direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C28.47D4, M4(2).32D14, (C2×C4).53D28, C4.67(C2×D28), C28.422(C2×D4), (C2×C28).176D4, C23.56(C4×D7), C4.29(D14⋊C4), C14⋊1(C4.10D4), C28.54(C22⋊C4), (C2×C28).418C23, (C2×Dic14).15C4, (C22×C4).144D14, (C2×M4(2)).17D7, (C22×Dic7).5C4, C22.51(D14⋊C4), (C14×M4(2)).28C2, C4.Dic7.43C22, (C22×C28).191C22, (C22×Dic14).15C2, (C7×M4(2)).35C22, (C2×Dic14).279C22, (C2×C4).55(C4×D7), C7⋊2(C2×C4.10D4), C22.22(C2×C4×D7), C2.33(C2×D14⋊C4), C4.115(C2×C7⋊D4), (C2×C28).111(C2×C4), C14.61(C2×C22⋊C4), (C2×Dic7).6(C2×C4), (C2×C4).257(C7⋊D4), (C2×C14).16(C22×C4), (C22×C14).72(C2×C4), (C2×C4).122(C22×D7), (C2×C4.Dic7).26C2, (C2×C14).67(C22⋊C4), SmallGroup(448,670)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C28.47D4
G = < a,b,c,d | a2=b28=1, c4=d2=b14, ab=ba, ac=ca, ad=da, cbc-1=dbd-1=b-1, dcd-1=b21c3 >
Subgroups: 612 in 146 conjugacy classes, 63 normal (39 characteristic)
C1, C2, C2 [×2], C2 [×2], C4 [×4], C4 [×4], C22 [×3], C22 [×2], C7, C8 [×4], C2×C4 [×6], C2×C4 [×8], Q8 [×8], C23, C14, C14 [×2], C14 [×2], C2×C8 [×2], M4(2) [×2], M4(2) [×4], C22×C4, C22×C4 [×2], C2×Q8 [×8], Dic7 [×4], C28 [×4], C2×C14 [×3], C2×C14 [×2], C4.10D4 [×4], C2×M4(2), C2×M4(2), C22×Q8, C7⋊C8 [×2], C56 [×2], Dic14 [×8], C2×Dic7 [×4], C2×Dic7 [×4], C2×C28 [×6], C22×C14, C2×C4.10D4, C2×C7⋊C8, C4.Dic7 [×2], C4.Dic7, C2×C56, C7×M4(2) [×2], C7×M4(2), C2×Dic14 [×4], C2×Dic14 [×4], C22×Dic7 [×2], C22×C28, C28.47D4 [×4], C2×C4.Dic7, C14×M4(2), C22×Dic14, C2×C28.47D4
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], D4 [×4], C23, D7, C22⋊C4 [×4], C22×C4, C2×D4 [×2], D14 [×3], C4.10D4 [×2], C2×C22⋊C4, C4×D7 [×2], D28 [×2], C7⋊D4 [×2], C22×D7, C2×C4.10D4, D14⋊C4 [×4], C2×C4×D7, C2×D28, C2×C7⋊D4, C28.47D4 [×2], C2×D14⋊C4, C2×C28.47D4
►On 224 points
Generators in S224
(1 99)(2 100)(3 101)(4 102)(5 103)(6 104)(7 105)(8 106)(9 107)(10 108)(11 109)(12 110)(13 111)(14 112)(15 85)(16 86)(17 87)(18 88)(19 89)(20 90)(21 91)(22 92)(23 93)(24 94)(25 95)(26 96)(27 97)(28 98)(29 57)(30 58)(31 59)(32 60)(33 61)(34 62)(35 63)(36 64)(37 65)(38 66)(39 67)(40 68)(41 69)(42 70)(43 71)(44 72)(45 73)(46 74)(47 75)(48 76)(49 77)(50 78)(51 79)(52 80)(53 81)(54 82)(55 83)(56 84)(113 162)(114 163)(115 164)(116 165)(117 166)(118 167)(119 168)(120 141)(121 142)(122 143)(123 144)(124 145)(125 146)(126 147)(127 148)(128 149)(129 150)(130 151)(131 152)(132 153)(133 154)(134 155)(135 156)(136 157)(137 158)(138 159)(139 160)(140 161)(169 207)(170 208)(171 209)(172 210)(173 211)(174 212)(175 213)(176 214)(177 215)(178 216)(179 217)(180 218)(181 219)(182 220)(183 221)(184 222)(185 223)(186 224)(187 197)(188 198)(189 199)(190 200)(191 201)(192 202)(193 203)(194 204)(195 205)(196 206)
(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 50 92 57 15 36 106 71)(2 49 93 84 16 35 107 70)(3 48 94 83 17 34 108 69)(4 47 95 82 18 33 109 68)(5 46 96 81 19 32 110 67)(6 45 97 80 20 31 111 66)(7 44 98 79 21 30 112 65)(8 43 99 78 22 29 85 64)(9 42 100 77 23 56 86 63)(10 41 101 76 24 55 87 62)(11 40 102 75 25 54 88 61)(12 39 103 74 26 53 89 60)(13 38 104 73 27 52 90 59)(14 37 105 72 28 51 91 58)(113 189 141 220 127 175 155 206)(114 188 142 219 128 174 156 205)(115 187 143 218 129 173 157 204)(116 186 144 217 130 172 158 203)(117 185 145 216 131 171 159 202)(118 184 146 215 132 170 160 201)(119 183 147 214 133 169 161 200)(120 182 148 213 134 196 162 199)(121 181 149 212 135 195 163 198)(122 180 150 211 136 194 164 197)(123 179 151 210 137 193 165 224)(124 178 152 209 138 192 166 223)(125 177 153 208 139 191 167 222)(126 176 154 207 140 190 168 221)
(1 197 15 211)(2 224 16 210)(3 223 17 209)(4 222 18 208)(5 221 19 207)(6 220 20 206)(7 219 21 205)(8 218 22 204)(9 217 23 203)(10 216 24 202)(11 215 25 201)(12 214 26 200)(13 213 27 199)(14 212 28 198)(29 150 43 164)(30 149 44 163)(31 148 45 162)(32 147 46 161)(33 146 47 160)(34 145 48 159)(35 144 49 158)(36 143 50 157)(37 142 51 156)(38 141 52 155)(39 168 53 154)(40 167 54 153)(41 166 55 152)(42 165 56 151)(57 129 71 115)(58 128 72 114)(59 127 73 113)(60 126 74 140)(61 125 75 139)(62 124 76 138)(63 123 77 137)(64 122 78 136)(65 121 79 135)(66 120 80 134)(67 119 81 133)(68 118 82 132)(69 117 83 131)(70 116 84 130)(85 173 99 187)(86 172 100 186)(87 171 101 185)(88 170 102 184)(89 169 103 183)(90 196 104 182)(91 195 105 181)(92 194 106 180)(93 193 107 179)(94 192 108 178)(95 191 109 177)(96 190 110 176)(97 189 111 175)(98 188 112 174)
G:=sub<Sym(224)| (1,99)(2,100)(3,101)(4,102)(5,103)(6,104)(7,105)(8,106)(9,107)(10,108)(11,109)(12,110)(13,111)(14,112)(15,85)(16,86)(17,87)(18,88)(19,89)(20,90)(21,91)(22,92)(23,93)(24,94)(25,95)(26,96)(27,97)(28,98)(29,57)(30,58)(31,59)(32,60)(33,61)(34,62)(35,63)(36,64)(37,65)(38,66)(39,67)(40,68)(41,69)(42,70)(43,71)(44,72)(45,73)(46,74)(47,75)(48,76)(49,77)(50,78)(51,79)(52,80)(53,81)(54,82)(55,83)(56,84)(113,162)(114,163)(115,164)(116,165)(117,166)(118,167)(119,168)(120,141)(121,142)(122,143)(123,144)(124,145)(125,146)(126,147)(127,148)(128,149)(129,150)(130,151)(131,152)(132,153)(133,154)(134,155)(135,156)(136,157)(137,158)(138,159)(139,160)(140,161)(169,207)(170,208)(171,209)(172,210)(173,211)(174,212)(175,213)(176,214)(177,215)(178,216)(179,217)(180,218)(181,219)(182,220)(183,221)(184,222)(185,223)(186,224)(187,197)(188,198)(189,199)(190,200)(191,201)(192,202)(193,203)(194,204)(195,205)(196,206), (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), (1,50,92,57,15,36,106,71)(2,49,93,84,16,35,107,70)(3,48,94,83,17,34,108,69)(4,47,95,82,18,33,109,68)(5,46,96,81,19,32,110,67)(6,45,97,80,20,31,111,66)(7,44,98,79,21,30,112,65)(8,43,99,78,22,29,85,64)(9,42,100,77,23,56,86,63)(10,41,101,76,24,55,87,62)(11,40,102,75,25,54,88,61)(12,39,103,74,26,53,89,60)(13,38,104,73,27,52,90,59)(14,37,105,72,28,51,91,58)(113,189,141,220,127,175,155,206)(114,188,142,219,128,174,156,205)(115,187,143,218,129,173,157,204)(116,186,144,217,130,172,158,203)(117,185,145,216,131,171,159,202)(118,184,146,215,132,170,160,201)(119,183,147,214,133,169,161,200)(120,182,148,213,134,196,162,199)(121,181,149,212,135,195,163,198)(122,180,150,211,136,194,164,197)(123,179,151,210,137,193,165,224)(124,178,152,209,138,192,166,223)(125,177,153,208,139,191,167,222)(126,176,154,207,140,190,168,221), (1,197,15,211)(2,224,16,210)(3,223,17,209)(4,222,18,208)(5,221,19,207)(6,220,20,206)(7,219,21,205)(8,218,22,204)(9,217,23,203)(10,216,24,202)(11,215,25,201)(12,214,26,200)(13,213,27,199)(14,212,28,198)(29,150,43,164)(30,149,44,163)(31,148,45,162)(32,147,46,161)(33,146,47,160)(34,145,48,159)(35,144,49,158)(36,143,50,157)(37,142,51,156)(38,141,52,155)(39,168,53,154)(40,167,54,153)(41,166,55,152)(42,165,56,151)(57,129,71,115)(58,128,72,114)(59,127,73,113)(60,126,74,140)(61,125,75,139)(62,124,76,138)(63,123,77,137)(64,122,78,136)(65,121,79,135)(66,120,80,134)(67,119,81,133)(68,118,82,132)(69,117,83,131)(70,116,84,130)(85,173,99,187)(86,172,100,186)(87,171,101,185)(88,170,102,184)(89,169,103,183)(90,196,104,182)(91,195,105,181)(92,194,106,180)(93,193,107,179)(94,192,108,178)(95,191,109,177)(96,190,110,176)(97,189,111,175)(98,188,112,174)>;
G:=Group( (1,99)(2,100)(3,101)(4,102)(5,103)(6,104)(7,105)(8,106)(9,107)(10,108)(11,109)(12,110)(13,111)(14,112)(15,85)(16,86)(17,87)(18,88)(19,89)(20,90)(21,91)(22,92)(23,93)(24,94)(25,95)(26,96)(27,97)(28,98)(29,57)(30,58)(31,59)(32,60)(33,61)(34,62)(35,63)(36,64)(37,65)(38,66)(39,67)(40,68)(41,69)(42,70)(43,71)(44,72)(45,73)(46,74)(47,75)(48,76)(49,77)(50,78)(51,79)(52,80)(53,81)(54,82)(55,83)(56,84)(113,162)(114,163)(115,164)(116,165)(117,166)(118,167)(119,168)(120,141)(121,142)(122,143)(123,144)(124,145)(125,146)(126,147)(127,148)(128,149)(129,150)(130,151)(131,152)(132,153)(133,154)(134,155)(135,156)(136,157)(137,158)(138,159)(139,160)(140,161)(169,207)(170,208)(171,209)(172,210)(173,211)(174,212)(175,213)(176,214)(177,215)(178,216)(179,217)(180,218)(181,219)(182,220)(183,221)(184,222)(185,223)(186,224)(187,197)(188,198)(189,199)(190,200)(191,201)(192,202)(193,203)(194,204)(195,205)(196,206), (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), (1,50,92,57,15,36,106,71)(2,49,93,84,16,35,107,70)(3,48,94,83,17,34,108,69)(4,47,95,82,18,33,109,68)(5,46,96,81,19,32,110,67)(6,45,97,80,20,31,111,66)(7,44,98,79,21,30,112,65)(8,43,99,78,22,29,85,64)(9,42,100,77,23,56,86,63)(10,41,101,76,24,55,87,62)(11,40,102,75,25,54,88,61)(12,39,103,74,26,53,89,60)(13,38,104,73,27,52,90,59)(14,37,105,72,28,51,91,58)(113,189,141,220,127,175,155,206)(114,188,142,219,128,174,156,205)(115,187,143,218,129,173,157,204)(116,186,144,217,130,172,158,203)(117,185,145,216,131,171,159,202)(118,184,146,215,132,170,160,201)(119,183,147,214,133,169,161,200)(120,182,148,213,134,196,162,199)(121,181,149,212,135,195,163,198)(122,180,150,211,136,194,164,197)(123,179,151,210,137,193,165,224)(124,178,152,209,138,192,166,223)(125,177,153,208,139,191,167,222)(126,176,154,207,140,190,168,221), (1,197,15,211)(2,224,16,210)(3,223,17,209)(4,222,18,208)(5,221,19,207)(6,220,20,206)(7,219,21,205)(8,218,22,204)(9,217,23,203)(10,216,24,202)(11,215,25,201)(12,214,26,200)(13,213,27,199)(14,212,28,198)(29,150,43,164)(30,149,44,163)(31,148,45,162)(32,147,46,161)(33,146,47,160)(34,145,48,159)(35,144,49,158)(36,143,50,157)(37,142,51,156)(38,141,52,155)(39,168,53,154)(40,167,54,153)(41,166,55,152)(42,165,56,151)(57,129,71,115)(58,128,72,114)(59,127,73,113)(60,126,74,140)(61,125,75,139)(62,124,76,138)(63,123,77,137)(64,122,78,136)(65,121,79,135)(66,120,80,134)(67,119,81,133)(68,118,82,132)(69,117,83,131)(70,116,84,130)(85,173,99,187)(86,172,100,186)(87,171,101,185)(88,170,102,184)(89,169,103,183)(90,196,104,182)(91,195,105,181)(92,194,106,180)(93,193,107,179)(94,192,108,178)(95,191,109,177)(96,190,110,176)(97,189,111,175)(98,188,112,174) );
G=PermutationGroup([(1,99),(2,100),(3,101),(4,102),(5,103),(6,104),(7,105),(8,106),(9,107),(10,108),(11,109),(12,110),(13,111),(14,112),(15,85),(16,86),(17,87),(18,88),(19,89),(20,90),(21,91),(22,92),(23,93),(24,94),(25,95),(26,96),(27,97),(28,98),(29,57),(30,58),(31,59),(32,60),(33,61),(34,62),(35,63),(36,64),(37,65),(38,66),(39,67),(40,68),(41,69),(42,70),(43,71),(44,72),(45,73),(46,74),(47,75),(48,76),(49,77),(50,78),(51,79),(52,80),(53,81),(54,82),(55,83),(56,84),(113,162),(114,163),(115,164),(116,165),(117,166),(118,167),(119,168),(120,141),(121,142),(122,143),(123,144),(124,145),(125,146),(126,147),(127,148),(128,149),(129,150),(130,151),(131,152),(132,153),(133,154),(134,155),(135,156),(136,157),(137,158),(138,159),(139,160),(140,161),(169,207),(170,208),(171,209),(172,210),(173,211),(174,212),(175,213),(176,214),(177,215),(178,216),(179,217),(180,218),(181,219),(182,220),(183,221),(184,222),(185,223),(186,224),(187,197),(188,198),(189,199),(190,200),(191,201),(192,202),(193,203),(194,204),(195,205),(196,206)], [(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)], [(1,50,92,57,15,36,106,71),(2,49,93,84,16,35,107,70),(3,48,94,83,17,34,108,69),(4,47,95,82,18,33,109,68),(5,46,96,81,19,32,110,67),(6,45,97,80,20,31,111,66),(7,44,98,79,21,30,112,65),(8,43,99,78,22,29,85,64),(9,42,100,77,23,56,86,63),(10,41,101,76,24,55,87,62),(11,40,102,75,25,54,88,61),(12,39,103,74,26,53,89,60),(13,38,104,73,27,52,90,59),(14,37,105,72,28,51,91,58),(113,189,141,220,127,175,155,206),(114,188,142,219,128,174,156,205),(115,187,143,218,129,173,157,204),(116,186,144,217,130,172,158,203),(117,185,145,216,131,171,159,202),(118,184,146,215,132,170,160,201),(119,183,147,214,133,169,161,200),(120,182,148,213,134,196,162,199),(121,181,149,212,135,195,163,198),(122,180,150,211,136,194,164,197),(123,179,151,210,137,193,165,224),(124,178,152,209,138,192,166,223),(125,177,153,208,139,191,167,222),(126,176,154,207,140,190,168,221)], [(1,197,15,211),(2,224,16,210),(3,223,17,209),(4,222,18,208),(5,221,19,207),(6,220,20,206),(7,219,21,205),(8,218,22,204),(9,217,23,203),(10,216,24,202),(11,215,25,201),(12,214,26,200),(13,213,27,199),(14,212,28,198),(29,150,43,164),(30,149,44,163),(31,148,45,162),(32,147,46,161),(33,146,47,160),(34,145,48,159),(35,144,49,158),(36,143,50,157),(37,142,51,156),(38,141,52,155),(39,168,53,154),(40,167,54,153),(41,166,55,152),(42,165,56,151),(57,129,71,115),(58,128,72,114),(59,127,73,113),(60,126,74,140),(61,125,75,139),(62,124,76,138),(63,123,77,137),(64,122,78,136),(65,121,79,135),(66,120,80,134),(67,119,81,133),(68,118,82,132),(69,117,83,131),(70,116,84,130),(85,173,99,187),(86,172,100,186),(87,171,101,185),(88,170,102,184),(89,169,103,183),(90,196,104,182),(91,195,105,181),(92,194,106,180),(93,193,107,179),(94,192,108,178),(95,191,109,177),(96,190,110,176),(97,189,111,175),(98,188,112,174)])
82 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 | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28R | 56A | ··· | 56X |
| 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 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | - | |||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | C4 | D4 | D7 | D14 | D14 | C4×D7 | D28 | C7⋊D4 | C4×D7 | C4.10D4 | C28.47D4 |
| kernel | C2×C28.47D4 | C28.47D4 | C2×C4.Dic7 | C14×M4(2) | C22×Dic14 | C2×Dic14 | C22×Dic7 | C2×C28 | C2×M4(2) | M4(2) | C22×C4 | C2×C4 | C2×C4 | C2×C4 | C23 | C14 | C2 |
| # reps | 1 | 4 | 1 | 1 | 1 | 4 | 4 | 4 | 3 | 6 | 3 | 6 | 12 | 12 | 6 | 2 | 12 |
Matrix representation of C2×C28.47D4 ►in GL6(𝔽113)
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 10 | 89 | 0 | 0 | 0 | 0 |
| 24 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 100 | 0 | 0 |
| 0 | 0 | 13 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 19 | 100 |
| 0 | 0 | 0 | 0 | 13 | 9 |
| 107 | 64 | 0 | 0 | 0 | 0 |
| 33 | 6 | 0 | 0 | 0 | 0 |
| 0 | 0 | 79 | 112 | 62 | 69 |
| 0 | 0 | 25 | 34 | 108 | 51 |
| 0 | 0 | 43 | 38 | 79 | 112 |
| 0 | 0 | 45 | 70 | 25 | 34 |
| 107 | 64 | 0 | 0 | 0 | 0 |
| 33 | 6 | 0 | 0 | 0 | 0 |
| 0 | 0 | 82 | 22 | 0 | 0 |
| 0 | 0 | 59 | 31 | 0 | 0 |
| 0 | 0 | 0 | 0 | 31 | 91 |
| 0 | 0 | 0 | 0 | 54 | 82 |
G:=sub<GL(6,GF(113))| [112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[10,24,0,0,0,0,89,112,0,0,0,0,0,0,19,13,0,0,0,0,100,9,0,0,0,0,0,0,19,13,0,0,0,0,100,9],[107,33,0,0,0,0,64,6,0,0,0,0,0,0,79,25,43,45,0,0,112,34,38,70,0,0,62,108,79,25,0,0,69,51,112,34],[107,33,0,0,0,0,64,6,0,0,0,0,0,0,82,59,0,0,0,0,22,31,0,0,0,0,0,0,31,54,0,0,0,0,91,82] >;
C2×C28.47D4 in GAP, Magma, Sage, TeX
C_2\times C_{28}._{47}D_4 % in TeX
G:=Group("C2xC28.47D4"); // GroupNames label
G:=SmallGroup(448,670);
// by ID
G=gap.SmallGroup(448,670);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,422,58,1123,136,438,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^28=1,c^4=d^2=b^14,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d^-1=b^-1,d*c*d^-1=b^21*c^3>;
// generators/relations