0,0,10,72,0,0,19,103] >;
D14⋊Q16 in GAP, Magma, Sage, TeX
D_{14}\rtimes Q_{16} % in TeX
G:=Group("D14:Q16"); // GroupNames label
G:=SmallGroup(448,347);
// by ID
G=gap.SmallGroup(448,347);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,64,590,555,184,297,136,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^2=c^8=1,d^2=c^4,b*a*b=c*a*c^-1=a^-1,a*d=d*a,c*b*c^-1=a^12*b,d*b*d^-1=a^7*b,d*c*d^-1=c^-1>;
// generators/relations