metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28.32D4, C23.11D28, Dic14.31D4, C22⋊C8⋊5D7, C4.121(D4×D7), C2.D56⋊5C2, C14.9C22≀C2, (C2×Dic28)⋊2C2, C14.8(C4○D8), (C2×C28).240D4, C28.333(C2×D4), (C2×C4).118D28, (C2×C8).108D14, C7⋊1(D4.7D4), (C2×C56).3C22, (C22×C4).83D14, (C22×C14).53D4, C28.48D4⋊16C2, C28.44D4⋊10C2, (C2×C28).743C23, C22.106(C2×D28), C14.9(C8.C22), C4⋊Dic7.12C22, C2.10(D56⋊7C2), C2.12(C22⋊D28), C2.12(C8.D14), (C2×D28).192C22, (C22×C28).96C22, (C2×Dic14).210C22, (C7×C22⋊C8)⋊7C2, (C2×C56⋊C2)⋊10C2, (C2×C4○D28).2C2, (C2×C14).126(C2×D4), (C2×C4).688(C22×D7), SmallGroup(448,267)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28.32D4
G = < a,b,c,d | a28=b2=1, c4=d2=a14, bab=a-1, ac=ca, ad=da, cbc-1=a7b, bd=db, dcd-1=a21c3 >
Subgroups: 892 in 152 conjugacy classes, 43 normal (39 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C22⋊C4, C4⋊C4, C2×C8, SD16, Q16, C22×C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic7, C28, C28, D14, C2×C14, C2×C14, C22⋊C8, D4⋊C4, Q8⋊C4, C22⋊Q8, C2×SD16, C2×Q16, C2×C4○D4, C56, Dic14, Dic14, C4×D7, D28, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C22×D7, C22×C14, D4.7D4, C56⋊C2, Dic28, Dic7⋊C4, C4⋊Dic7, C23.D7, C2×C56, C2×Dic14, C2×C4×D7, C2×D28, C4○D28, C2×C7⋊D4, C22×C28, C28.44D4, C2.D56, C7×C22⋊C8, C2×C56⋊C2, C2×Dic28, C28.48D4, C2×C4○D28, D28.32D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, D14, C22≀C2, C4○D8, C8.C22, D28, C22×D7, D4.7D4, C2×D28, D4×D7, C22⋊D28, D56⋊7C2, C8.D14, D28.32D4
►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 28)(2 27)(3 26)(4 25)(5 24)(6 23)(7 22)(8 21)(9 20)(10 19)(11 18)(12 17)(13 16)(14 15)(30 56)(31 55)(32 54)(33 53)(34 52)(35 51)(36 50)(37 49)(38 48)(39 47)(40 46)(41 45)(42 44)(57 71)(58 70)(59 69)(60 68)(61 67)(62 66)(63 65)(72 84)(73 83)(74 82)(75 81)(76 80)(77 79)(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)(113 118)(114 117)(115 116)(119 140)(120 139)(121 138)(122 137)(123 136)(124 135)(125 134)(126 133)(127 132)(128 131)(129 130)(141 156)(142 155)(143 154)(144 153)(145 152)(146 151)(147 150)(148 149)(157 168)(158 167)(159 166)(160 165)(161 164)(162 163)(169 171)(172 196)(173 195)(174 194)(175 193)(176 192)(177 191)(178 190)(179 189)(180 188)(181 187)(182 186)(183 185)(197 212)(198 211)(199 210)(200 209)(201 208)(202 207)(203 206)(204 205)(213 224)(214 223)(215 222)(216 221)(217 220)(218 219)
(1 98 123 54 15 112 137 40)(2 99 124 55 16 85 138 41)(3 100 125 56 17 86 139 42)(4 101 126 29 18 87 140 43)(5 102 127 30 19 88 113 44)(6 103 128 31 20 89 114 45)(7 104 129 32 21 90 115 46)(8 105 130 33 22 91 116 47)(9 106 131 34 23 92 117 48)(10 107 132 35 24 93 118 49)(11 108 133 36 25 94 119 50)(12 109 134 37 26 95 120 51)(13 110 135 38 27 96 121 52)(14 111 136 39 28 97 122 53)(57 159 184 222 71 145 170 208)(58 160 185 223 72 146 171 209)(59 161 186 224 73 147 172 210)(60 162 187 197 74 148 173 211)(61 163 188 198 75 149 174 212)(62 164 189 199 76 150 175 213)(63 165 190 200 77 151 176 214)(64 166 191 201 78 152 177 215)(65 167 192 202 79 153 178 216)(66 168 193 203 80 154 179 217)(67 141 194 204 81 155 180 218)(68 142 195 205 82 156 181 219)(69 143 196 206 83 157 182 220)(70 144 169 207 84 158 183 221)
(1 205 15 219)(2 206 16 220)(3 207 17 221)(4 208 18 222)(5 209 19 223)(6 210 20 224)(7 211 21 197)(8 212 22 198)(9 213 23 199)(10 214 24 200)(11 215 25 201)(12 216 26 202)(13 217 27 203)(14 218 28 204)(29 64 43 78)(30 65 44 79)(31 66 45 80)(32 67 46 81)(33 68 47 82)(34 69 48 83)(35 70 49 84)(36 71 50 57)(37 72 51 58)(38 73 52 59)(39 74 53 60)(40 75 54 61)(41 76 55 62)(42 77 56 63)(85 189 99 175)(86 190 100 176)(87 191 101 177)(88 192 102 178)(89 193 103 179)(90 194 104 180)(91 195 105 181)(92 196 106 182)(93 169 107 183)(94 170 108 184)(95 171 109 185)(96 172 110 186)(97 173 111 187)(98 174 112 188)(113 146 127 160)(114 147 128 161)(115 148 129 162)(116 149 130 163)(117 150 131 164)(118 151 132 165)(119 152 133 166)(120 153 134 167)(121 154 135 168)(122 155 136 141)(123 156 137 142)(124 157 138 143)(125 158 139 144)(126 159 140 145)
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), (1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(30,56)(31,55)(32,54)(33,53)(34,52)(35,51)(36,50)(37,49)(38,48)(39,47)(40,46)(41,45)(42,44)(57,71)(58,70)(59,69)(60,68)(61,67)(62,66)(63,65)(72,84)(73,83)(74,82)(75,81)(76,80)(77,79)(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)(113,118)(114,117)(115,116)(119,140)(120,139)(121,138)(122,137)(123,136)(124,135)(125,134)(126,133)(127,132)(128,131)(129,130)(141,156)(142,155)(143,154)(144,153)(145,152)(146,151)(147,150)(148,149)(157,168)(158,167)(159,166)(160,165)(161,164)(162,163)(169,171)(172,196)(173,195)(174,194)(175,193)(176,192)(177,191)(178,190)(179,189)(180,188)(181,187)(182,186)(183,185)(197,212)(198,211)(199,210)(200,209)(201,208)(202,207)(203,206)(204,205)(213,224)(214,223)(215,222)(216,221)(217,220)(218,219), (1,98,123,54,15,112,137,40)(2,99,124,55,16,85,138,41)(3,100,125,56,17,86,139,42)(4,101,126,29,18,87,140,43)(5,102,127,30,19,88,113,44)(6,103,128,31,20,89,114,45)(7,104,129,32,21,90,115,46)(8,105,130,33,22,91,116,47)(9,106,131,34,23,92,117,48)(10,107,132,35,24,93,118,49)(11,108,133,36,25,94,119,50)(12,109,134,37,26,95,120,51)(13,110,135,38,27,96,121,52)(14,111,136,39,28,97,122,53)(57,159,184,222,71,145,170,208)(58,160,185,223,72,146,171,209)(59,161,186,224,73,147,172,210)(60,162,187,197,74,148,173,211)(61,163,188,198,75,149,174,212)(62,164,189,199,76,150,175,213)(63,165,190,200,77,151,176,214)(64,166,191,201,78,152,177,215)(65,167,192,202,79,153,178,216)(66,168,193,203,80,154,179,217)(67,141,194,204,81,155,180,218)(68,142,195,205,82,156,181,219)(69,143,196,206,83,157,182,220)(70,144,169,207,84,158,183,221), (1,205,15,219)(2,206,16,220)(3,207,17,221)(4,208,18,222)(5,209,19,223)(6,210,20,224)(7,211,21,197)(8,212,22,198)(9,213,23,199)(10,214,24,200)(11,215,25,201)(12,216,26,202)(13,217,27,203)(14,218,28,204)(29,64,43,78)(30,65,44,79)(31,66,45,80)(32,67,46,81)(33,68,47,82)(34,69,48,83)(35,70,49,84)(36,71,50,57)(37,72,51,58)(38,73,52,59)(39,74,53,60)(40,75,54,61)(41,76,55,62)(42,77,56,63)(85,189,99,175)(86,190,100,176)(87,191,101,177)(88,192,102,178)(89,193,103,179)(90,194,104,180)(91,195,105,181)(92,196,106,182)(93,169,107,183)(94,170,108,184)(95,171,109,185)(96,172,110,186)(97,173,111,187)(98,174,112,188)(113,146,127,160)(114,147,128,161)(115,148,129,162)(116,149,130,163)(117,150,131,164)(118,151,132,165)(119,152,133,166)(120,153,134,167)(121,154,135,168)(122,155,136,141)(123,156,137,142)(124,157,138,143)(125,158,139,144)(126,159,140,145)>;
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), (1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(30,56)(31,55)(32,54)(33,53)(34,52)(35,51)(36,50)(37,49)(38,48)(39,47)(40,46)(41,45)(42,44)(57,71)(58,70)(59,69)(60,68)(61,67)(62,66)(63,65)(72,84)(73,83)(74,82)(75,81)(76,80)(77,79)(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)(113,118)(114,117)(115,116)(119,140)(120,139)(121,138)(122,137)(123,136)(124,135)(125,134)(126,133)(127,132)(128,131)(129,130)(141,156)(142,155)(143,154)(144,153)(145,152)(146,151)(147,150)(148,149)(157,168)(158,167)(159,166)(160,165)(161,164)(162,163)(169,171)(172,196)(173,195)(174,194)(175,193)(176,192)(177,191)(178,190)(179,189)(180,188)(181,187)(182,186)(183,185)(197,212)(198,211)(199,210)(200,209)(201,208)(202,207)(203,206)(204,205)(213,224)(214,223)(215,222)(216,221)(217,220)(218,219), (1,98,123,54,15,112,137,40)(2,99,124,55,16,85,138,41)(3,100,125,56,17,86,139,42)(4,101,126,29,18,87,140,43)(5,102,127,30,19,88,113,44)(6,103,128,31,20,89,114,45)(7,104,129,32,21,90,115,46)(8,105,130,33,22,91,116,47)(9,106,131,34,23,92,117,48)(10,107,132,35,24,93,118,49)(11,108,133,36,25,94,119,50)(12,109,134,37,26,95,120,51)(13,110,135,38,27,96,121,52)(14,111,136,39,28,97,122,53)(57,159,184,222,71,145,170,208)(58,160,185,223,72,146,171,209)(59,161,186,224,73,147,172,210)(60,162,187,197,74,148,173,211)(61,163,188,198,75,149,174,212)(62,164,189,199,76,150,175,213)(63,165,190,200,77,151,176,214)(64,166,191,201,78,152,177,215)(65,167,192,202,79,153,178,216)(66,168,193,203,80,154,179,217)(67,141,194,204,81,155,180,218)(68,142,195,205,82,156,181,219)(69,143,196,206,83,157,182,220)(70,144,169,207,84,158,183,221), (1,205,15,219)(2,206,16,220)(3,207,17,221)(4,208,18,222)(5,209,19,223)(6,210,20,224)(7,211,21,197)(8,212,22,198)(9,213,23,199)(10,214,24,200)(11,215,25,201)(12,216,26,202)(13,217,27,203)(14,218,28,204)(29,64,43,78)(30,65,44,79)(31,66,45,80)(32,67,46,81)(33,68,47,82)(34,69,48,83)(35,70,49,84)(36,71,50,57)(37,72,51,58)(38,73,52,59)(39,74,53,60)(40,75,54,61)(41,76,55,62)(42,77,56,63)(85,189,99,175)(86,190,100,176)(87,191,101,177)(88,192,102,178)(89,193,103,179)(90,194,104,180)(91,195,105,181)(92,196,106,182)(93,169,107,183)(94,170,108,184)(95,171,109,185)(96,172,110,186)(97,173,111,187)(98,174,112,188)(113,146,127,160)(114,147,128,161)(115,148,129,162)(116,149,130,163)(117,150,131,164)(118,151,132,165)(119,152,133,166)(120,153,134,167)(121,154,135,168)(122,155,136,141)(123,156,137,142)(124,157,138,143)(125,158,139,144)(126,159,140,145) );
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)], [(1,28),(2,27),(3,26),(4,25),(5,24),(6,23),(7,22),(8,21),(9,20),(10,19),(11,18),(12,17),(13,16),(14,15),(30,56),(31,55),(32,54),(33,53),(34,52),(35,51),(36,50),(37,49),(38,48),(39,47),(40,46),(41,45),(42,44),(57,71),(58,70),(59,69),(60,68),(61,67),(62,66),(63,65),(72,84),(73,83),(74,82),(75,81),(76,80),(77,79),(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),(113,118),(114,117),(115,116),(119,140),(120,139),(121,138),(122,137),(123,136),(124,135),(125,134),(126,133),(127,132),(128,131),(129,130),(141,156),(142,155),(143,154),(144,153),(145,152),(146,151),(147,150),(148,149),(157,168),(158,167),(159,166),(160,165),(161,164),(162,163),(169,171),(172,196),(173,195),(174,194),(175,193),(176,192),(177,191),(178,190),(179,189),(180,188),(181,187),(182,186),(183,185),(197,212),(198,211),(199,210),(200,209),(201,208),(202,207),(203,206),(204,205),(213,224),(214,223),(215,222),(216,221),(217,220),(218,219)], [(1,98,123,54,15,112,137,40),(2,99,124,55,16,85,138,41),(3,100,125,56,17,86,139,42),(4,101,126,29,18,87,140,43),(5,102,127,30,19,88,113,44),(6,103,128,31,20,89,114,45),(7,104,129,32,21,90,115,46),(8,105,130,33,22,91,116,47),(9,106,131,34,23,92,117,48),(10,107,132,35,24,93,118,49),(11,108,133,36,25,94,119,50),(12,109,134,37,26,95,120,51),(13,110,135,38,27,96,121,52),(14,111,136,39,28,97,122,53),(57,159,184,222,71,145,170,208),(58,160,185,223,72,146,171,209),(59,161,186,224,73,147,172,210),(60,162,187,197,74,148,173,211),(61,163,188,198,75,149,174,212),(62,164,189,199,76,150,175,213),(63,165,190,200,77,151,176,214),(64,166,191,201,78,152,177,215),(65,167,192,202,79,153,178,216),(66,168,193,203,80,154,179,217),(67,141,194,204,81,155,180,218),(68,142,195,205,82,156,181,219),(69,143,196,206,83,157,182,220),(70,144,169,207,84,158,183,221)], [(1,205,15,219),(2,206,16,220),(3,207,17,221),(4,208,18,222),(5,209,19,223),(6,210,20,224),(7,211,21,197),(8,212,22,198),(9,213,23,199),(10,214,24,200),(11,215,25,201),(12,216,26,202),(13,217,27,203),(14,218,28,204),(29,64,43,78),(30,65,44,79),(31,66,45,80),(32,67,46,81),(33,68,47,82),(34,69,48,83),(35,70,49,84),(36,71,50,57),(37,72,51,58),(38,73,52,59),(39,74,53,60),(40,75,54,61),(41,76,55,62),(42,77,56,63),(85,189,99,175),(86,190,100,176),(87,191,101,177),(88,192,102,178),(89,193,103,179),(90,194,104,180),(91,195,105,181),(92,196,106,182),(93,169,107,183),(94,170,108,184),(95,171,109,185),(96,172,110,186),(97,173,111,187),(98,174,112,188),(113,146,127,160),(114,147,128,161),(115,148,129,162),(116,149,130,163),(117,150,131,164),(118,151,132,165),(119,152,133,166),(120,153,134,167),(121,154,135,168),(122,155,136,141),(123,156,137,142),(124,157,138,143),(125,158,139,144),(126,159,140,145)]])
79 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28R | 56A | ··· | 56X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 4 | 28 | 28 | 2 | 2 | 2 | 2 | 28 | 28 | 56 | 56 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
79 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 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D4 | D7 | D14 | D14 | C4○D8 | D28 | D28 | D56⋊7C2 | C8.C22 | D4×D7 | C8.D14 |
| kernel | D28.32D4 | C28.44D4 | C2.D56 | C7×C22⋊C8 | C2×C56⋊C2 | C2×Dic28 | C28.48D4 | C2×C4○D28 | Dic14 | D28 | C2×C28 | C22×C14 | C22⋊C8 | C2×C8 | C22×C4 | C14 | C2×C4 | C23 | C2 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 3 | 6 | 3 | 4 | 6 | 6 | 24 | 1 | 6 | 6 |
Matrix representation of D28.32D4 ►in GL4(𝔽113) generated by
| 4 | 81 | 0 | 0 |
| 32 | 55 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 4 | 81 | 0 | 0 |
| 4 | 109 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 78 | 1 |
| 72 | 65 | 0 | 0 |
| 48 | 92 | 0 | 0 |
| 0 | 0 | 66 | 106 |
| 0 | 0 | 41 | 47 |
| 15 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 35 | 112 |
G:=sub<GL(4,GF(113))| [4,32,0,0,81,55,0,0,0,0,112,0,0,0,0,112],[4,4,0,0,81,109,0,0,0,0,112,78,0,0,0,1],[72,48,0,0,65,92,0,0,0,0,66,41,0,0,106,47],[15,0,0,0,0,15,0,0,0,0,1,35,0,0,0,112] >;
D28.32D4 in GAP, Magma, Sage, TeX
D_{28}._{32}D_4 % in TeX
G:=Group("D28.32D4"); // GroupNames label
G:=SmallGroup(448,267);
// by ID
G=gap.SmallGroup(448,267);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,254,219,58,1123,136,18822]);
// 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,c*b*c^-1=a^7*b,b*d=d*b,d*c*d^-1=a^21*c^3>;
// generators/relations