metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28.1Q8, C4.4(Q8×D7), C7⋊4(D4.Q8), C4.Q8⋊12D7, C28.16(C2×Q8), Dic7⋊C8⋊31C2, C4⋊C4.165D14, (C2×C8).142D14, C28.3Q8⋊6C2, D28⋊C4.6C2, C14.D8.6C2, C14.58(C4○D8), C4.77(C4○D28), C28.Q8⋊18C2, (C2×Dic7).45D4, C22.222(D4×D7), C2.D56.14C2, C28.169(C4○D4), C2.25(D56⋊C2), C14.74(C8⋊C22), (C2×C56).289C22, (C2×C28).287C23, (C2×D28).79C22, C14.38(C22⋊Q8), C2.15(D14⋊Q8), C4⋊Dic7.115C22, (C4×Dic7).33C22, C2.25(SD16⋊3D7), (C7×C4.Q8)⋊20C2, (C2×C7⋊C8).64C22, (C2×C14).292(C2×D4), (C7×C4⋊C4).80C22, (C2×C4).390(C22×D7), SmallGroup(448,405)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28.Q8
G = < a,b,c,d | a28=b2=1, c4=a14, d2=a21c2, bab=a-1, ac=ca, dad-1=a15, cbc-1=a7b, bd=db, dcd-1=c3 >
Subgroups: 588 in 102 conjugacy classes, 39 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, C23, D7, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, C22×C4, C2×D4, Dic7, C28, C28, D14, C2×C14, D4⋊C4, C4⋊C8, C4.Q8, C2.D8, C4×D4, C42.C2, C7⋊C8, C56, C4×D7, D28, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, D4.Q8, C2×C7⋊C8, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C7×C4⋊C4, C2×C56, C2×C4×D7, C2×D28, C28.Q8, C14.D8, Dic7⋊C8, C2.D56, C7×C4.Q8, C28.3Q8, D28⋊C4, D28.Q8
Quotients: C1, C2, C22, D4, Q8, C23, D7, C2×D4, C2×Q8, C4○D4, D14, C22⋊Q8, C4○D8, C8⋊C22, C22×D7, D4.Q8, C4○D28, D4×D7, Q8×D7, D14⋊Q8, D56⋊C2, SD16⋊3D7, D28.Q8
►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)(29 51)(30 50)(31 49)(32 48)(33 47)(34 46)(35 45)(36 44)(37 43)(38 42)(39 41)(52 56)(53 55)(57 65)(58 64)(59 63)(60 62)(66 84)(67 83)(68 82)(69 81)(70 80)(71 79)(72 78)(73 77)(74 76)(85 97)(86 96)(87 95)(88 94)(89 93)(90 92)(98 112)(99 111)(100 110)(101 109)(102 108)(103 107)(104 106)(113 120)(114 119)(115 118)(116 117)(121 140)(122 139)(123 138)(124 137)(125 136)(126 135)(127 134)(128 133)(129 132)(130 131)(141 145)(142 144)(146 168)(147 167)(148 166)(149 165)(150 164)(151 163)(152 162)(153 161)(154 160)(155 159)(156 158)(169 194)(170 193)(171 192)(172 191)(173 190)(174 189)(175 188)(176 187)(177 186)(178 185)(179 184)(180 183)(181 182)(195 196)(197 216)(198 215)(199 214)(200 213)(201 212)(202 211)(203 210)(204 209)(205 208)(206 207)(217 224)(218 223)(219 222)(220 221)
(1 30 214 58 15 44 200 72)(2 31 215 59 16 45 201 73)(3 32 216 60 17 46 202 74)(4 33 217 61 18 47 203 75)(5 34 218 62 19 48 204 76)(6 35 219 63 20 49 205 77)(7 36 220 64 21 50 206 78)(8 37 221 65 22 51 207 79)(9 38 222 66 23 52 208 80)(10 39 223 67 24 53 209 81)(11 40 224 68 25 54 210 82)(12 41 197 69 26 55 211 83)(13 42 198 70 27 56 212 84)(14 43 199 71 28 29 213 57)(85 128 158 172 99 114 144 186)(86 129 159 173 100 115 145 187)(87 130 160 174 101 116 146 188)(88 131 161 175 102 117 147 189)(89 132 162 176 103 118 148 190)(90 133 163 177 104 119 149 191)(91 134 164 178 105 120 150 192)(92 135 165 179 106 121 151 193)(93 136 166 180 107 122 152 194)(94 137 167 181 108 123 153 195)(95 138 168 182 109 124 154 196)(96 139 141 183 110 125 155 169)(97 140 142 184 111 126 156 170)(98 113 143 185 112 127 157 171)
(1 124 207 189)(2 139 208 176)(3 126 209 191)(4 113 210 178)(5 128 211 193)(6 115 212 180)(7 130 213 195)(8 117 214 182)(9 132 215 169)(10 119 216 184)(11 134 217 171)(12 121 218 186)(13 136 219 173)(14 123 220 188)(15 138 221 175)(16 125 222 190)(17 140 223 177)(18 127 224 192)(19 114 197 179)(20 129 198 194)(21 116 199 181)(22 131 200 196)(23 118 201 183)(24 133 202 170)(25 120 203 185)(26 135 204 172)(27 122 205 187)(28 137 206 174)(29 108 78 146)(30 95 79 161)(31 110 80 148)(32 97 81 163)(33 112 82 150)(34 99 83 165)(35 86 84 152)(36 101 57 167)(37 88 58 154)(38 103 59 141)(39 90 60 156)(40 105 61 143)(41 92 62 158)(42 107 63 145)(43 94 64 160)(44 109 65 147)(45 96 66 162)(46 111 67 149)(47 98 68 164)(48 85 69 151)(49 100 70 166)(50 87 71 153)(51 102 72 168)(52 89 73 155)(53 104 74 142)(54 91 75 157)(55 106 76 144)(56 93 77 159)
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)(29,51)(30,50)(31,49)(32,48)(33,47)(34,46)(35,45)(36,44)(37,43)(38,42)(39,41)(52,56)(53,55)(57,65)(58,64)(59,63)(60,62)(66,84)(67,83)(68,82)(69,81)(70,80)(71,79)(72,78)(73,77)(74,76)(85,97)(86,96)(87,95)(88,94)(89,93)(90,92)(98,112)(99,111)(100,110)(101,109)(102,108)(103,107)(104,106)(113,120)(114,119)(115,118)(116,117)(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(127,134)(128,133)(129,132)(130,131)(141,145)(142,144)(146,168)(147,167)(148,166)(149,165)(150,164)(151,163)(152,162)(153,161)(154,160)(155,159)(156,158)(169,194)(170,193)(171,192)(172,191)(173,190)(174,189)(175,188)(176,187)(177,186)(178,185)(179,184)(180,183)(181,182)(195,196)(197,216)(198,215)(199,214)(200,213)(201,212)(202,211)(203,210)(204,209)(205,208)(206,207)(217,224)(218,223)(219,222)(220,221), (1,30,214,58,15,44,200,72)(2,31,215,59,16,45,201,73)(3,32,216,60,17,46,202,74)(4,33,217,61,18,47,203,75)(5,34,218,62,19,48,204,76)(6,35,219,63,20,49,205,77)(7,36,220,64,21,50,206,78)(8,37,221,65,22,51,207,79)(9,38,222,66,23,52,208,80)(10,39,223,67,24,53,209,81)(11,40,224,68,25,54,210,82)(12,41,197,69,26,55,211,83)(13,42,198,70,27,56,212,84)(14,43,199,71,28,29,213,57)(85,128,158,172,99,114,144,186)(86,129,159,173,100,115,145,187)(87,130,160,174,101,116,146,188)(88,131,161,175,102,117,147,189)(89,132,162,176,103,118,148,190)(90,133,163,177,104,119,149,191)(91,134,164,178,105,120,150,192)(92,135,165,179,106,121,151,193)(93,136,166,180,107,122,152,194)(94,137,167,181,108,123,153,195)(95,138,168,182,109,124,154,196)(96,139,141,183,110,125,155,169)(97,140,142,184,111,126,156,170)(98,113,143,185,112,127,157,171), (1,124,207,189)(2,139,208,176)(3,126,209,191)(4,113,210,178)(5,128,211,193)(6,115,212,180)(7,130,213,195)(8,117,214,182)(9,132,215,169)(10,119,216,184)(11,134,217,171)(12,121,218,186)(13,136,219,173)(14,123,220,188)(15,138,221,175)(16,125,222,190)(17,140,223,177)(18,127,224,192)(19,114,197,179)(20,129,198,194)(21,116,199,181)(22,131,200,196)(23,118,201,183)(24,133,202,170)(25,120,203,185)(26,135,204,172)(27,122,205,187)(28,137,206,174)(29,108,78,146)(30,95,79,161)(31,110,80,148)(32,97,81,163)(33,112,82,150)(34,99,83,165)(35,86,84,152)(36,101,57,167)(37,88,58,154)(38,103,59,141)(39,90,60,156)(40,105,61,143)(41,92,62,158)(42,107,63,145)(43,94,64,160)(44,109,65,147)(45,96,66,162)(46,111,67,149)(47,98,68,164)(48,85,69,151)(49,100,70,166)(50,87,71,153)(51,102,72,168)(52,89,73,155)(53,104,74,142)(54,91,75,157)(55,106,76,144)(56,93,77,159)>;
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)(29,51)(30,50)(31,49)(32,48)(33,47)(34,46)(35,45)(36,44)(37,43)(38,42)(39,41)(52,56)(53,55)(57,65)(58,64)(59,63)(60,62)(66,84)(67,83)(68,82)(69,81)(70,80)(71,79)(72,78)(73,77)(74,76)(85,97)(86,96)(87,95)(88,94)(89,93)(90,92)(98,112)(99,111)(100,110)(101,109)(102,108)(103,107)(104,106)(113,120)(114,119)(115,118)(116,117)(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(127,134)(128,133)(129,132)(130,131)(141,145)(142,144)(146,168)(147,167)(148,166)(149,165)(150,164)(151,163)(152,162)(153,161)(154,160)(155,159)(156,158)(169,194)(170,193)(171,192)(172,191)(173,190)(174,189)(175,188)(176,187)(177,186)(178,185)(179,184)(180,183)(181,182)(195,196)(197,216)(198,215)(199,214)(200,213)(201,212)(202,211)(203,210)(204,209)(205,208)(206,207)(217,224)(218,223)(219,222)(220,221), (1,30,214,58,15,44,200,72)(2,31,215,59,16,45,201,73)(3,32,216,60,17,46,202,74)(4,33,217,61,18,47,203,75)(5,34,218,62,19,48,204,76)(6,35,219,63,20,49,205,77)(7,36,220,64,21,50,206,78)(8,37,221,65,22,51,207,79)(9,38,222,66,23,52,208,80)(10,39,223,67,24,53,209,81)(11,40,224,68,25,54,210,82)(12,41,197,69,26,55,211,83)(13,42,198,70,27,56,212,84)(14,43,199,71,28,29,213,57)(85,128,158,172,99,114,144,186)(86,129,159,173,100,115,145,187)(87,130,160,174,101,116,146,188)(88,131,161,175,102,117,147,189)(89,132,162,176,103,118,148,190)(90,133,163,177,104,119,149,191)(91,134,164,178,105,120,150,192)(92,135,165,179,106,121,151,193)(93,136,166,180,107,122,152,194)(94,137,167,181,108,123,153,195)(95,138,168,182,109,124,154,196)(96,139,141,183,110,125,155,169)(97,140,142,184,111,126,156,170)(98,113,143,185,112,127,157,171), (1,124,207,189)(2,139,208,176)(3,126,209,191)(4,113,210,178)(5,128,211,193)(6,115,212,180)(7,130,213,195)(8,117,214,182)(9,132,215,169)(10,119,216,184)(11,134,217,171)(12,121,218,186)(13,136,219,173)(14,123,220,188)(15,138,221,175)(16,125,222,190)(17,140,223,177)(18,127,224,192)(19,114,197,179)(20,129,198,194)(21,116,199,181)(22,131,200,196)(23,118,201,183)(24,133,202,170)(25,120,203,185)(26,135,204,172)(27,122,205,187)(28,137,206,174)(29,108,78,146)(30,95,79,161)(31,110,80,148)(32,97,81,163)(33,112,82,150)(34,99,83,165)(35,86,84,152)(36,101,57,167)(37,88,58,154)(38,103,59,141)(39,90,60,156)(40,105,61,143)(41,92,62,158)(42,107,63,145)(43,94,64,160)(44,109,65,147)(45,96,66,162)(46,111,67,149)(47,98,68,164)(48,85,69,151)(49,100,70,166)(50,87,71,153)(51,102,72,168)(52,89,73,155)(53,104,74,142)(54,91,75,157)(55,106,76,144)(56,93,77,159) );
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),(29,51),(30,50),(31,49),(32,48),(33,47),(34,46),(35,45),(36,44),(37,43),(38,42),(39,41),(52,56),(53,55),(57,65),(58,64),(59,63),(60,62),(66,84),(67,83),(68,82),(69,81),(70,80),(71,79),(72,78),(73,77),(74,76),(85,97),(86,96),(87,95),(88,94),(89,93),(90,92),(98,112),(99,111),(100,110),(101,109),(102,108),(103,107),(104,106),(113,120),(114,119),(115,118),(116,117),(121,140),(122,139),(123,138),(124,137),(125,136),(126,135),(127,134),(128,133),(129,132),(130,131),(141,145),(142,144),(146,168),(147,167),(148,166),(149,165),(150,164),(151,163),(152,162),(153,161),(154,160),(155,159),(156,158),(169,194),(170,193),(171,192),(172,191),(173,190),(174,189),(175,188),(176,187),(177,186),(178,185),(179,184),(180,183),(181,182),(195,196),(197,216),(198,215),(199,214),(200,213),(201,212),(202,211),(203,210),(204,209),(205,208),(206,207),(217,224),(218,223),(219,222),(220,221)], [(1,30,214,58,15,44,200,72),(2,31,215,59,16,45,201,73),(3,32,216,60,17,46,202,74),(4,33,217,61,18,47,203,75),(5,34,218,62,19,48,204,76),(6,35,219,63,20,49,205,77),(7,36,220,64,21,50,206,78),(8,37,221,65,22,51,207,79),(9,38,222,66,23,52,208,80),(10,39,223,67,24,53,209,81),(11,40,224,68,25,54,210,82),(12,41,197,69,26,55,211,83),(13,42,198,70,27,56,212,84),(14,43,199,71,28,29,213,57),(85,128,158,172,99,114,144,186),(86,129,159,173,100,115,145,187),(87,130,160,174,101,116,146,188),(88,131,161,175,102,117,147,189),(89,132,162,176,103,118,148,190),(90,133,163,177,104,119,149,191),(91,134,164,178,105,120,150,192),(92,135,165,179,106,121,151,193),(93,136,166,180,107,122,152,194),(94,137,167,181,108,123,153,195),(95,138,168,182,109,124,154,196),(96,139,141,183,110,125,155,169),(97,140,142,184,111,126,156,170),(98,113,143,185,112,127,157,171)], [(1,124,207,189),(2,139,208,176),(3,126,209,191),(4,113,210,178),(5,128,211,193),(6,115,212,180),(7,130,213,195),(8,117,214,182),(9,132,215,169),(10,119,216,184),(11,134,217,171),(12,121,218,186),(13,136,219,173),(14,123,220,188),(15,138,221,175),(16,125,222,190),(17,140,223,177),(18,127,224,192),(19,114,197,179),(20,129,198,194),(21,116,199,181),(22,131,200,196),(23,118,201,183),(24,133,202,170),(25,120,203,185),(26,135,204,172),(27,122,205,187),(28,137,206,174),(29,108,78,146),(30,95,79,161),(31,110,80,148),(32,97,81,163),(33,112,82,150),(34,99,83,165),(35,86,84,152),(36,101,57,167),(37,88,58,154),(38,103,59,141),(39,90,60,156),(40,105,61,143),(41,92,62,158),(42,107,63,145),(43,94,64,160),(44,109,65,147),(45,96,66,162),(46,111,67,149),(47,98,68,164),(48,85,69,151),(49,100,70,166),(50,87,71,153),(51,102,72,168),(52,89,73,155),(53,104,74,142),(54,91,75,157),(55,106,76,144),(56,93,77,159)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 28A | ··· | 28F | 28G | ··· | 28R | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 2 | 2 | 4 | 4 | 8 | 14 | 14 | 28 | 56 | 2 | 2 | 2 | 4 | 4 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | + | + | + | + | + | - | + | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | Q8 | D4 | D7 | C4○D4 | D14 | D14 | C4○D8 | C4○D28 | C8⋊C22 | Q8×D7 | D4×D7 | D56⋊C2 | SD16⋊3D7 |
| kernel | D28.Q8 | C28.Q8 | C14.D8 | Dic7⋊C8 | C2.D56 | C7×C4.Q8 | C28.3Q8 | D28⋊C4 | D28 | C2×Dic7 | C4.Q8 | C28 | C4⋊C4 | C2×C8 | C14 | C4 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 3 | 2 | 6 | 3 | 4 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of D28.Q8 ►in GL4(𝔽113) generated by
| 33 | 9 | 0 | 0 |
| 104 | 1 | 0 | 0 |
| 0 | 0 | 1 | 41 |
| 0 | 0 | 22 | 112 |
| 33 | 9 | 0 | 0 |
| 80 | 80 | 0 | 0 |
| 0 | 0 | 1 | 41 |
| 0 | 0 | 0 | 112 |
| 79 | 108 | 0 | 0 |
| 5 | 34 | 0 | 0 |
| 0 | 0 | 0 | 32 |
| 0 | 0 | 53 | 26 |
| 98 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 15 | 50 |
| 0 | 0 | 0 | 98 |
G:=sub<GL(4,GF(113))| [33,104,0,0,9,1,0,0,0,0,1,22,0,0,41,112],[33,80,0,0,9,80,0,0,0,0,1,0,0,0,41,112],[79,5,0,0,108,34,0,0,0,0,0,53,0,0,32,26],[98,0,0,0,0,98,0,0,0,0,15,0,0,0,50,98] >;
D28.Q8 in GAP, Magma, Sage, TeX
D_{28}.Q_8 % in TeX
G:=Group("D28.Q8"); // GroupNames label
G:=SmallGroup(448,405);
// by ID
G=gap.SmallGroup(448,405);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,64,590,555,268,1684,851,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=b^2=1,c^4=a^14,d^2=a^21*c^2,b*a*b=a^-1,a*c=c*a,d*a*d^-1=a^15,c*b*c^-1=a^7*b,b*d=d*b,d*c*d^-1=c^3>;
// generators/relations