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## G = D14⋊2SD16order 448 = 26·7

### 2nd semidirect product of D14 and SD16 acting via SD16/C8=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C28 — D14⋊2SD16
 Chief series C1 — C7 — C14 — C28 — C2×C28 — C2×C4×D7 — D7×C2×C8 — D14⋊2SD16
 Lower central C7 — C14 — C2×C28 — D14⋊2SD16
 Upper central C1 — C22 — C2×C4 — Q8⋊C4

Generators and relations for D142SD16
G = < a,b,c,d | a14=b2=c8=d2=1, bab=cac-1=dad=a-1, cbc-1=a12b, dbd=a5b, dcd=c3 >

Subgroups: 756 in 124 conjugacy classes, 41 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, SD16, C22×C4, C2×D4, C2×Q8, Dic7, C28, C28, D14, D14, C2×C14, D4⋊C4, Q8⋊C4, C4.Q8, C4⋊D4, C22⋊Q8, C22×C8, C2×SD16, C7⋊C8, C56, C4×D7, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C22×D7, C88D4, C8×D7, C2×C7⋊C8, Dic7⋊C4, C4⋊Dic7, D14⋊C4, Q8⋊D7, C7×C4⋊C4, C2×C56, C2×C4×D7, C2×D28, C2×D28, Q8×C14, C4.Dic14, C2.D56, C7×Q8⋊C4, C4⋊D28, D7×C2×C8, C2×Q8⋊D7, D143Q8, D142SD16
Quotients: C1, C2, C22, D4, C23, D7, SD16, C2×D4, C4○D4, D14, C4⋊D4, C2×SD16, C4○D8, C22×D7, C88D4, C4○D28, D4×D7, D14⋊D4, D7×SD16, Q8.D14, D142SD16

Smallest permutation representation of D142SD16
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)
(1 200)(2 199)(3 198)(4 197)(5 210)(6 209)(7 208)(8 207)(9 206)(10 205)(11 204)(12 203)(13 202)(14 201)(15 42)(16 41)(17 40)(18 39)(19 38)(20 37)(21 36)(22 35)(23 34)(24 33)(25 32)(26 31)(27 30)(28 29)(43 156)(44 155)(45 168)(46 167)(47 166)(48 165)(49 164)(50 163)(51 162)(52 161)(53 160)(54 159)(55 158)(56 157)(57 85)(58 98)(59 97)(60 96)(61 95)(62 94)(63 93)(64 92)(65 91)(66 90)(67 89)(68 88)(69 87)(70 86)(71 106)(72 105)(73 104)(74 103)(75 102)(76 101)(77 100)(78 99)(79 112)(80 111)(81 110)(82 109)(83 108)(84 107)(113 138)(114 137)(115 136)(116 135)(117 134)(118 133)(119 132)(120 131)(121 130)(122 129)(123 128)(124 127)(125 140)(126 139)(141 178)(142 177)(143 176)(144 175)(145 174)(146 173)(147 172)(148 171)(149 170)(150 169)(151 182)(152 181)(153 180)(154 179)(183 215)(184 214)(185 213)(186 212)(187 211)(188 224)(189 223)(190 222)(191 221)(192 220)(193 219)(194 218)(195 217)(196 216)
(1 145 62 21 201 175 95 37)(2 144 63 20 202 174 96 36)(3 143 64 19 203 173 97 35)(4 142 65 18 204 172 98 34)(5 141 66 17 205 171 85 33)(6 154 67 16 206 170 86 32)(7 153 68 15 207 169 87 31)(8 152 69 28 208 182 88 30)(9 151 70 27 209 181 89 29)(10 150 57 26 210 180 90 42)(11 149 58 25 197 179 91 41)(12 148 59 24 198 178 92 40)(13 147 60 23 199 177 93 39)(14 146 61 22 200 176 94 38)(43 135 109 183 162 126 74 211)(44 134 110 196 163 125 75 224)(45 133 111 195 164 124 76 223)(46 132 112 194 165 123 77 222)(47 131 99 193 166 122 78 221)(48 130 100 192 167 121 79 220)(49 129 101 191 168 120 80 219)(50 128 102 190 155 119 81 218)(51 127 103 189 156 118 82 217)(52 140 104 188 157 117 83 216)(53 139 105 187 158 116 84 215)(54 138 106 186 159 115 71 214)(55 137 107 185 160 114 72 213)(56 136 108 184 161 113 73 212)
(1 51)(2 50)(3 49)(4 48)(5 47)(6 46)(7 45)(8 44)(9 43)(10 56)(11 55)(12 54)(13 53)(14 52)(15 133)(16 132)(17 131)(18 130)(19 129)(20 128)(21 127)(22 140)(23 139)(24 138)(25 137)(26 136)(27 135)(28 134)(29 126)(30 125)(31 124)(32 123)(33 122)(34 121)(35 120)(36 119)(37 118)(38 117)(39 116)(40 115)(41 114)(42 113)(57 73)(58 72)(59 71)(60 84)(61 83)(62 82)(63 81)(64 80)(65 79)(66 78)(67 77)(68 76)(69 75)(70 74)(85 99)(86 112)(87 111)(88 110)(89 109)(90 108)(91 107)(92 106)(93 105)(94 104)(95 103)(96 102)(97 101)(98 100)(141 193)(142 192)(143 191)(144 190)(145 189)(146 188)(147 187)(148 186)(149 185)(150 184)(151 183)(152 196)(153 195)(154 194)(155 202)(156 201)(157 200)(158 199)(159 198)(160 197)(161 210)(162 209)(163 208)(164 207)(165 206)(166 205)(167 204)(168 203)(169 223)(170 222)(171 221)(172 220)(173 219)(174 218)(175 217)(176 216)(177 215)(178 214)(179 213)(180 212)(181 211)(182 224)

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), (1,200)(2,199)(3,198)(4,197)(5,210)(6,209)(7,208)(8,207)(9,206)(10,205)(11,204)(12,203)(13,202)(14,201)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)(43,156)(44,155)(45,168)(46,167)(47,166)(48,165)(49,164)(50,163)(51,162)(52,161)(53,160)(54,159)(55,158)(56,157)(57,85)(58,98)(59,97)(60,96)(61,95)(62,94)(63,93)(64,92)(65,91)(66,90)(67,89)(68,88)(69,87)(70,86)(71,106)(72,105)(73,104)(74,103)(75,102)(76,101)(77,100)(78,99)(79,112)(80,111)(81,110)(82,109)(83,108)(84,107)(113,138)(114,137)(115,136)(116,135)(117,134)(118,133)(119,132)(120,131)(121,130)(122,129)(123,128)(124,127)(125,140)(126,139)(141,178)(142,177)(143,176)(144,175)(145,174)(146,173)(147,172)(148,171)(149,170)(150,169)(151,182)(152,181)(153,180)(154,179)(183,215)(184,214)(185,213)(186,212)(187,211)(188,224)(189,223)(190,222)(191,221)(192,220)(193,219)(194,218)(195,217)(196,216), (1,145,62,21,201,175,95,37)(2,144,63,20,202,174,96,36)(3,143,64,19,203,173,97,35)(4,142,65,18,204,172,98,34)(5,141,66,17,205,171,85,33)(6,154,67,16,206,170,86,32)(7,153,68,15,207,169,87,31)(8,152,69,28,208,182,88,30)(9,151,70,27,209,181,89,29)(10,150,57,26,210,180,90,42)(11,149,58,25,197,179,91,41)(12,148,59,24,198,178,92,40)(13,147,60,23,199,177,93,39)(14,146,61,22,200,176,94,38)(43,135,109,183,162,126,74,211)(44,134,110,196,163,125,75,224)(45,133,111,195,164,124,76,223)(46,132,112,194,165,123,77,222)(47,131,99,193,166,122,78,221)(48,130,100,192,167,121,79,220)(49,129,101,191,168,120,80,219)(50,128,102,190,155,119,81,218)(51,127,103,189,156,118,82,217)(52,140,104,188,157,117,83,216)(53,139,105,187,158,116,84,215)(54,138,106,186,159,115,71,214)(55,137,107,185,160,114,72,213)(56,136,108,184,161,113,73,212), (1,51)(2,50)(3,49)(4,48)(5,47)(6,46)(7,45)(8,44)(9,43)(10,56)(11,55)(12,54)(13,53)(14,52)(15,133)(16,132)(17,131)(18,130)(19,129)(20,128)(21,127)(22,140)(23,139)(24,138)(25,137)(26,136)(27,135)(28,134)(29,126)(30,125)(31,124)(32,123)(33,122)(34,121)(35,120)(36,119)(37,118)(38,117)(39,116)(40,115)(41,114)(42,113)(57,73)(58,72)(59,71)(60,84)(61,83)(62,82)(63,81)(64,80)(65,79)(66,78)(67,77)(68,76)(69,75)(70,74)(85,99)(86,112)(87,111)(88,110)(89,109)(90,108)(91,107)(92,106)(93,105)(94,104)(95,103)(96,102)(97,101)(98,100)(141,193)(142,192)(143,191)(144,190)(145,189)(146,188)(147,187)(148,186)(149,185)(150,184)(151,183)(152,196)(153,195)(154,194)(155,202)(156,201)(157,200)(158,199)(159,198)(160,197)(161,210)(162,209)(163,208)(164,207)(165,206)(166,205)(167,204)(168,203)(169,223)(170,222)(171,221)(172,220)(173,219)(174,218)(175,217)(176,216)(177,215)(178,214)(179,213)(180,212)(181,211)(182,224)>;

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), (1,200)(2,199)(3,198)(4,197)(5,210)(6,209)(7,208)(8,207)(9,206)(10,205)(11,204)(12,203)(13,202)(14,201)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)(43,156)(44,155)(45,168)(46,167)(47,166)(48,165)(49,164)(50,163)(51,162)(52,161)(53,160)(54,159)(55,158)(56,157)(57,85)(58,98)(59,97)(60,96)(61,95)(62,94)(63,93)(64,92)(65,91)(66,90)(67,89)(68,88)(69,87)(70,86)(71,106)(72,105)(73,104)(74,103)(75,102)(76,101)(77,100)(78,99)(79,112)(80,111)(81,110)(82,109)(83,108)(84,107)(113,138)(114,137)(115,136)(116,135)(117,134)(118,133)(119,132)(120,131)(121,130)(122,129)(123,128)(124,127)(125,140)(126,139)(141,178)(142,177)(143,176)(144,175)(145,174)(146,173)(147,172)(148,171)(149,170)(150,169)(151,182)(152,181)(153,180)(154,179)(183,215)(184,214)(185,213)(186,212)(187,211)(188,224)(189,223)(190,222)(191,221)(192,220)(193,219)(194,218)(195,217)(196,216), (1,145,62,21,201,175,95,37)(2,144,63,20,202,174,96,36)(3,143,64,19,203,173,97,35)(4,142,65,18,204,172,98,34)(5,141,66,17,205,171,85,33)(6,154,67,16,206,170,86,32)(7,153,68,15,207,169,87,31)(8,152,69,28,208,182,88,30)(9,151,70,27,209,181,89,29)(10,150,57,26,210,180,90,42)(11,149,58,25,197,179,91,41)(12,148,59,24,198,178,92,40)(13,147,60,23,199,177,93,39)(14,146,61,22,200,176,94,38)(43,135,109,183,162,126,74,211)(44,134,110,196,163,125,75,224)(45,133,111,195,164,124,76,223)(46,132,112,194,165,123,77,222)(47,131,99,193,166,122,78,221)(48,130,100,192,167,121,79,220)(49,129,101,191,168,120,80,219)(50,128,102,190,155,119,81,218)(51,127,103,189,156,118,82,217)(52,140,104,188,157,117,83,216)(53,139,105,187,158,116,84,215)(54,138,106,186,159,115,71,214)(55,137,107,185,160,114,72,213)(56,136,108,184,161,113,73,212), (1,51)(2,50)(3,49)(4,48)(5,47)(6,46)(7,45)(8,44)(9,43)(10,56)(11,55)(12,54)(13,53)(14,52)(15,133)(16,132)(17,131)(18,130)(19,129)(20,128)(21,127)(22,140)(23,139)(24,138)(25,137)(26,136)(27,135)(28,134)(29,126)(30,125)(31,124)(32,123)(33,122)(34,121)(35,120)(36,119)(37,118)(38,117)(39,116)(40,115)(41,114)(42,113)(57,73)(58,72)(59,71)(60,84)(61,83)(62,82)(63,81)(64,80)(65,79)(66,78)(67,77)(68,76)(69,75)(70,74)(85,99)(86,112)(87,111)(88,110)(89,109)(90,108)(91,107)(92,106)(93,105)(94,104)(95,103)(96,102)(97,101)(98,100)(141,193)(142,192)(143,191)(144,190)(145,189)(146,188)(147,187)(148,186)(149,185)(150,184)(151,183)(152,196)(153,195)(154,194)(155,202)(156,201)(157,200)(158,199)(159,198)(160,197)(161,210)(162,209)(163,208)(164,207)(165,206)(166,205)(167,204)(168,203)(169,223)(170,222)(171,221)(172,220)(173,219)(174,218)(175,217)(176,216)(177,215)(178,214)(179,213)(180,212)(181,211)(182,224) );

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)], [(1,200),(2,199),(3,198),(4,197),(5,210),(6,209),(7,208),(8,207),(9,206),(10,205),(11,204),(12,203),(13,202),(14,201),(15,42),(16,41),(17,40),(18,39),(19,38),(20,37),(21,36),(22,35),(23,34),(24,33),(25,32),(26,31),(27,30),(28,29),(43,156),(44,155),(45,168),(46,167),(47,166),(48,165),(49,164),(50,163),(51,162),(52,161),(53,160),(54,159),(55,158),(56,157),(57,85),(58,98),(59,97),(60,96),(61,95),(62,94),(63,93),(64,92),(65,91),(66,90),(67,89),(68,88),(69,87),(70,86),(71,106),(72,105),(73,104),(74,103),(75,102),(76,101),(77,100),(78,99),(79,112),(80,111),(81,110),(82,109),(83,108),(84,107),(113,138),(114,137),(115,136),(116,135),(117,134),(118,133),(119,132),(120,131),(121,130),(122,129),(123,128),(124,127),(125,140),(126,139),(141,178),(142,177),(143,176),(144,175),(145,174),(146,173),(147,172),(148,171),(149,170),(150,169),(151,182),(152,181),(153,180),(154,179),(183,215),(184,214),(185,213),(186,212),(187,211),(188,224),(189,223),(190,222),(191,221),(192,220),(193,219),(194,218),(195,217),(196,216)], [(1,145,62,21,201,175,95,37),(2,144,63,20,202,174,96,36),(3,143,64,19,203,173,97,35),(4,142,65,18,204,172,98,34),(5,141,66,17,205,171,85,33),(6,154,67,16,206,170,86,32),(7,153,68,15,207,169,87,31),(8,152,69,28,208,182,88,30),(9,151,70,27,209,181,89,29),(10,150,57,26,210,180,90,42),(11,149,58,25,197,179,91,41),(12,148,59,24,198,178,92,40),(13,147,60,23,199,177,93,39),(14,146,61,22,200,176,94,38),(43,135,109,183,162,126,74,211),(44,134,110,196,163,125,75,224),(45,133,111,195,164,124,76,223),(46,132,112,194,165,123,77,222),(47,131,99,193,166,122,78,221),(48,130,100,192,167,121,79,220),(49,129,101,191,168,120,80,219),(50,128,102,190,155,119,81,218),(51,127,103,189,156,118,82,217),(52,140,104,188,157,117,83,216),(53,139,105,187,158,116,84,215),(54,138,106,186,159,115,71,214),(55,137,107,185,160,114,72,213),(56,136,108,184,161,113,73,212)], [(1,51),(2,50),(3,49),(4,48),(5,47),(6,46),(7,45),(8,44),(9,43),(10,56),(11,55),(12,54),(13,53),(14,52),(15,133),(16,132),(17,131),(18,130),(19,129),(20,128),(21,127),(22,140),(23,139),(24,138),(25,137),(26,136),(27,135),(28,134),(29,126),(30,125),(31,124),(32,123),(33,122),(34,121),(35,120),(36,119),(37,118),(38,117),(39,116),(40,115),(41,114),(42,113),(57,73),(58,72),(59,71),(60,84),(61,83),(62,82),(63,81),(64,80),(65,79),(66,78),(67,77),(68,76),(69,75),(70,74),(85,99),(86,112),(87,111),(88,110),(89,109),(90,108),(91,107),(92,106),(93,105),(94,104),(95,103),(96,102),(97,101),(98,100),(141,193),(142,192),(143,191),(144,190),(145,189),(146,188),(147,187),(148,186),(149,185),(150,184),(151,183),(152,196),(153,195),(154,194),(155,202),(156,201),(157,200),(158,199),(159,198),(160,197),(161,210),(162,209),(163,208),(164,207),(165,206),(166,205),(167,204),(168,203),(169,223),(170,222),(171,221),(172,220),(173,219),(174,218),(175,217),(176,216),(177,215),(178,214),(179,213),(180,212),(181,211),(182,224)]])

64 conjugacy classes

 class 1 2A 2B 2C 2D 2E 2F 4A 4B 4C 4D 4E 4F 4G 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 2 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 56 2 2 8 8 14 14 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 SD16 D14 D14 D14 C4○D8 C4○D28 D4×D7 D4×D7 D7×SD16 Q8.D14 kernel D14⋊2SD16 C4.Dic14 C2.D56 C7×Q8⋊C4 C4⋊D28 D7×C2×C8 C2×Q8⋊D7 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 D142SD16 in GL6(𝔽113)

 112 0 0 0 0 0 0 112 0 0 0 0 0 0 112 103 0 0 0 0 42 80 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 112 0 0 0 0 0 32 1 0 0 0 0 0 0 80 112 0 0 0 0 71 33 0 0 0 0 0 0 112 0 0 0 0 0 0 112
,
 112 0 0 0 0 0 0 112 0 0 0 0 0 0 112 103 0 0 0 0 0 1 0 0 0 0 0 0 26 91 0 0 0 0 77 0
,
 102 77 0 0 0 0 41 11 0 0 0 0 0 0 1 10 0 0 0 0 0 112 0 0 0 0 0 0 1 0 0 0 0 0 32 112

G:=sub<GL(6,GF(113))| [112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,42,0,0,0,0,103,80,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[112,32,0,0,0,0,0,1,0,0,0,0,0,0,80,71,0,0,0,0,112,33,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,103,1,0,0,0,0,0,0,26,77,0,0,0,0,91,0],[102,41,0,0,0,0,77,11,0,0,0,0,0,0,1,0,0,0,0,0,10,112,0,0,0,0,0,0,1,32,0,0,0,0,0,112] >;

D142SD16 in GAP, Magma, Sage, TeX

D_{14}\rtimes_2{\rm SD}_{16}
% in TeX

G:=Group("D14:2SD16");
// GroupNames label

G:=SmallGroup(448,341);
// by ID

G=gap.SmallGroup(448,341);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,64,590,219,184,297,136,438,102,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^14=b^2=c^8=d^2=1,b*a*b=c*a*c^-1=d*a*d=a^-1,c*b*c^-1=a^12*b,d*b*d=a^5*b,d*c*d=c^3>;
// generators/relations

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