metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28.47D4, D8.10D14, C28.18C24, C56.39C23, Q16.12D14, SD16.2D14, Dic14.47D4, Dic14.12C23, Dic28.16C22, C4○D8⋊6D7, C7⋊3(Q8○D8), (D7×Q16)⋊7C2, C7⋊D4.3D4, C7⋊C8.9C23, D8⋊3D7⋊7C2, C4.145(D4×D7), D4.D7.C22, C4○D4.13D14, D14.31(C2×D4), C28.351(C2×D4), (C2×C8).106D14, SD16⋊D7⋊6C2, (C8×D7).8C22, C4.18(C23×D7), C22.10(D4×D7), C8.18(C22×D7), (C2×Dic28)⋊23C2, D4.9D14⋊8C2, D28.2C4⋊8C2, (Q8×D7).2C22, Dic7.36(C2×D4), (C7×D8).10C22, (C7×D4).12C23, D4.12(C22×D7), (C4×D7).11C23, C8⋊D7.2C22, D4.10D14⋊6C2, (C7×Q8).12C23, Q8.12(C22×D7), C7⋊Q16.2C22, (C2×C56).106C22, (C2×C28).535C23, C4○D28.56C22, D4⋊2D7.2C22, C14.119(C22×D4), (C7×Q16).12C22, (C7×SD16).2C22, C4.Dic7.49C22, (C2×Dic14).200C22, C2.92(C2×D4×D7), (C7×C4○D8)⋊6C2, (C2×C14).15(C2×D4), (C7×C4○D4).23C22, (C2×C4).234(C22×D7), SmallGroup(448,1224)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28.47D4
G = < a,b,c,d | a28=b2=1, c4=d2=a14, bab=a-1, ac=ca, ad=da, bc=cb, bd=db, dcd-1=a14c3 >
Subgroups: 1108 in 248 conjugacy classes, 99 normal (31 characteristic)
C1, C2, C2 [×5], C4 [×2], C4 [×8], C22, C22 [×4], C7, C8 [×2], C8 [×2], C2×C4, C2×C4 [×14], D4 [×2], D4 [×9], Q8 [×2], Q8 [×11], D7 [×2], C14, C14 [×3], C2×C8, C2×C8 [×2], M4(2) [×3], D8, SD16 [×2], SD16 [×4], Q16, Q16 [×8], C2×Q8 [×8], C4○D4 [×2], C4○D4 [×11], Dic7 [×2], Dic7 [×4], C28 [×2], C28 [×2], D14 [×2], C2×C14, C2×C14 [×2], C8○D4, C2×Q16 [×3], C4○D8, C4○D8 [×2], C8.C22 [×6], 2- 1+4 [×2], C7⋊C8 [×2], C56 [×2], Dic14, Dic14 [×4], Dic14 [×6], C4×D7 [×2], C4×D7 [×4], D28, C2×Dic7 [×6], C7⋊D4 [×2], C7⋊D4 [×4], C2×C28, C2×C28 [×2], C7×D4 [×2], C7×D4 [×2], C7×Q8 [×2], Q8○D8, C8×D7 [×2], C8⋊D7 [×2], Dic28 [×4], C4.Dic7, D4.D7 [×4], C7⋊Q16 [×4], C2×C56, C7×D8, C7×SD16 [×2], C7×Q16, C2×Dic14 [×2], C2×Dic14 [×2], C4○D28, C4○D28 [×2], D4⋊2D7 [×4], D4⋊2D7 [×4], Q8×D7 [×4], C7×C4○D4 [×2], D28.2C4, C2×Dic28, D8⋊3D7 [×2], SD16⋊D7 [×4], D7×Q16 [×2], D4.9D14 [×2], C7×C4○D8, D4.10D14 [×2], D28.47D4
Quotients: C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D7, C2×D4 [×6], C24, D14 [×7], C22×D4, C22×D7 [×7], Q8○D8, D4×D7 [×2], C23×D7, C2×D4×D7, D28.47D4
►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 7)(2 6)(3 5)(8 28)(9 27)(10 26)(11 25)(12 24)(13 23)(14 22)(15 21)(16 20)(17 19)(29 35)(30 34)(31 33)(36 56)(37 55)(38 54)(39 53)(40 52)(41 51)(42 50)(43 49)(44 48)(45 47)(57 75)(58 74)(59 73)(60 72)(61 71)(62 70)(63 69)(64 68)(65 67)(76 84)(77 83)(78 82)(79 81)(85 103)(86 102)(87 101)(88 100)(89 99)(90 98)(91 97)(92 96)(93 95)(104 112)(105 111)(106 110)(107 109)(113 139)(114 138)(115 137)(116 136)(117 135)(118 134)(119 133)(120 132)(121 131)(122 130)(123 129)(124 128)(125 127)(141 157)(142 156)(143 155)(144 154)(145 153)(146 152)(147 151)(148 150)(158 168)(159 167)(160 166)(161 165)(162 164)(169 185)(170 184)(171 183)(172 182)(173 181)(174 180)(175 179)(176 178)(186 196)(187 195)(188 194)(189 193)(190 192)(197 215)(198 214)(199 213)(200 212)(201 211)(202 210)(203 209)(204 208)(205 207)(216 224)(217 223)(218 222)(219 221)
(1 91 203 43 15 105 217 29)(2 92 204 44 16 106 218 30)(3 93 205 45 17 107 219 31)(4 94 206 46 18 108 220 32)(5 95 207 47 19 109 221 33)(6 96 208 48 20 110 222 34)(7 97 209 49 21 111 223 35)(8 98 210 50 22 112 224 36)(9 99 211 51 23 85 197 37)(10 100 212 52 24 86 198 38)(11 101 213 53 25 87 199 39)(12 102 214 54 26 88 200 40)(13 103 215 55 27 89 201 41)(14 104 216 56 28 90 202 42)(57 154 131 196 71 168 117 182)(58 155 132 169 72 141 118 183)(59 156 133 170 73 142 119 184)(60 157 134 171 74 143 120 185)(61 158 135 172 75 144 121 186)(62 159 136 173 76 145 122 187)(63 160 137 174 77 146 123 188)(64 161 138 175 78 147 124 189)(65 162 139 176 79 148 125 190)(66 163 140 177 80 149 126 191)(67 164 113 178 81 150 127 192)(68 165 114 179 82 151 128 193)(69 166 115 180 83 152 129 194)(70 167 116 181 84 153 130 195)
(1 174 15 188)(2 175 16 189)(3 176 17 190)(4 177 18 191)(5 178 19 192)(6 179 20 193)(7 180 21 194)(8 181 22 195)(9 182 23 196)(10 183 24 169)(11 184 25 170)(12 185 26 171)(13 186 27 172)(14 187 28 173)(29 77 43 63)(30 78 44 64)(31 79 45 65)(32 80 46 66)(33 81 47 67)(34 82 48 68)(35 83 49 69)(36 84 50 70)(37 57 51 71)(38 58 52 72)(39 59 53 73)(40 60 54 74)(41 61 55 75)(42 62 56 76)(85 131 99 117)(86 132 100 118)(87 133 101 119)(88 134 102 120)(89 135 103 121)(90 136 104 122)(91 137 105 123)(92 138 106 124)(93 139 107 125)(94 140 108 126)(95 113 109 127)(96 114 110 128)(97 115 111 129)(98 116 112 130)(141 198 155 212)(142 199 156 213)(143 200 157 214)(144 201 158 215)(145 202 159 216)(146 203 160 217)(147 204 161 218)(148 205 162 219)(149 206 163 220)(150 207 164 221)(151 208 165 222)(152 209 166 223)(153 210 167 224)(154 211 168 197)
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), (1,7)(2,6)(3,5)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)(29,35)(30,34)(31,33)(36,56)(37,55)(38,54)(39,53)(40,52)(41,51)(42,50)(43,49)(44,48)(45,47)(57,75)(58,74)(59,73)(60,72)(61,71)(62,70)(63,69)(64,68)(65,67)(76,84)(77,83)(78,82)(79,81)(85,103)(86,102)(87,101)(88,100)(89,99)(90,98)(91,97)(92,96)(93,95)(104,112)(105,111)(106,110)(107,109)(113,139)(114,138)(115,137)(116,136)(117,135)(118,134)(119,133)(120,132)(121,131)(122,130)(123,129)(124,128)(125,127)(141,157)(142,156)(143,155)(144,154)(145,153)(146,152)(147,151)(148,150)(158,168)(159,167)(160,166)(161,165)(162,164)(169,185)(170,184)(171,183)(172,182)(173,181)(174,180)(175,179)(176,178)(186,196)(187,195)(188,194)(189,193)(190,192)(197,215)(198,214)(199,213)(200,212)(201,211)(202,210)(203,209)(204,208)(205,207)(216,224)(217,223)(218,222)(219,221), (1,91,203,43,15,105,217,29)(2,92,204,44,16,106,218,30)(3,93,205,45,17,107,219,31)(4,94,206,46,18,108,220,32)(5,95,207,47,19,109,221,33)(6,96,208,48,20,110,222,34)(7,97,209,49,21,111,223,35)(8,98,210,50,22,112,224,36)(9,99,211,51,23,85,197,37)(10,100,212,52,24,86,198,38)(11,101,213,53,25,87,199,39)(12,102,214,54,26,88,200,40)(13,103,215,55,27,89,201,41)(14,104,216,56,28,90,202,42)(57,154,131,196,71,168,117,182)(58,155,132,169,72,141,118,183)(59,156,133,170,73,142,119,184)(60,157,134,171,74,143,120,185)(61,158,135,172,75,144,121,186)(62,159,136,173,76,145,122,187)(63,160,137,174,77,146,123,188)(64,161,138,175,78,147,124,189)(65,162,139,176,79,148,125,190)(66,163,140,177,80,149,126,191)(67,164,113,178,81,150,127,192)(68,165,114,179,82,151,128,193)(69,166,115,180,83,152,129,194)(70,167,116,181,84,153,130,195), (1,174,15,188)(2,175,16,189)(3,176,17,190)(4,177,18,191)(5,178,19,192)(6,179,20,193)(7,180,21,194)(8,181,22,195)(9,182,23,196)(10,183,24,169)(11,184,25,170)(12,185,26,171)(13,186,27,172)(14,187,28,173)(29,77,43,63)(30,78,44,64)(31,79,45,65)(32,80,46,66)(33,81,47,67)(34,82,48,68)(35,83,49,69)(36,84,50,70)(37,57,51,71)(38,58,52,72)(39,59,53,73)(40,60,54,74)(41,61,55,75)(42,62,56,76)(85,131,99,117)(86,132,100,118)(87,133,101,119)(88,134,102,120)(89,135,103,121)(90,136,104,122)(91,137,105,123)(92,138,106,124)(93,139,107,125)(94,140,108,126)(95,113,109,127)(96,114,110,128)(97,115,111,129)(98,116,112,130)(141,198,155,212)(142,199,156,213)(143,200,157,214)(144,201,158,215)(145,202,159,216)(146,203,160,217)(147,204,161,218)(148,205,162,219)(149,206,163,220)(150,207,164,221)(151,208,165,222)(152,209,166,223)(153,210,167,224)(154,211,168,197)>;
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), (1,7)(2,6)(3,5)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)(29,35)(30,34)(31,33)(36,56)(37,55)(38,54)(39,53)(40,52)(41,51)(42,50)(43,49)(44,48)(45,47)(57,75)(58,74)(59,73)(60,72)(61,71)(62,70)(63,69)(64,68)(65,67)(76,84)(77,83)(78,82)(79,81)(85,103)(86,102)(87,101)(88,100)(89,99)(90,98)(91,97)(92,96)(93,95)(104,112)(105,111)(106,110)(107,109)(113,139)(114,138)(115,137)(116,136)(117,135)(118,134)(119,133)(120,132)(121,131)(122,130)(123,129)(124,128)(125,127)(141,157)(142,156)(143,155)(144,154)(145,153)(146,152)(147,151)(148,150)(158,168)(159,167)(160,166)(161,165)(162,164)(169,185)(170,184)(171,183)(172,182)(173,181)(174,180)(175,179)(176,178)(186,196)(187,195)(188,194)(189,193)(190,192)(197,215)(198,214)(199,213)(200,212)(201,211)(202,210)(203,209)(204,208)(205,207)(216,224)(217,223)(218,222)(219,221), (1,91,203,43,15,105,217,29)(2,92,204,44,16,106,218,30)(3,93,205,45,17,107,219,31)(4,94,206,46,18,108,220,32)(5,95,207,47,19,109,221,33)(6,96,208,48,20,110,222,34)(7,97,209,49,21,111,223,35)(8,98,210,50,22,112,224,36)(9,99,211,51,23,85,197,37)(10,100,212,52,24,86,198,38)(11,101,213,53,25,87,199,39)(12,102,214,54,26,88,200,40)(13,103,215,55,27,89,201,41)(14,104,216,56,28,90,202,42)(57,154,131,196,71,168,117,182)(58,155,132,169,72,141,118,183)(59,156,133,170,73,142,119,184)(60,157,134,171,74,143,120,185)(61,158,135,172,75,144,121,186)(62,159,136,173,76,145,122,187)(63,160,137,174,77,146,123,188)(64,161,138,175,78,147,124,189)(65,162,139,176,79,148,125,190)(66,163,140,177,80,149,126,191)(67,164,113,178,81,150,127,192)(68,165,114,179,82,151,128,193)(69,166,115,180,83,152,129,194)(70,167,116,181,84,153,130,195), (1,174,15,188)(2,175,16,189)(3,176,17,190)(4,177,18,191)(5,178,19,192)(6,179,20,193)(7,180,21,194)(8,181,22,195)(9,182,23,196)(10,183,24,169)(11,184,25,170)(12,185,26,171)(13,186,27,172)(14,187,28,173)(29,77,43,63)(30,78,44,64)(31,79,45,65)(32,80,46,66)(33,81,47,67)(34,82,48,68)(35,83,49,69)(36,84,50,70)(37,57,51,71)(38,58,52,72)(39,59,53,73)(40,60,54,74)(41,61,55,75)(42,62,56,76)(85,131,99,117)(86,132,100,118)(87,133,101,119)(88,134,102,120)(89,135,103,121)(90,136,104,122)(91,137,105,123)(92,138,106,124)(93,139,107,125)(94,140,108,126)(95,113,109,127)(96,114,110,128)(97,115,111,129)(98,116,112,130)(141,198,155,212)(142,199,156,213)(143,200,157,214)(144,201,158,215)(145,202,159,216)(146,203,160,217)(147,204,161,218)(148,205,162,219)(149,206,163,220)(150,207,164,221)(151,208,165,222)(152,209,166,223)(153,210,167,224)(154,211,168,197) );
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)], [(1,7),(2,6),(3,5),(8,28),(9,27),(10,26),(11,25),(12,24),(13,23),(14,22),(15,21),(16,20),(17,19),(29,35),(30,34),(31,33),(36,56),(37,55),(38,54),(39,53),(40,52),(41,51),(42,50),(43,49),(44,48),(45,47),(57,75),(58,74),(59,73),(60,72),(61,71),(62,70),(63,69),(64,68),(65,67),(76,84),(77,83),(78,82),(79,81),(85,103),(86,102),(87,101),(88,100),(89,99),(90,98),(91,97),(92,96),(93,95),(104,112),(105,111),(106,110),(107,109),(113,139),(114,138),(115,137),(116,136),(117,135),(118,134),(119,133),(120,132),(121,131),(122,130),(123,129),(124,128),(125,127),(141,157),(142,156),(143,155),(144,154),(145,153),(146,152),(147,151),(148,150),(158,168),(159,167),(160,166),(161,165),(162,164),(169,185),(170,184),(171,183),(172,182),(173,181),(174,180),(175,179),(176,178),(186,196),(187,195),(188,194),(189,193),(190,192),(197,215),(198,214),(199,213),(200,212),(201,211),(202,210),(203,209),(204,208),(205,207),(216,224),(217,223),(218,222),(219,221)], [(1,91,203,43,15,105,217,29),(2,92,204,44,16,106,218,30),(3,93,205,45,17,107,219,31),(4,94,206,46,18,108,220,32),(5,95,207,47,19,109,221,33),(6,96,208,48,20,110,222,34),(7,97,209,49,21,111,223,35),(8,98,210,50,22,112,224,36),(9,99,211,51,23,85,197,37),(10,100,212,52,24,86,198,38),(11,101,213,53,25,87,199,39),(12,102,214,54,26,88,200,40),(13,103,215,55,27,89,201,41),(14,104,216,56,28,90,202,42),(57,154,131,196,71,168,117,182),(58,155,132,169,72,141,118,183),(59,156,133,170,73,142,119,184),(60,157,134,171,74,143,120,185),(61,158,135,172,75,144,121,186),(62,159,136,173,76,145,122,187),(63,160,137,174,77,146,123,188),(64,161,138,175,78,147,124,189),(65,162,139,176,79,148,125,190),(66,163,140,177,80,149,126,191),(67,164,113,178,81,150,127,192),(68,165,114,179,82,151,128,193),(69,166,115,180,83,152,129,194),(70,167,116,181,84,153,130,195)], [(1,174,15,188),(2,175,16,189),(3,176,17,190),(4,177,18,191),(5,178,19,192),(6,179,20,193),(7,180,21,194),(8,181,22,195),(9,182,23,196),(10,183,24,169),(11,184,25,170),(12,185,26,171),(13,186,27,172),(14,187,28,173),(29,77,43,63),(30,78,44,64),(31,79,45,65),(32,80,46,66),(33,81,47,67),(34,82,48,68),(35,83,49,69),(36,84,50,70),(37,57,51,71),(38,58,52,72),(39,59,53,73),(40,60,54,74),(41,61,55,75),(42,62,56,76),(85,131,99,117),(86,132,100,118),(87,133,101,119),(88,134,102,120),(89,135,103,121),(90,136,104,122),(91,137,105,123),(92,138,106,124),(93,139,107,125),(94,140,108,126),(95,113,109,127),(96,114,110,128),(97,115,111,129),(98,116,112,130),(141,198,155,212),(142,199,156,213),(143,200,157,214),(144,201,158,215),(145,202,159,216),(146,203,160,217),(147,204,161,218),(148,205,162,219),(149,206,163,220),(150,207,164,221),(151,208,165,222),(152,209,166,223),(153,210,167,224),(154,211,168,197)])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 8E | 14A | 14B | 14C | 14D | 14E | 14F | 14G | ··· | 14L | 28A | ··· | 28F | 28G | 28H | 28I | 28J | ··· | 28O | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 14 | 14 | 14 | 14 | 14 | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | 28 | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 2 | 4 | 4 | 14 | 14 | 2 | 2 | 4 | 4 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | 2 | 4 | 28 | 28 | 2 | 2 | 2 | 4 | 4 | 4 | 8 | ··· | 8 | 2 | ··· | 2 | 4 | 4 | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | - |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D7 | D14 | D14 | D14 | D14 | D14 | Q8○D8 | D4×D7 | D4×D7 | D28.47D4 |
| kernel | D28.47D4 | D28.2C4 | C2×Dic28 | D8⋊3D7 | SD16⋊D7 | D7×Q16 | D4.9D14 | C7×C4○D8 | D4.10D14 | Dic14 | D28 | C7⋊D4 | C4○D8 | C2×C8 | D8 | SD16 | Q16 | C4○D4 | C7 | C4 | C22 | C1 |
| # reps | 1 | 1 | 1 | 2 | 4 | 2 | 2 | 1 | 2 | 1 | 1 | 2 | 3 | 3 | 3 | 6 | 3 | 6 | 2 | 3 | 3 | 12 |
Matrix representation of D28.47D4 ►in GL4(𝔽113) generated by
| 4 | 36 | 0 | 0 |
| 41 | 2 | 0 | 0 |
| 0 | 0 | 96 | 36 |
| 0 | 0 | 77 | 23 |
| 23 | 103 | 0 | 0 |
| 98 | 90 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 89 | 112 |
| 62 | 0 | 32 | 58 |
| 0 | 62 | 74 | 94 |
| 96 | 73 | 0 | 0 |
| 23 | 100 | 0 | 0 |
| 97 | 0 | 62 | 70 |
| 0 | 97 | 101 | 55 |
| 67 | 38 | 16 | 0 |
| 29 | 18 | 0 | 16 |
G:=sub<GL(4,GF(113))| [4,41,0,0,36,2,0,0,0,0,96,77,0,0,36,23],[23,98,0,0,103,90,0,0,0,0,1,89,0,0,0,112],[62,0,96,23,0,62,73,100,32,74,0,0,58,94,0,0],[97,0,67,29,0,97,38,18,62,101,16,0,70,55,0,16] >;
D28.47D4 in GAP, Magma, Sage, TeX
D_{28}._{47}D_4 % in TeX
G:=Group("D28.47D4"); // GroupNames label
G:=SmallGroup(448,1224);
// by ID
G=gap.SmallGroup(448,1224);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,387,184,570,185,136,438,235,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=b^2=1,c^4=d^2=a^14,b*a*b=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=a^14*c^3>;
// generators/relations