direct product, metabelian, nilpotent (class 3), monomial, 2-elementary
Aliases: SD16×C2×C14, C56⋊14C23, C28.79C24, C8⋊3(C22×C14), C4.19(D4×C14), (C22×C8)⋊10C14, (C22×C56)⋊24C2, (C2×C56)⋊52C22, (C2×C28).433D4, C28.326(C2×D4), C4.2(C23×C14), Q8⋊1(C22×C14), (C22×Q8)⋊8C14, (C7×Q8)⋊11C23, C23.61(C7×D4), (Q8×C14)⋊53C22, (C7×D4).34C23, D4.1(C22×C14), C22.66(D4×C14), (C2×C28).972C23, (C22×D4).12C14, (C22×C14).222D4, C14.200(C22×D4), (D4×C14).327C22, (C22×C28).602C22, (Q8×C2×C14)⋊20C2, C2.24(D4×C2×C14), (C2×C8)⋊14(C2×C14), (D4×C2×C14).25C2, (C2×C4).89(C7×D4), (C2×Q8)⋊13(C2×C14), (C2×D4).73(C2×C14), (C2×C14).687(C2×D4), (C2×C4).142(C22×C14), (C22×C4).129(C2×C14), SmallGroup(448,1353)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for SD16×C2×C14
G = < a,b,c,d | a2=b14=c8=d2=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd=c3 >
Subgroups: 498 in 298 conjugacy classes, 178 normal (18 characteristic)
C1, C2, C2, C2, C4, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, D4, Q8, Q8, C23, C23, C14, C14, C14, C2×C8, SD16, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, C24, C28, C28, C28, C2×C14, C2×C14, C22×C8, C2×SD16, C22×D4, C22×Q8, C56, C2×C28, C2×C28, C7×D4, C7×D4, C7×Q8, C7×Q8, C22×C14, C22×C14, C22×SD16, C2×C56, C7×SD16, C22×C28, C22×C28, D4×C14, D4×C14, Q8×C14, Q8×C14, C23×C14, C22×C56, C14×SD16, D4×C2×C14, Q8×C2×C14, SD16×C2×C14
Quotients: C1, C2, C22, C7, D4, C23, C14, SD16, C2×D4, C24, C2×C14, C2×SD16, C22×D4, C7×D4, C22×C14, C22×SD16, C7×SD16, D4×C14, C23×C14, C14×SD16, D4×C2×C14, SD16×C2×C14
►On 224 points
Generators in S224
(1 182)(2 169)(3 170)(4 171)(5 172)(6 173)(7 174)(8 175)(9 176)(10 177)(11 178)(12 179)(13 180)(14 181)(15 51)(16 52)(17 53)(18 54)(19 55)(20 56)(21 43)(22 44)(23 45)(24 46)(25 47)(26 48)(27 49)(28 50)(29 144)(30 145)(31 146)(32 147)(33 148)(34 149)(35 150)(36 151)(37 152)(38 153)(39 154)(40 141)(41 142)(42 143)(57 168)(58 155)(59 156)(60 157)(61 158)(62 159)(63 160)(64 161)(65 162)(66 163)(67 164)(68 165)(69 166)(70 167)(71 97)(72 98)(73 85)(74 86)(75 87)(76 88)(77 89)(78 90)(79 91)(80 92)(81 93)(82 94)(83 95)(84 96)(99 121)(100 122)(101 123)(102 124)(103 125)(104 126)(105 113)(106 114)(107 115)(108 116)(109 117)(110 118)(111 119)(112 120)(127 214)(128 215)(129 216)(130 217)(131 218)(132 219)(133 220)(134 221)(135 222)(136 223)(137 224)(138 211)(139 212)(140 213)(183 203)(184 204)(185 205)(186 206)(187 207)(188 208)(189 209)(190 210)(191 197)(192 198)(193 199)(194 200)(195 201)(196 202)
(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)
(1 110 40 207 97 59 129 52)(2 111 41 208 98 60 130 53)(3 112 42 209 85 61 131 54)(4 99 29 210 86 62 132 55)(5 100 30 197 87 63 133 56)(6 101 31 198 88 64 134 43)(7 102 32 199 89 65 135 44)(8 103 33 200 90 66 136 45)(9 104 34 201 91 67 137 46)(10 105 35 202 92 68 138 47)(11 106 36 203 93 69 139 48)(12 107 37 204 94 70 140 49)(13 108 38 205 95 57 127 50)(14 109 39 206 96 58 128 51)(15 181 117 154 186 84 155 215)(16 182 118 141 187 71 156 216)(17 169 119 142 188 72 157 217)(18 170 120 143 189 73 158 218)(19 171 121 144 190 74 159 219)(20 172 122 145 191 75 160 220)(21 173 123 146 192 76 161 221)(22 174 124 147 193 77 162 222)(23 175 125 148 194 78 163 223)(24 176 126 149 195 79 164 224)(25 177 113 150 196 80 165 211)(26 178 114 151 183 81 166 212)(27 179 115 152 184 82 167 213)(28 180 116 153 185 83 168 214)
(1 8)(2 9)(3 10)(4 11)(5 12)(6 13)(7 14)(15 162)(16 163)(17 164)(18 165)(19 166)(20 167)(21 168)(22 155)(23 156)(24 157)(25 158)(26 159)(27 160)(28 161)(29 139)(30 140)(31 127)(32 128)(33 129)(34 130)(35 131)(36 132)(37 133)(38 134)(39 135)(40 136)(41 137)(42 138)(43 57)(44 58)(45 59)(46 60)(47 61)(48 62)(49 63)(50 64)(51 65)(52 66)(53 67)(54 68)(55 69)(56 70)(71 78)(72 79)(73 80)(74 81)(75 82)(76 83)(77 84)(85 92)(86 93)(87 94)(88 95)(89 96)(90 97)(91 98)(99 203)(100 204)(101 205)(102 206)(103 207)(104 208)(105 209)(106 210)(107 197)(108 198)(109 199)(110 200)(111 201)(112 202)(113 189)(114 190)(115 191)(116 192)(117 193)(118 194)(119 195)(120 196)(121 183)(122 184)(123 185)(124 186)(125 187)(126 188)(141 223)(142 224)(143 211)(144 212)(145 213)(146 214)(147 215)(148 216)(149 217)(150 218)(151 219)(152 220)(153 221)(154 222)(169 176)(170 177)(171 178)(172 179)(173 180)(174 181)(175 182)
G:=sub<Sym(224)| (1,182)(2,169)(3,170)(4,171)(5,172)(6,173)(7,174)(8,175)(9,176)(10,177)(11,178)(12,179)(13,180)(14,181)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)(21,43)(22,44)(23,45)(24,46)(25,47)(26,48)(27,49)(28,50)(29,144)(30,145)(31,146)(32,147)(33,148)(34,149)(35,150)(36,151)(37,152)(38,153)(39,154)(40,141)(41,142)(42,143)(57,168)(58,155)(59,156)(60,157)(61,158)(62,159)(63,160)(64,161)(65,162)(66,163)(67,164)(68,165)(69,166)(70,167)(71,97)(72,98)(73,85)(74,86)(75,87)(76,88)(77,89)(78,90)(79,91)(80,92)(81,93)(82,94)(83,95)(84,96)(99,121)(100,122)(101,123)(102,124)(103,125)(104,126)(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(111,119)(112,120)(127,214)(128,215)(129,216)(130,217)(131,218)(132,219)(133,220)(134,221)(135,222)(136,223)(137,224)(138,211)(139,212)(140,213)(183,203)(184,204)(185,205)(186,206)(187,207)(188,208)(189,209)(190,210)(191,197)(192,198)(193,199)(194,200)(195,201)(196,202), (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), (1,110,40,207,97,59,129,52)(2,111,41,208,98,60,130,53)(3,112,42,209,85,61,131,54)(4,99,29,210,86,62,132,55)(5,100,30,197,87,63,133,56)(6,101,31,198,88,64,134,43)(7,102,32,199,89,65,135,44)(8,103,33,200,90,66,136,45)(9,104,34,201,91,67,137,46)(10,105,35,202,92,68,138,47)(11,106,36,203,93,69,139,48)(12,107,37,204,94,70,140,49)(13,108,38,205,95,57,127,50)(14,109,39,206,96,58,128,51)(15,181,117,154,186,84,155,215)(16,182,118,141,187,71,156,216)(17,169,119,142,188,72,157,217)(18,170,120,143,189,73,158,218)(19,171,121,144,190,74,159,219)(20,172,122,145,191,75,160,220)(21,173,123,146,192,76,161,221)(22,174,124,147,193,77,162,222)(23,175,125,148,194,78,163,223)(24,176,126,149,195,79,164,224)(25,177,113,150,196,80,165,211)(26,178,114,151,183,81,166,212)(27,179,115,152,184,82,167,213)(28,180,116,153,185,83,168,214), (1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14)(15,162)(16,163)(17,164)(18,165)(19,166)(20,167)(21,168)(22,155)(23,156)(24,157)(25,158)(26,159)(27,160)(28,161)(29,139)(30,140)(31,127)(32,128)(33,129)(34,130)(35,131)(36,132)(37,133)(38,134)(39,135)(40,136)(41,137)(42,138)(43,57)(44,58)(45,59)(46,60)(47,61)(48,62)(49,63)(50,64)(51,65)(52,66)(53,67)(54,68)(55,69)(56,70)(71,78)(72,79)(73,80)(74,81)(75,82)(76,83)(77,84)(85,92)(86,93)(87,94)(88,95)(89,96)(90,97)(91,98)(99,203)(100,204)(101,205)(102,206)(103,207)(104,208)(105,209)(106,210)(107,197)(108,198)(109,199)(110,200)(111,201)(112,202)(113,189)(114,190)(115,191)(116,192)(117,193)(118,194)(119,195)(120,196)(121,183)(122,184)(123,185)(124,186)(125,187)(126,188)(141,223)(142,224)(143,211)(144,212)(145,213)(146,214)(147,215)(148,216)(149,217)(150,218)(151,219)(152,220)(153,221)(154,222)(169,176)(170,177)(171,178)(172,179)(173,180)(174,181)(175,182)>;
G:=Group( (1,182)(2,169)(3,170)(4,171)(5,172)(6,173)(7,174)(8,175)(9,176)(10,177)(11,178)(12,179)(13,180)(14,181)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)(21,43)(22,44)(23,45)(24,46)(25,47)(26,48)(27,49)(28,50)(29,144)(30,145)(31,146)(32,147)(33,148)(34,149)(35,150)(36,151)(37,152)(38,153)(39,154)(40,141)(41,142)(42,143)(57,168)(58,155)(59,156)(60,157)(61,158)(62,159)(63,160)(64,161)(65,162)(66,163)(67,164)(68,165)(69,166)(70,167)(71,97)(72,98)(73,85)(74,86)(75,87)(76,88)(77,89)(78,90)(79,91)(80,92)(81,93)(82,94)(83,95)(84,96)(99,121)(100,122)(101,123)(102,124)(103,125)(104,126)(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(111,119)(112,120)(127,214)(128,215)(129,216)(130,217)(131,218)(132,219)(133,220)(134,221)(135,222)(136,223)(137,224)(138,211)(139,212)(140,213)(183,203)(184,204)(185,205)(186,206)(187,207)(188,208)(189,209)(190,210)(191,197)(192,198)(193,199)(194,200)(195,201)(196,202), (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), (1,110,40,207,97,59,129,52)(2,111,41,208,98,60,130,53)(3,112,42,209,85,61,131,54)(4,99,29,210,86,62,132,55)(5,100,30,197,87,63,133,56)(6,101,31,198,88,64,134,43)(7,102,32,199,89,65,135,44)(8,103,33,200,90,66,136,45)(9,104,34,201,91,67,137,46)(10,105,35,202,92,68,138,47)(11,106,36,203,93,69,139,48)(12,107,37,204,94,70,140,49)(13,108,38,205,95,57,127,50)(14,109,39,206,96,58,128,51)(15,181,117,154,186,84,155,215)(16,182,118,141,187,71,156,216)(17,169,119,142,188,72,157,217)(18,170,120,143,189,73,158,218)(19,171,121,144,190,74,159,219)(20,172,122,145,191,75,160,220)(21,173,123,146,192,76,161,221)(22,174,124,147,193,77,162,222)(23,175,125,148,194,78,163,223)(24,176,126,149,195,79,164,224)(25,177,113,150,196,80,165,211)(26,178,114,151,183,81,166,212)(27,179,115,152,184,82,167,213)(28,180,116,153,185,83,168,214), (1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14)(15,162)(16,163)(17,164)(18,165)(19,166)(20,167)(21,168)(22,155)(23,156)(24,157)(25,158)(26,159)(27,160)(28,161)(29,139)(30,140)(31,127)(32,128)(33,129)(34,130)(35,131)(36,132)(37,133)(38,134)(39,135)(40,136)(41,137)(42,138)(43,57)(44,58)(45,59)(46,60)(47,61)(48,62)(49,63)(50,64)(51,65)(52,66)(53,67)(54,68)(55,69)(56,70)(71,78)(72,79)(73,80)(74,81)(75,82)(76,83)(77,84)(85,92)(86,93)(87,94)(88,95)(89,96)(90,97)(91,98)(99,203)(100,204)(101,205)(102,206)(103,207)(104,208)(105,209)(106,210)(107,197)(108,198)(109,199)(110,200)(111,201)(112,202)(113,189)(114,190)(115,191)(116,192)(117,193)(118,194)(119,195)(120,196)(121,183)(122,184)(123,185)(124,186)(125,187)(126,188)(141,223)(142,224)(143,211)(144,212)(145,213)(146,214)(147,215)(148,216)(149,217)(150,218)(151,219)(152,220)(153,221)(154,222)(169,176)(170,177)(171,178)(172,179)(173,180)(174,181)(175,182) );
G=PermutationGroup([[(1,182),(2,169),(3,170),(4,171),(5,172),(6,173),(7,174),(8,175),(9,176),(10,177),(11,178),(12,179),(13,180),(14,181),(15,51),(16,52),(17,53),(18,54),(19,55),(20,56),(21,43),(22,44),(23,45),(24,46),(25,47),(26,48),(27,49),(28,50),(29,144),(30,145),(31,146),(32,147),(33,148),(34,149),(35,150),(36,151),(37,152),(38,153),(39,154),(40,141),(41,142),(42,143),(57,168),(58,155),(59,156),(60,157),(61,158),(62,159),(63,160),(64,161),(65,162),(66,163),(67,164),(68,165),(69,166),(70,167),(71,97),(72,98),(73,85),(74,86),(75,87),(76,88),(77,89),(78,90),(79,91),(80,92),(81,93),(82,94),(83,95),(84,96),(99,121),(100,122),(101,123),(102,124),(103,125),(104,126),(105,113),(106,114),(107,115),(108,116),(109,117),(110,118),(111,119),(112,120),(127,214),(128,215),(129,216),(130,217),(131,218),(132,219),(133,220),(134,221),(135,222),(136,223),(137,224),(138,211),(139,212),(140,213),(183,203),(184,204),(185,205),(186,206),(187,207),(188,208),(189,209),(190,210),(191,197),(192,198),(193,199),(194,200),(195,201),(196,202)], [(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)], [(1,110,40,207,97,59,129,52),(2,111,41,208,98,60,130,53),(3,112,42,209,85,61,131,54),(4,99,29,210,86,62,132,55),(5,100,30,197,87,63,133,56),(6,101,31,198,88,64,134,43),(7,102,32,199,89,65,135,44),(8,103,33,200,90,66,136,45),(9,104,34,201,91,67,137,46),(10,105,35,202,92,68,138,47),(11,106,36,203,93,69,139,48),(12,107,37,204,94,70,140,49),(13,108,38,205,95,57,127,50),(14,109,39,206,96,58,128,51),(15,181,117,154,186,84,155,215),(16,182,118,141,187,71,156,216),(17,169,119,142,188,72,157,217),(18,170,120,143,189,73,158,218),(19,171,121,144,190,74,159,219),(20,172,122,145,191,75,160,220),(21,173,123,146,192,76,161,221),(22,174,124,147,193,77,162,222),(23,175,125,148,194,78,163,223),(24,176,126,149,195,79,164,224),(25,177,113,150,196,80,165,211),(26,178,114,151,183,81,166,212),(27,179,115,152,184,82,167,213),(28,180,116,153,185,83,168,214)], [(1,8),(2,9),(3,10),(4,11),(5,12),(6,13),(7,14),(15,162),(16,163),(17,164),(18,165),(19,166),(20,167),(21,168),(22,155),(23,156),(24,157),(25,158),(26,159),(27,160),(28,161),(29,139),(30,140),(31,127),(32,128),(33,129),(34,130),(35,131),(36,132),(37,133),(38,134),(39,135),(40,136),(41,137),(42,138),(43,57),(44,58),(45,59),(46,60),(47,61),(48,62),(49,63),(50,64),(51,65),(52,66),(53,67),(54,68),(55,69),(56,70),(71,78),(72,79),(73,80),(74,81),(75,82),(76,83),(77,84),(85,92),(86,93),(87,94),(88,95),(89,96),(90,97),(91,98),(99,203),(100,204),(101,205),(102,206),(103,207),(104,208),(105,209),(106,210),(107,197),(108,198),(109,199),(110,200),(111,201),(112,202),(113,189),(114,190),(115,191),(116,192),(117,193),(118,194),(119,195),(120,196),(121,183),(122,184),(123,185),(124,186),(125,187),(126,188),(141,223),(142,224),(143,211),(144,212),(145,213),(146,214),(147,215),(148,216),(149,217),(150,218),(151,219),(152,220),(153,221),(154,222),(169,176),(170,177),(171,178),(172,179),(173,180),(174,181),(175,182)]])
196 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 7A | ··· | 7F | 8A | ··· | 8H | 14A | ··· | 14AP | 14AQ | ··· | 14BN | 28A | ··· | 28X | 28Y | ··· | 28AV | 56A | ··· | 56AV |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | ··· | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | ··· | 1 | 4 | 4 | 4 | 4 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 |
196 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | |||||||||
| image | C1 | C2 | C2 | C2 | C2 | C7 | C14 | C14 | C14 | C14 | D4 | D4 | SD16 | C7×D4 | C7×D4 | C7×SD16 |
| kernel | SD16×C2×C14 | C22×C56 | C14×SD16 | D4×C2×C14 | Q8×C2×C14 | C22×SD16 | C22×C8 | C2×SD16 | C22×D4 | C22×Q8 | C2×C28 | C22×C14 | C2×C14 | C2×C4 | C23 | C22 |
| # reps | 1 | 1 | 12 | 1 | 1 | 6 | 6 | 72 | 6 | 6 | 3 | 1 | 8 | 18 | 6 | 48 |
Matrix representation of SD16×C2×C14 ►in GL4(𝔽113) generated by
| 1 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 109 | 0 |
| 0 | 0 | 0 | 109 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 100 |
| 0 | 0 | 26 | 87 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 112 |
| 0 | 0 | 0 | 112 |
G:=sub<GL(4,GF(113))| [1,0,0,0,0,112,0,0,0,0,1,0,0,0,0,1],[112,0,0,0,0,112,0,0,0,0,109,0,0,0,0,109],[1,0,0,0,0,1,0,0,0,0,0,26,0,0,100,87],[1,0,0,0,0,1,0,0,0,0,1,0,0,0,112,112] >;
SD16×C2×C14 in GAP, Magma, Sage, TeX
{\rm SD}_{16}\times C_2\times C_{14} % in TeX
G:=Group("SD16xC2xC14"); // GroupNames label
G:=SmallGroup(448,1353);
// by ID
G=gap.SmallGroup(448,1353);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,1568,1597,14117,7068,124]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^14=c^8=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d=c^3>;
// generators/relations