metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14⋊4Q16, Q8.6D28, Dic14.12D4, C4.6(C2×D28), C4.93(D4×D7), (C7×Q8).1D4, C2.9(D7×Q16), D14⋊C8.2C2, C4⋊C4.25D14, Q8⋊C4⋊4D7, (C2×C8).16D14, (C2×Dic28)⋊6C2, C28.122(C2×D4), C14.17(C2×Q16), C7⋊2(C22⋊Q16), C14.24C22≀C2, C14.Q16⋊12C2, (C2×C56).16C22, D14⋊2Q8.1C2, (C2×Q8).108D14, (C2×Dic7).31D4, (C22×D7).78D4, C22.198(D4×D7), (C2×C28).248C23, (Q8×C14).31C22, C2.27(C22⋊D28), C2.17(SD16⋊D7), C14.35(C8.C22), (C2×Dic14).71C22, (C2×Q8×D7).4C2, (C2×C7⋊Q16)⋊3C2, (C7×Q8⋊C4)⋊4C2, (C2×C7⋊C8).39C22, (C2×C4×D7).21C22, (C2×C14).261(C2×D4), (C7×C4⋊C4).49C22, (C2×C4).355(C22×D7), SmallGroup(448,342)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14⋊4Q16
G = < a,b,c,d | a14=b2=c8=1, d2=c4, bab=cac-1=dad-1=a-1, cbc-1=dbd-1=a5b, dcd-1=c-1 >
Subgroups: 788 in 148 conjugacy classes, 45 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, Q8, 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, C22⋊C8, Q8⋊C4, Q8⋊C4, C22⋊Q8, C2×Q16, C22×Q8, C7⋊C8, C56, Dic14, Dic14, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C7×Q8, C22×D7, C22⋊Q16, Dic28, C2×C7⋊C8, C4⋊Dic7, D14⋊C4, C7⋊Q16, C7×C4⋊C4, C2×C56, C2×Dic14, C2×Dic14, C2×C4×D7, C2×C4×D7, Q8×D7, Q8×C14, C14.Q16, D14⋊C8, C7×Q8⋊C4, D14⋊2Q8, C2×Dic28, C2×C7⋊Q16, C2×Q8×D7, D14⋊4Q16
Quotients: C1, C2, C22, D4, C23, D7, Q16, C2×D4, D14, C22≀C2, C2×Q16, C8.C22, D28, C22×D7, C22⋊Q16, C2×D28, D4×D7, C22⋊D28, SD16⋊D7, D7×Q16, D14⋊4Q16
►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 14)(2 13)(3 12)(4 11)(5 10)(6 9)(7 8)(15 20)(16 19)(17 18)(21 28)(22 27)(23 26)(24 25)(29 37)(30 36)(31 35)(32 34)(38 42)(39 41)(43 53)(44 52)(45 51)(46 50)(47 49)(54 56)(57 59)(60 70)(61 69)(62 68)(63 67)(64 66)(71 77)(72 76)(73 75)(78 84)(79 83)(80 82)(85 89)(86 88)(90 98)(91 97)(92 96)(93 95)(99 109)(100 108)(101 107)(102 106)(103 105)(110 112)(113 116)(114 115)(117 126)(118 125)(119 124)(120 123)(121 122)(127 140)(128 139)(129 138)(130 137)(131 136)(132 135)(133 134)(141 154)(142 153)(143 152)(144 151)(145 150)(146 149)(147 148)(155 164)(156 163)(157 162)(158 161)(159 160)(165 168)(166 167)(169 172)(170 171)(173 182)(174 181)(175 180)(176 179)(177 178)(183 193)(184 192)(185 191)(186 190)(187 189)(194 196)(197 203)(198 202)(199 201)(204 210)(205 209)(206 208)(211 220)(212 219)(213 218)(214 217)(215 216)(221 224)(222 223)
(1 108 141 91 18 185 178 37)(2 107 142 90 19 184 179 36)(3 106 143 89 20 183 180 35)(4 105 144 88 21 196 181 34)(5 104 145 87 22 195 182 33)(6 103 146 86 23 194 169 32)(7 102 147 85 24 193 170 31)(8 101 148 98 25 192 171 30)(9 100 149 97 26 191 172 29)(10 99 150 96 27 190 173 42)(11 112 151 95 28 189 174 41)(12 111 152 94 15 188 175 40)(13 110 153 93 16 187 176 39)(14 109 154 92 17 186 177 38)(43 155 60 218 202 129 76 117)(44 168 61 217 203 128 77 116)(45 167 62 216 204 127 78 115)(46 166 63 215 205 140 79 114)(47 165 64 214 206 139 80 113)(48 164 65 213 207 138 81 126)(49 163 66 212 208 137 82 125)(50 162 67 211 209 136 83 124)(51 161 68 224 210 135 84 123)(52 160 69 223 197 134 71 122)(53 159 70 222 198 133 72 121)(54 158 57 221 199 132 73 120)(55 157 58 220 200 131 74 119)(56 156 59 219 201 130 75 118)
(1 62 18 78)(2 61 19 77)(3 60 20 76)(4 59 21 75)(5 58 22 74)(6 57 23 73)(7 70 24 72)(8 69 25 71)(9 68 26 84)(10 67 27 83)(11 66 28 82)(12 65 15 81)(13 64 16 80)(14 63 17 79)(29 224 97 123)(30 223 98 122)(31 222 85 121)(32 221 86 120)(33 220 87 119)(34 219 88 118)(35 218 89 117)(36 217 90 116)(37 216 91 115)(38 215 92 114)(39 214 93 113)(40 213 94 126)(41 212 95 125)(42 211 96 124)(43 180 202 143)(44 179 203 142)(45 178 204 141)(46 177 205 154)(47 176 206 153)(48 175 207 152)(49 174 208 151)(50 173 209 150)(51 172 210 149)(52 171 197 148)(53 170 198 147)(54 169 199 146)(55 182 200 145)(56 181 201 144)(99 162 190 136)(100 161 191 135)(101 160 192 134)(102 159 193 133)(103 158 194 132)(104 157 195 131)(105 156 196 130)(106 155 183 129)(107 168 184 128)(108 167 185 127)(109 166 186 140)(110 165 187 139)(111 164 188 138)(112 163 189 137)
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), (1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,20)(16,19)(17,18)(21,28)(22,27)(23,26)(24,25)(29,37)(30,36)(31,35)(32,34)(38,42)(39,41)(43,53)(44,52)(45,51)(46,50)(47,49)(54,56)(57,59)(60,70)(61,69)(62,68)(63,67)(64,66)(71,77)(72,76)(73,75)(78,84)(79,83)(80,82)(85,89)(86,88)(90,98)(91,97)(92,96)(93,95)(99,109)(100,108)(101,107)(102,106)(103,105)(110,112)(113,116)(114,115)(117,126)(118,125)(119,124)(120,123)(121,122)(127,140)(128,139)(129,138)(130,137)(131,136)(132,135)(133,134)(141,154)(142,153)(143,152)(144,151)(145,150)(146,149)(147,148)(155,164)(156,163)(157,162)(158,161)(159,160)(165,168)(166,167)(169,172)(170,171)(173,182)(174,181)(175,180)(176,179)(177,178)(183,193)(184,192)(185,191)(186,190)(187,189)(194,196)(197,203)(198,202)(199,201)(204,210)(205,209)(206,208)(211,220)(212,219)(213,218)(214,217)(215,216)(221,224)(222,223), (1,108,141,91,18,185,178,37)(2,107,142,90,19,184,179,36)(3,106,143,89,20,183,180,35)(4,105,144,88,21,196,181,34)(5,104,145,87,22,195,182,33)(6,103,146,86,23,194,169,32)(7,102,147,85,24,193,170,31)(8,101,148,98,25,192,171,30)(9,100,149,97,26,191,172,29)(10,99,150,96,27,190,173,42)(11,112,151,95,28,189,174,41)(12,111,152,94,15,188,175,40)(13,110,153,93,16,187,176,39)(14,109,154,92,17,186,177,38)(43,155,60,218,202,129,76,117)(44,168,61,217,203,128,77,116)(45,167,62,216,204,127,78,115)(46,166,63,215,205,140,79,114)(47,165,64,214,206,139,80,113)(48,164,65,213,207,138,81,126)(49,163,66,212,208,137,82,125)(50,162,67,211,209,136,83,124)(51,161,68,224,210,135,84,123)(52,160,69,223,197,134,71,122)(53,159,70,222,198,133,72,121)(54,158,57,221,199,132,73,120)(55,157,58,220,200,131,74,119)(56,156,59,219,201,130,75,118), (1,62,18,78)(2,61,19,77)(3,60,20,76)(4,59,21,75)(5,58,22,74)(6,57,23,73)(7,70,24,72)(8,69,25,71)(9,68,26,84)(10,67,27,83)(11,66,28,82)(12,65,15,81)(13,64,16,80)(14,63,17,79)(29,224,97,123)(30,223,98,122)(31,222,85,121)(32,221,86,120)(33,220,87,119)(34,219,88,118)(35,218,89,117)(36,217,90,116)(37,216,91,115)(38,215,92,114)(39,214,93,113)(40,213,94,126)(41,212,95,125)(42,211,96,124)(43,180,202,143)(44,179,203,142)(45,178,204,141)(46,177,205,154)(47,176,206,153)(48,175,207,152)(49,174,208,151)(50,173,209,150)(51,172,210,149)(52,171,197,148)(53,170,198,147)(54,169,199,146)(55,182,200,145)(56,181,201,144)(99,162,190,136)(100,161,191,135)(101,160,192,134)(102,159,193,133)(103,158,194,132)(104,157,195,131)(105,156,196,130)(106,155,183,129)(107,168,184,128)(108,167,185,127)(109,166,186,140)(110,165,187,139)(111,164,188,138)(112,163,189,137)>;
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), (1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,20)(16,19)(17,18)(21,28)(22,27)(23,26)(24,25)(29,37)(30,36)(31,35)(32,34)(38,42)(39,41)(43,53)(44,52)(45,51)(46,50)(47,49)(54,56)(57,59)(60,70)(61,69)(62,68)(63,67)(64,66)(71,77)(72,76)(73,75)(78,84)(79,83)(80,82)(85,89)(86,88)(90,98)(91,97)(92,96)(93,95)(99,109)(100,108)(101,107)(102,106)(103,105)(110,112)(113,116)(114,115)(117,126)(118,125)(119,124)(120,123)(121,122)(127,140)(128,139)(129,138)(130,137)(131,136)(132,135)(133,134)(141,154)(142,153)(143,152)(144,151)(145,150)(146,149)(147,148)(155,164)(156,163)(157,162)(158,161)(159,160)(165,168)(166,167)(169,172)(170,171)(173,182)(174,181)(175,180)(176,179)(177,178)(183,193)(184,192)(185,191)(186,190)(187,189)(194,196)(197,203)(198,202)(199,201)(204,210)(205,209)(206,208)(211,220)(212,219)(213,218)(214,217)(215,216)(221,224)(222,223), (1,108,141,91,18,185,178,37)(2,107,142,90,19,184,179,36)(3,106,143,89,20,183,180,35)(4,105,144,88,21,196,181,34)(5,104,145,87,22,195,182,33)(6,103,146,86,23,194,169,32)(7,102,147,85,24,193,170,31)(8,101,148,98,25,192,171,30)(9,100,149,97,26,191,172,29)(10,99,150,96,27,190,173,42)(11,112,151,95,28,189,174,41)(12,111,152,94,15,188,175,40)(13,110,153,93,16,187,176,39)(14,109,154,92,17,186,177,38)(43,155,60,218,202,129,76,117)(44,168,61,217,203,128,77,116)(45,167,62,216,204,127,78,115)(46,166,63,215,205,140,79,114)(47,165,64,214,206,139,80,113)(48,164,65,213,207,138,81,126)(49,163,66,212,208,137,82,125)(50,162,67,211,209,136,83,124)(51,161,68,224,210,135,84,123)(52,160,69,223,197,134,71,122)(53,159,70,222,198,133,72,121)(54,158,57,221,199,132,73,120)(55,157,58,220,200,131,74,119)(56,156,59,219,201,130,75,118), (1,62,18,78)(2,61,19,77)(3,60,20,76)(4,59,21,75)(5,58,22,74)(6,57,23,73)(7,70,24,72)(8,69,25,71)(9,68,26,84)(10,67,27,83)(11,66,28,82)(12,65,15,81)(13,64,16,80)(14,63,17,79)(29,224,97,123)(30,223,98,122)(31,222,85,121)(32,221,86,120)(33,220,87,119)(34,219,88,118)(35,218,89,117)(36,217,90,116)(37,216,91,115)(38,215,92,114)(39,214,93,113)(40,213,94,126)(41,212,95,125)(42,211,96,124)(43,180,202,143)(44,179,203,142)(45,178,204,141)(46,177,205,154)(47,176,206,153)(48,175,207,152)(49,174,208,151)(50,173,209,150)(51,172,210,149)(52,171,197,148)(53,170,198,147)(54,169,199,146)(55,182,200,145)(56,181,201,144)(99,162,190,136)(100,161,191,135)(101,160,192,134)(102,159,193,133)(103,158,194,132)(104,157,195,131)(105,156,196,130)(106,155,183,129)(107,168,184,128)(108,167,185,127)(109,166,186,140)(110,165,187,139)(111,164,188,138)(112,163,189,137) );
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)], [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,20),(16,19),(17,18),(21,28),(22,27),(23,26),(24,25),(29,37),(30,36),(31,35),(32,34),(38,42),(39,41),(43,53),(44,52),(45,51),(46,50),(47,49),(54,56),(57,59),(60,70),(61,69),(62,68),(63,67),(64,66),(71,77),(72,76),(73,75),(78,84),(79,83),(80,82),(85,89),(86,88),(90,98),(91,97),(92,96),(93,95),(99,109),(100,108),(101,107),(102,106),(103,105),(110,112),(113,116),(114,115),(117,126),(118,125),(119,124),(120,123),(121,122),(127,140),(128,139),(129,138),(130,137),(131,136),(132,135),(133,134),(141,154),(142,153),(143,152),(144,151),(145,150),(146,149),(147,148),(155,164),(156,163),(157,162),(158,161),(159,160),(165,168),(166,167),(169,172),(170,171),(173,182),(174,181),(175,180),(176,179),(177,178),(183,193),(184,192),(185,191),(186,190),(187,189),(194,196),(197,203),(198,202),(199,201),(204,210),(205,209),(206,208),(211,220),(212,219),(213,218),(214,217),(215,216),(221,224),(222,223)], [(1,108,141,91,18,185,178,37),(2,107,142,90,19,184,179,36),(3,106,143,89,20,183,180,35),(4,105,144,88,21,196,181,34),(5,104,145,87,22,195,182,33),(6,103,146,86,23,194,169,32),(7,102,147,85,24,193,170,31),(8,101,148,98,25,192,171,30),(9,100,149,97,26,191,172,29),(10,99,150,96,27,190,173,42),(11,112,151,95,28,189,174,41),(12,111,152,94,15,188,175,40),(13,110,153,93,16,187,176,39),(14,109,154,92,17,186,177,38),(43,155,60,218,202,129,76,117),(44,168,61,217,203,128,77,116),(45,167,62,216,204,127,78,115),(46,166,63,215,205,140,79,114),(47,165,64,214,206,139,80,113),(48,164,65,213,207,138,81,126),(49,163,66,212,208,137,82,125),(50,162,67,211,209,136,83,124),(51,161,68,224,210,135,84,123),(52,160,69,223,197,134,71,122),(53,159,70,222,198,133,72,121),(54,158,57,221,199,132,73,120),(55,157,58,220,200,131,74,119),(56,156,59,219,201,130,75,118)], [(1,62,18,78),(2,61,19,77),(3,60,20,76),(4,59,21,75),(5,58,22,74),(6,57,23,73),(7,70,24,72),(8,69,25,71),(9,68,26,84),(10,67,27,83),(11,66,28,82),(12,65,15,81),(13,64,16,80),(14,63,17,79),(29,224,97,123),(30,223,98,122),(31,222,85,121),(32,221,86,120),(33,220,87,119),(34,219,88,118),(35,218,89,117),(36,217,90,116),(37,216,91,115),(38,215,92,114),(39,214,93,113),(40,213,94,126),(41,212,95,125),(42,211,96,124),(43,180,202,143),(44,179,203,142),(45,178,204,141),(46,177,205,154),(47,176,206,153),(48,175,207,152),(49,174,208,151),(50,173,209,150),(51,172,210,149),(52,171,197,148),(53,170,198,147),(54,169,199,146),(55,182,200,145),(56,181,201,144),(99,162,190,136),(100,161,191,135),(101,160,192,134),(102,159,193,133),(103,158,194,132),(104,157,195,131),(105,156,196,130),(106,155,183,129),(107,168,184,128),(108,167,185,127),(109,166,186,140),(110,165,187,139),(111,164,188,138),(112,163,189,137)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 28A | ··· | 28F | 28G | ··· | 28R | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 2 | 2 | 4 | 4 | 8 | 28 | 28 | 28 | 56 | 2 | 2 | 2 | 4 | 4 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | + | + | - | + | + | - | - |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D4 | D7 | Q16 | D14 | D14 | D14 | D28 | C8.C22 | D4×D7 | D4×D7 | SD16⋊D7 | D7×Q16 |
| kernel | D14⋊4Q16 | C14.Q16 | D14⋊C8 | C7×Q8⋊C4 | D14⋊2Q8 | C2×Dic28 | C2×C7⋊Q16 | C2×Q8×D7 | Dic14 | C2×Dic7 | C7×Q8 | C22×D7 | Q8⋊C4 | D14 | C4⋊C4 | C2×C8 | C2×Q8 | Q8 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 2 | 1 | 3 | 4 | 3 | 3 | 3 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of D14⋊4Q16 ►in GL4(𝔽113) generated by
| 10 | 10 | 0 | 0 |
| 103 | 24 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 10 | 10 | 0 | 0 |
| 24 | 103 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 17 | 8 | 0 | 0 |
| 77 | 96 | 0 | 0 |
| 0 | 0 | 0 | 28 |
| 0 | 0 | 4 | 62 |
| 17 | 8 | 0 | 0 |
| 77 | 96 | 0 | 0 |
| 0 | 0 | 29 | 69 |
| 0 | 0 | 14 | 84 |
G:=sub<GL(4,GF(113))| [10,103,0,0,10,24,0,0,0,0,1,0,0,0,0,1],[10,24,0,0,10,103,0,0,0,0,1,0,0,0,0,1],[17,77,0,0,8,96,0,0,0,0,0,4,0,0,28,62],[17,77,0,0,8,96,0,0,0,0,29,14,0,0,69,84] >;
D14⋊4Q16 in GAP, Magma, Sage, TeX
D_{14}\rtimes_4Q_{16} % in TeX
G:=Group("D14:4Q16"); // GroupNames label
G:=SmallGroup(448,342);
// by ID
G=gap.SmallGroup(448,342);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,254,219,226,851,438,102,18822]);
// 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=d*a*d^-1=a^-1,c*b*c^-1=d*b*d^-1=a^5*b,d*c*d^-1=c^-1>;
// generators/relations