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×C56)⋊24C2, (C22×C8)⋊10C14, (C2×C56)⋊52C22, C28.326(C2×D4), (C2×C28).433D4, C4.2(C23×C14), (C7×Q8)⋊11C23, (C22×Q8)⋊8C14, Q8⋊1(C22×C14), C23.61(C7×D4), (Q8×C14)⋊53C22, (C7×D4).34C23, D4.1(C22×C14), C22.66(D4×C14), (C2×C28).972C23, (C22×D4).12C14, C14.200(C22×D4), (C22×C14).222D4, (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
Subgroups: 498 in 298 conjugacy classes, 178 normal (18 characteristic)
C1, C2, C2 [×6], C2 [×4], C4, C4 [×3], C4 [×4], C22 [×7], C22 [×16], C7, C8 [×4], C2×C4 [×6], C2×C4 [×6], D4 [×4], D4 [×6], Q8 [×4], Q8 [×6], C23, C23 [×10], C14, C14 [×6], C14 [×4], C2×C8 [×6], SD16 [×16], C22×C4, C22×C4, C2×D4 [×6], C2×D4 [×3], C2×Q8 [×6], C2×Q8 [×3], C24, C28, C28 [×3], C28 [×4], C2×C14 [×7], C2×C14 [×16], C22×C8, C2×SD16 [×12], C22×D4, C22×Q8, C56 [×4], C2×C28 [×6], C2×C28 [×6], C7×D4 [×4], C7×D4 [×6], C7×Q8 [×4], C7×Q8 [×6], C22×C14, C22×C14 [×10], C22×SD16, C2×C56 [×6], C7×SD16 [×16], C22×C28, C22×C28, D4×C14 [×6], D4×C14 [×3], Q8×C14 [×6], Q8×C14 [×3], C23×C14, C22×C56, C14×SD16 [×12], D4×C2×C14, Q8×C2×C14, SD16×C2×C14
Quotients:
C1, C2 [×15], C22 [×35], C7, D4 [×4], C23 [×15], C14 [×15], SD16 [×4], C2×D4 [×6], C24, C2×C14 [×35], C2×SD16 [×6], C22×D4, C7×D4 [×4], C22×C14 [×15], C22×SD16, C7×SD16 [×4], D4×C14 [×6], C23×C14, C14×SD16 [×6], D4×C2×C14, SD16×C2×C14
Generators and relations
G = < a,b,c,d | a2=b14=c8=d2=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd=c3 >
►On 224 points
Generators in S224
(1 94)(2 95)(3 96)(4 97)(5 98)(6 85)(7 86)(8 87)(9 88)(10 89)(11 90)(12 91)(13 92)(14 93)(15 72)(16 73)(17 74)(18 75)(19 76)(20 77)(21 78)(22 79)(23 80)(24 81)(25 82)(26 83)(27 84)(28 71)(29 121)(30 122)(31 123)(32 124)(33 125)(34 126)(35 113)(36 114)(37 115)(38 116)(39 117)(40 118)(41 119)(42 120)(43 201)(44 202)(45 203)(46 204)(47 205)(48 206)(49 207)(50 208)(51 209)(52 210)(53 197)(54 198)(55 199)(56 200)(57 150)(58 151)(59 152)(60 153)(61 154)(62 141)(63 142)(64 143)(65 144)(66 145)(67 146)(68 147)(69 148)(70 149)(99 162)(100 163)(101 164)(102 165)(103 166)(104 167)(105 168)(106 155)(107 156)(108 157)(109 158)(110 159)(111 160)(112 161)(127 213)(128 214)(129 215)(130 216)(131 217)(132 218)(133 219)(134 220)(135 221)(136 222)(137 223)(138 224)(139 211)(140 212)(169 191)(170 192)(171 193)(172 194)(173 195)(174 196)(175 183)(176 184)(177 185)(178 186)(179 187)(180 188)(181 189)(182 190)
(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)
(1 147 21 106 123 173 214 45)(2 148 22 107 124 174 215 46)(3 149 23 108 125 175 216 47)(4 150 24 109 126 176 217 48)(5 151 25 110 113 177 218 49)(6 152 26 111 114 178 219 50)(7 153 27 112 115 179 220 51)(8 154 28 99 116 180 221 52)(9 141 15 100 117 181 222 53)(10 142 16 101 118 182 223 54)(11 143 17 102 119 169 224 55)(12 144 18 103 120 170 211 56)(13 145 19 104 121 171 212 43)(14 146 20 105 122 172 213 44)(29 193 140 201 92 66 76 167)(30 194 127 202 93 67 77 168)(31 195 128 203 94 68 78 155)(32 196 129 204 95 69 79 156)(33 183 130 205 96 70 80 157)(34 184 131 206 97 57 81 158)(35 185 132 207 98 58 82 159)(36 186 133 208 85 59 83 160)(37 187 134 209 86 60 84 161)(38 188 135 210 87 61 71 162)(39 189 136 197 88 62 72 163)(40 190 137 198 89 63 73 164)(41 191 138 199 90 64 74 165)(42 192 139 200 91 65 75 166)
(1 8)(2 9)(3 10)(4 11)(5 12)(6 13)(7 14)(15 215)(16 216)(17 217)(18 218)(19 219)(20 220)(21 221)(22 222)(23 223)(24 224)(25 211)(26 212)(27 213)(28 214)(29 36)(30 37)(31 38)(32 39)(33 40)(34 41)(35 42)(43 178)(44 179)(45 180)(46 181)(47 182)(48 169)(49 170)(50 171)(51 172)(52 173)(53 174)(54 175)(55 176)(56 177)(57 165)(58 166)(59 167)(60 168)(61 155)(62 156)(63 157)(64 158)(65 159)(66 160)(67 161)(68 162)(69 163)(70 164)(71 128)(72 129)(73 130)(74 131)(75 132)(76 133)(77 134)(78 135)(79 136)(80 137)(81 138)(82 139)(83 140)(84 127)(85 92)(86 93)(87 94)(88 95)(89 96)(90 97)(91 98)(99 147)(100 148)(101 149)(102 150)(103 151)(104 152)(105 153)(106 154)(107 141)(108 142)(109 143)(110 144)(111 145)(112 146)(113 120)(114 121)(115 122)(116 123)(117 124)(118 125)(119 126)(183 198)(184 199)(185 200)(186 201)(187 202)(188 203)(189 204)(190 205)(191 206)(192 207)(193 208)(194 209)(195 210)(196 197)
G:=sub<Sym(224)| (1,94)(2,95)(3,96)(4,97)(5,98)(6,85)(7,86)(8,87)(9,88)(10,89)(11,90)(12,91)(13,92)(14,93)(15,72)(16,73)(17,74)(18,75)(19,76)(20,77)(21,78)(22,79)(23,80)(24,81)(25,82)(26,83)(27,84)(28,71)(29,121)(30,122)(31,123)(32,124)(33,125)(34,126)(35,113)(36,114)(37,115)(38,116)(39,117)(40,118)(41,119)(42,120)(43,201)(44,202)(45,203)(46,204)(47,205)(48,206)(49,207)(50,208)(51,209)(52,210)(53,197)(54,198)(55,199)(56,200)(57,150)(58,151)(59,152)(60,153)(61,154)(62,141)(63,142)(64,143)(65,144)(66,145)(67,146)(68,147)(69,148)(70,149)(99,162)(100,163)(101,164)(102,165)(103,166)(104,167)(105,168)(106,155)(107,156)(108,157)(109,158)(110,159)(111,160)(112,161)(127,213)(128,214)(129,215)(130,216)(131,217)(132,218)(133,219)(134,220)(135,221)(136,222)(137,223)(138,224)(139,211)(140,212)(169,191)(170,192)(171,193)(172,194)(173,195)(174,196)(175,183)(176,184)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190), (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), (1,147,21,106,123,173,214,45)(2,148,22,107,124,174,215,46)(3,149,23,108,125,175,216,47)(4,150,24,109,126,176,217,48)(5,151,25,110,113,177,218,49)(6,152,26,111,114,178,219,50)(7,153,27,112,115,179,220,51)(8,154,28,99,116,180,221,52)(9,141,15,100,117,181,222,53)(10,142,16,101,118,182,223,54)(11,143,17,102,119,169,224,55)(12,144,18,103,120,170,211,56)(13,145,19,104,121,171,212,43)(14,146,20,105,122,172,213,44)(29,193,140,201,92,66,76,167)(30,194,127,202,93,67,77,168)(31,195,128,203,94,68,78,155)(32,196,129,204,95,69,79,156)(33,183,130,205,96,70,80,157)(34,184,131,206,97,57,81,158)(35,185,132,207,98,58,82,159)(36,186,133,208,85,59,83,160)(37,187,134,209,86,60,84,161)(38,188,135,210,87,61,71,162)(39,189,136,197,88,62,72,163)(40,190,137,198,89,63,73,164)(41,191,138,199,90,64,74,165)(42,192,139,200,91,65,75,166), (1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14)(15,215)(16,216)(17,217)(18,218)(19,219)(20,220)(21,221)(22,222)(23,223)(24,224)(25,211)(26,212)(27,213)(28,214)(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,178)(44,179)(45,180)(46,181)(47,182)(48,169)(49,170)(50,171)(51,172)(52,173)(53,174)(54,175)(55,176)(56,177)(57,165)(58,166)(59,167)(60,168)(61,155)(62,156)(63,157)(64,158)(65,159)(66,160)(67,161)(68,162)(69,163)(70,164)(71,128)(72,129)(73,130)(74,131)(75,132)(76,133)(77,134)(78,135)(79,136)(80,137)(81,138)(82,139)(83,140)(84,127)(85,92)(86,93)(87,94)(88,95)(89,96)(90,97)(91,98)(99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)(106,154)(107,141)(108,142)(109,143)(110,144)(111,145)(112,146)(113,120)(114,121)(115,122)(116,123)(117,124)(118,125)(119,126)(183,198)(184,199)(185,200)(186,201)(187,202)(188,203)(189,204)(190,205)(191,206)(192,207)(193,208)(194,209)(195,210)(196,197)>;
G:=Group( (1,94)(2,95)(3,96)(4,97)(5,98)(6,85)(7,86)(8,87)(9,88)(10,89)(11,90)(12,91)(13,92)(14,93)(15,72)(16,73)(17,74)(18,75)(19,76)(20,77)(21,78)(22,79)(23,80)(24,81)(25,82)(26,83)(27,84)(28,71)(29,121)(30,122)(31,123)(32,124)(33,125)(34,126)(35,113)(36,114)(37,115)(38,116)(39,117)(40,118)(41,119)(42,120)(43,201)(44,202)(45,203)(46,204)(47,205)(48,206)(49,207)(50,208)(51,209)(52,210)(53,197)(54,198)(55,199)(56,200)(57,150)(58,151)(59,152)(60,153)(61,154)(62,141)(63,142)(64,143)(65,144)(66,145)(67,146)(68,147)(69,148)(70,149)(99,162)(100,163)(101,164)(102,165)(103,166)(104,167)(105,168)(106,155)(107,156)(108,157)(109,158)(110,159)(111,160)(112,161)(127,213)(128,214)(129,215)(130,216)(131,217)(132,218)(133,219)(134,220)(135,221)(136,222)(137,223)(138,224)(139,211)(140,212)(169,191)(170,192)(171,193)(172,194)(173,195)(174,196)(175,183)(176,184)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190), (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), (1,147,21,106,123,173,214,45)(2,148,22,107,124,174,215,46)(3,149,23,108,125,175,216,47)(4,150,24,109,126,176,217,48)(5,151,25,110,113,177,218,49)(6,152,26,111,114,178,219,50)(7,153,27,112,115,179,220,51)(8,154,28,99,116,180,221,52)(9,141,15,100,117,181,222,53)(10,142,16,101,118,182,223,54)(11,143,17,102,119,169,224,55)(12,144,18,103,120,170,211,56)(13,145,19,104,121,171,212,43)(14,146,20,105,122,172,213,44)(29,193,140,201,92,66,76,167)(30,194,127,202,93,67,77,168)(31,195,128,203,94,68,78,155)(32,196,129,204,95,69,79,156)(33,183,130,205,96,70,80,157)(34,184,131,206,97,57,81,158)(35,185,132,207,98,58,82,159)(36,186,133,208,85,59,83,160)(37,187,134,209,86,60,84,161)(38,188,135,210,87,61,71,162)(39,189,136,197,88,62,72,163)(40,190,137,198,89,63,73,164)(41,191,138,199,90,64,74,165)(42,192,139,200,91,65,75,166), (1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14)(15,215)(16,216)(17,217)(18,218)(19,219)(20,220)(21,221)(22,222)(23,223)(24,224)(25,211)(26,212)(27,213)(28,214)(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,178)(44,179)(45,180)(46,181)(47,182)(48,169)(49,170)(50,171)(51,172)(52,173)(53,174)(54,175)(55,176)(56,177)(57,165)(58,166)(59,167)(60,168)(61,155)(62,156)(63,157)(64,158)(65,159)(66,160)(67,161)(68,162)(69,163)(70,164)(71,128)(72,129)(73,130)(74,131)(75,132)(76,133)(77,134)(78,135)(79,136)(80,137)(81,138)(82,139)(83,140)(84,127)(85,92)(86,93)(87,94)(88,95)(89,96)(90,97)(91,98)(99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)(106,154)(107,141)(108,142)(109,143)(110,144)(111,145)(112,146)(113,120)(114,121)(115,122)(116,123)(117,124)(118,125)(119,126)(183,198)(184,199)(185,200)(186,201)(187,202)(188,203)(189,204)(190,205)(191,206)(192,207)(193,208)(194,209)(195,210)(196,197) );
G=PermutationGroup([(1,94),(2,95),(3,96),(4,97),(5,98),(6,85),(7,86),(8,87),(9,88),(10,89),(11,90),(12,91),(13,92),(14,93),(15,72),(16,73),(17,74),(18,75),(19,76),(20,77),(21,78),(22,79),(23,80),(24,81),(25,82),(26,83),(27,84),(28,71),(29,121),(30,122),(31,123),(32,124),(33,125),(34,126),(35,113),(36,114),(37,115),(38,116),(39,117),(40,118),(41,119),(42,120),(43,201),(44,202),(45,203),(46,204),(47,205),(48,206),(49,207),(50,208),(51,209),(52,210),(53,197),(54,198),(55,199),(56,200),(57,150),(58,151),(59,152),(60,153),(61,154),(62,141),(63,142),(64,143),(65,144),(66,145),(67,146),(68,147),(69,148),(70,149),(99,162),(100,163),(101,164),(102,165),(103,166),(104,167),(105,168),(106,155),(107,156),(108,157),(109,158),(110,159),(111,160),(112,161),(127,213),(128,214),(129,215),(130,216),(131,217),(132,218),(133,219),(134,220),(135,221),(136,222),(137,223),(138,224),(139,211),(140,212),(169,191),(170,192),(171,193),(172,194),(173,195),(174,196),(175,183),(176,184),(177,185),(178,186),(179,187),(180,188),(181,189),(182,190)], [(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)], [(1,147,21,106,123,173,214,45),(2,148,22,107,124,174,215,46),(3,149,23,108,125,175,216,47),(4,150,24,109,126,176,217,48),(5,151,25,110,113,177,218,49),(6,152,26,111,114,178,219,50),(7,153,27,112,115,179,220,51),(8,154,28,99,116,180,221,52),(9,141,15,100,117,181,222,53),(10,142,16,101,118,182,223,54),(11,143,17,102,119,169,224,55),(12,144,18,103,120,170,211,56),(13,145,19,104,121,171,212,43),(14,146,20,105,122,172,213,44),(29,193,140,201,92,66,76,167),(30,194,127,202,93,67,77,168),(31,195,128,203,94,68,78,155),(32,196,129,204,95,69,79,156),(33,183,130,205,96,70,80,157),(34,184,131,206,97,57,81,158),(35,185,132,207,98,58,82,159),(36,186,133,208,85,59,83,160),(37,187,134,209,86,60,84,161),(38,188,135,210,87,61,71,162),(39,189,136,197,88,62,72,163),(40,190,137,198,89,63,73,164),(41,191,138,199,90,64,74,165),(42,192,139,200,91,65,75,166)], [(1,8),(2,9),(3,10),(4,11),(5,12),(6,13),(7,14),(15,215),(16,216),(17,217),(18,218),(19,219),(20,220),(21,221),(22,222),(23,223),(24,224),(25,211),(26,212),(27,213),(28,214),(29,36),(30,37),(31,38),(32,39),(33,40),(34,41),(35,42),(43,178),(44,179),(45,180),(46,181),(47,182),(48,169),(49,170),(50,171),(51,172),(52,173),(53,174),(54,175),(55,176),(56,177),(57,165),(58,166),(59,167),(60,168),(61,155),(62,156),(63,157),(64,158),(65,159),(66,160),(67,161),(68,162),(69,163),(70,164),(71,128),(72,129),(73,130),(74,131),(75,132),(76,133),(77,134),(78,135),(79,136),(80,137),(81,138),(82,139),(83,140),(84,127),(85,92),(86,93),(87,94),(88,95),(89,96),(90,97),(91,98),(99,147),(100,148),(101,149),(102,150),(103,151),(104,152),(105,153),(106,154),(107,141),(108,142),(109,143),(110,144),(111,145),(112,146),(113,120),(114,121),(115,122),(116,123),(117,124),(118,125),(119,126),(183,198),(184,199),(185,200),(186,201),(187,202),(188,203),(189,204),(190,205),(191,206),(192,207),(193,208),(194,209),(195,210),(196,197)])
Matrix representation ►G ⊆ 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] >;
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 |
In GAP, Magma, Sage, TeX
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
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