metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28.2Q8, C4.8(Q8×D7), C2.D8⋊9D7, C7⋊5(D4.Q8), (C2×C8).32D14, C28.24(C2×Q8), Dic7⋊C8⋊26C2, C4⋊C4.174D14, C28.3Q8⋊7C2, D28⋊C4.9C2, C14.D8.9C2, C14.77(C4○D8), C4.85(C4○D28), C4.Dic14⋊23C2, (C2×Dic7).52D4, C22.236(D4×D7), C2.D56.11C2, C28.173(C4○D4), C2.25(D8⋊D7), C14.45(C8⋊C22), (C2×C56).246C22, (C2×C28).307C23, (C2×D28).87C22, C14.42(C22⋊Q8), C2.15(Q8.D14), C2.19(D14⋊Q8), C4⋊Dic7.129C22, (C4×Dic7).39C22, (C7×C2.D8)⋊16C2, (C2×C7⋊C8).76C22, (C2×C14).312(C2×D4), (C7×C4⋊C4).100C22, (C2×C4).410(C22×D7), SmallGroup(448,425)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28.2Q8
G = < a,b,c,d | a28=b2=1, c4=a14, d2=a7c2, bab=a-1, ac=ca, dad-1=a15, cbc-1=a7b, bd=db, dcd-1=a14c3 >
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, C4.Dic14, C14.D8, Dic7⋊C8, C2.D56, C7×C2.D8, C28.3Q8, D28⋊C4, D28.2Q8
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, D8⋊D7, Q8.D14, D28.2Q8
►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 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 84)(58 83)(59 82)(60 81)(61 80)(62 79)(63 78)(64 77)(65 76)(66 75)(67 74)(68 73)(69 72)(70 71)(85 92)(86 91)(87 90)(88 89)(93 112)(94 111)(95 110)(96 109)(97 108)(98 107)(99 106)(100 105)(101 104)(102 103)(113 123)(114 122)(115 121)(116 120)(117 119)(124 140)(125 139)(126 138)(127 137)(128 136)(129 135)(130 134)(131 133)(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)(169 186)(170 185)(171 184)(172 183)(173 182)(174 181)(175 180)(176 179)(177 178)(187 196)(188 195)(189 194)(190 193)(191 192)(197 211)(198 210)(199 209)(200 208)(201 207)(202 206)(203 205)(212 224)(213 223)(214 222)(215 221)(216 220)(217 219)
(1 222 64 154 15 208 78 168)(2 223 65 155 16 209 79 141)(3 224 66 156 17 210 80 142)(4 197 67 157 18 211 81 143)(5 198 68 158 19 212 82 144)(6 199 69 159 20 213 83 145)(7 200 70 160 21 214 84 146)(8 201 71 161 22 215 57 147)(9 202 72 162 23 216 58 148)(10 203 73 163 24 217 59 149)(11 204 74 164 25 218 60 150)(12 205 75 165 26 219 61 151)(13 206 76 166 27 220 62 152)(14 207 77 167 28 221 63 153)(29 178 122 110 43 192 136 96)(30 179 123 111 44 193 137 97)(31 180 124 112 45 194 138 98)(32 181 125 85 46 195 139 99)(33 182 126 86 47 196 140 100)(34 183 127 87 48 169 113 101)(35 184 128 88 49 170 114 102)(36 185 129 89 50 171 115 103)(37 186 130 90 51 172 116 104)(38 187 131 91 52 173 117 105)(39 188 132 92 53 174 118 106)(40 189 133 93 54 175 119 107)(41 190 134 94 55 176 120 108)(42 191 135 95 56 177 121 109)
(1 96 71 185)(2 111 72 172)(3 98 73 187)(4 85 74 174)(5 100 75 189)(6 87 76 176)(7 102 77 191)(8 89 78 178)(9 104 79 193)(10 91 80 180)(11 106 81 195)(12 93 82 182)(13 108 83 169)(14 95 84 184)(15 110 57 171)(16 97 58 186)(17 112 59 173)(18 99 60 188)(19 86 61 175)(20 101 62 190)(21 88 63 177)(22 103 64 192)(23 90 65 179)(24 105 66 194)(25 92 67 181)(26 107 68 196)(27 94 69 183)(28 109 70 170)(29 201 129 168)(30 216 130 155)(31 203 131 142)(32 218 132 157)(33 205 133 144)(34 220 134 159)(35 207 135 146)(36 222 136 161)(37 209 137 148)(38 224 138 163)(39 211 139 150)(40 198 140 165)(41 213 113 152)(42 200 114 167)(43 215 115 154)(44 202 116 141)(45 217 117 156)(46 204 118 143)(47 219 119 158)(48 206 120 145)(49 221 121 160)(50 208 122 147)(51 223 123 162)(52 210 124 149)(53 197 125 164)(54 212 126 151)(55 199 127 166)(56 214 128 153)
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)(29,35)(30,34)(31,33)(36,56)(37,55)(38,54)(39,53)(40,52)(41,51)(42,50)(43,49)(44,48)(45,47)(57,84)(58,83)(59,82)(60,81)(61,80)(62,79)(63,78)(64,77)(65,76)(66,75)(67,74)(68,73)(69,72)(70,71)(85,92)(86,91)(87,90)(88,89)(93,112)(94,111)(95,110)(96,109)(97,108)(98,107)(99,106)(100,105)(101,104)(102,103)(113,123)(114,122)(115,121)(116,120)(117,119)(124,140)(125,139)(126,138)(127,137)(128,136)(129,135)(130,134)(131,133)(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)(169,186)(170,185)(171,184)(172,183)(173,182)(174,181)(175,180)(176,179)(177,178)(187,196)(188,195)(189,194)(190,193)(191,192)(197,211)(198,210)(199,209)(200,208)(201,207)(202,206)(203,205)(212,224)(213,223)(214,222)(215,221)(216,220)(217,219), (1,222,64,154,15,208,78,168)(2,223,65,155,16,209,79,141)(3,224,66,156,17,210,80,142)(4,197,67,157,18,211,81,143)(5,198,68,158,19,212,82,144)(6,199,69,159,20,213,83,145)(7,200,70,160,21,214,84,146)(8,201,71,161,22,215,57,147)(9,202,72,162,23,216,58,148)(10,203,73,163,24,217,59,149)(11,204,74,164,25,218,60,150)(12,205,75,165,26,219,61,151)(13,206,76,166,27,220,62,152)(14,207,77,167,28,221,63,153)(29,178,122,110,43,192,136,96)(30,179,123,111,44,193,137,97)(31,180,124,112,45,194,138,98)(32,181,125,85,46,195,139,99)(33,182,126,86,47,196,140,100)(34,183,127,87,48,169,113,101)(35,184,128,88,49,170,114,102)(36,185,129,89,50,171,115,103)(37,186,130,90,51,172,116,104)(38,187,131,91,52,173,117,105)(39,188,132,92,53,174,118,106)(40,189,133,93,54,175,119,107)(41,190,134,94,55,176,120,108)(42,191,135,95,56,177,121,109), (1,96,71,185)(2,111,72,172)(3,98,73,187)(4,85,74,174)(5,100,75,189)(6,87,76,176)(7,102,77,191)(8,89,78,178)(9,104,79,193)(10,91,80,180)(11,106,81,195)(12,93,82,182)(13,108,83,169)(14,95,84,184)(15,110,57,171)(16,97,58,186)(17,112,59,173)(18,99,60,188)(19,86,61,175)(20,101,62,190)(21,88,63,177)(22,103,64,192)(23,90,65,179)(24,105,66,194)(25,92,67,181)(26,107,68,196)(27,94,69,183)(28,109,70,170)(29,201,129,168)(30,216,130,155)(31,203,131,142)(32,218,132,157)(33,205,133,144)(34,220,134,159)(35,207,135,146)(36,222,136,161)(37,209,137,148)(38,224,138,163)(39,211,139,150)(40,198,140,165)(41,213,113,152)(42,200,114,167)(43,215,115,154)(44,202,116,141)(45,217,117,156)(46,204,118,143)(47,219,119,158)(48,206,120,145)(49,221,121,160)(50,208,122,147)(51,223,123,162)(52,210,124,149)(53,197,125,164)(54,212,126,151)(55,199,127,166)(56,214,128,153)>;
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)(29,35)(30,34)(31,33)(36,56)(37,55)(38,54)(39,53)(40,52)(41,51)(42,50)(43,49)(44,48)(45,47)(57,84)(58,83)(59,82)(60,81)(61,80)(62,79)(63,78)(64,77)(65,76)(66,75)(67,74)(68,73)(69,72)(70,71)(85,92)(86,91)(87,90)(88,89)(93,112)(94,111)(95,110)(96,109)(97,108)(98,107)(99,106)(100,105)(101,104)(102,103)(113,123)(114,122)(115,121)(116,120)(117,119)(124,140)(125,139)(126,138)(127,137)(128,136)(129,135)(130,134)(131,133)(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)(169,186)(170,185)(171,184)(172,183)(173,182)(174,181)(175,180)(176,179)(177,178)(187,196)(188,195)(189,194)(190,193)(191,192)(197,211)(198,210)(199,209)(200,208)(201,207)(202,206)(203,205)(212,224)(213,223)(214,222)(215,221)(216,220)(217,219), (1,222,64,154,15,208,78,168)(2,223,65,155,16,209,79,141)(3,224,66,156,17,210,80,142)(4,197,67,157,18,211,81,143)(5,198,68,158,19,212,82,144)(6,199,69,159,20,213,83,145)(7,200,70,160,21,214,84,146)(8,201,71,161,22,215,57,147)(9,202,72,162,23,216,58,148)(10,203,73,163,24,217,59,149)(11,204,74,164,25,218,60,150)(12,205,75,165,26,219,61,151)(13,206,76,166,27,220,62,152)(14,207,77,167,28,221,63,153)(29,178,122,110,43,192,136,96)(30,179,123,111,44,193,137,97)(31,180,124,112,45,194,138,98)(32,181,125,85,46,195,139,99)(33,182,126,86,47,196,140,100)(34,183,127,87,48,169,113,101)(35,184,128,88,49,170,114,102)(36,185,129,89,50,171,115,103)(37,186,130,90,51,172,116,104)(38,187,131,91,52,173,117,105)(39,188,132,92,53,174,118,106)(40,189,133,93,54,175,119,107)(41,190,134,94,55,176,120,108)(42,191,135,95,56,177,121,109), (1,96,71,185)(2,111,72,172)(3,98,73,187)(4,85,74,174)(5,100,75,189)(6,87,76,176)(7,102,77,191)(8,89,78,178)(9,104,79,193)(10,91,80,180)(11,106,81,195)(12,93,82,182)(13,108,83,169)(14,95,84,184)(15,110,57,171)(16,97,58,186)(17,112,59,173)(18,99,60,188)(19,86,61,175)(20,101,62,190)(21,88,63,177)(22,103,64,192)(23,90,65,179)(24,105,66,194)(25,92,67,181)(26,107,68,196)(27,94,69,183)(28,109,70,170)(29,201,129,168)(30,216,130,155)(31,203,131,142)(32,218,132,157)(33,205,133,144)(34,220,134,159)(35,207,135,146)(36,222,136,161)(37,209,137,148)(38,224,138,163)(39,211,139,150)(40,198,140,165)(41,213,113,152)(42,200,114,167)(43,215,115,154)(44,202,116,141)(45,217,117,156)(46,204,118,143)(47,219,119,158)(48,206,120,145)(49,221,121,160)(50,208,122,147)(51,223,123,162)(52,210,124,149)(53,197,125,164)(54,212,126,151)(55,199,127,166)(56,214,128,153) );
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),(29,35),(30,34),(31,33),(36,56),(37,55),(38,54),(39,53),(40,52),(41,51),(42,50),(43,49),(44,48),(45,47),(57,84),(58,83),(59,82),(60,81),(61,80),(62,79),(63,78),(64,77),(65,76),(66,75),(67,74),(68,73),(69,72),(70,71),(85,92),(86,91),(87,90),(88,89),(93,112),(94,111),(95,110),(96,109),(97,108),(98,107),(99,106),(100,105),(101,104),(102,103),(113,123),(114,122),(115,121),(116,120),(117,119),(124,140),(125,139),(126,138),(127,137),(128,136),(129,135),(130,134),(131,133),(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),(169,186),(170,185),(171,184),(172,183),(173,182),(174,181),(175,180),(176,179),(177,178),(187,196),(188,195),(189,194),(190,193),(191,192),(197,211),(198,210),(199,209),(200,208),(201,207),(202,206),(203,205),(212,224),(213,223),(214,222),(215,221),(216,220),(217,219)], [(1,222,64,154,15,208,78,168),(2,223,65,155,16,209,79,141),(3,224,66,156,17,210,80,142),(4,197,67,157,18,211,81,143),(5,198,68,158,19,212,82,144),(6,199,69,159,20,213,83,145),(7,200,70,160,21,214,84,146),(8,201,71,161,22,215,57,147),(9,202,72,162,23,216,58,148),(10,203,73,163,24,217,59,149),(11,204,74,164,25,218,60,150),(12,205,75,165,26,219,61,151),(13,206,76,166,27,220,62,152),(14,207,77,167,28,221,63,153),(29,178,122,110,43,192,136,96),(30,179,123,111,44,193,137,97),(31,180,124,112,45,194,138,98),(32,181,125,85,46,195,139,99),(33,182,126,86,47,196,140,100),(34,183,127,87,48,169,113,101),(35,184,128,88,49,170,114,102),(36,185,129,89,50,171,115,103),(37,186,130,90,51,172,116,104),(38,187,131,91,52,173,117,105),(39,188,132,92,53,174,118,106),(40,189,133,93,54,175,119,107),(41,190,134,94,55,176,120,108),(42,191,135,95,56,177,121,109)], [(1,96,71,185),(2,111,72,172),(3,98,73,187),(4,85,74,174),(5,100,75,189),(6,87,76,176),(7,102,77,191),(8,89,78,178),(9,104,79,193),(10,91,80,180),(11,106,81,195),(12,93,82,182),(13,108,83,169),(14,95,84,184),(15,110,57,171),(16,97,58,186),(17,112,59,173),(18,99,60,188),(19,86,61,175),(20,101,62,190),(21,88,63,177),(22,103,64,192),(23,90,65,179),(24,105,66,194),(25,92,67,181),(26,107,68,196),(27,94,69,183),(28,109,70,170),(29,201,129,168),(30,216,130,155),(31,203,131,142),(32,218,132,157),(33,205,133,144),(34,220,134,159),(35,207,135,146),(36,222,136,161),(37,209,137,148),(38,224,138,163),(39,211,139,150),(40,198,140,165),(41,213,113,152),(42,200,114,167),(43,215,115,154),(44,202,116,141),(45,217,117,156),(46,204,118,143),(47,219,119,158),(48,206,120,145),(49,221,121,160),(50,208,122,147),(51,223,123,162),(52,210,124,149),(53,197,125,164),(54,212,126,151),(55,199,127,166),(56,214,128,153)]])
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 | D8⋊D7 | Q8.D14 |
| kernel | D28.2Q8 | C4.Dic14 | C14.D8 | Dic7⋊C8 | C2.D56 | C7×C2.D8 | C28.3Q8 | D28⋊C4 | D28 | C2×Dic7 | C2.D8 | 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 D28.2Q8 ►in GL4(𝔽113) generated by
| 1 | 9 | 0 | 0 |
| 104 | 33 | 0 | 0 |
| 0 | 0 | 112 | 2 |
| 0 | 0 | 112 | 1 |
| 33 | 80 | 0 | 0 |
| 9 | 80 | 0 | 0 |
| 0 | 0 | 112 | 2 |
| 0 | 0 | 0 | 1 |
| 79 | 5 | 0 | 0 |
| 108 | 34 | 0 | 0 |
| 0 | 0 | 51 | 62 |
| 0 | 0 | 82 | 0 |
| 98 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 98 | 30 |
| 0 | 0 | 0 | 15 |
G:=sub<GL(4,GF(113))| [1,104,0,0,9,33,0,0,0,0,112,112,0,0,2,1],[33,9,0,0,80,80,0,0,0,0,112,0,0,0,2,1],[79,108,0,0,5,34,0,0,0,0,51,82,0,0,62,0],[98,0,0,0,0,98,0,0,0,0,98,0,0,0,30,15] >;
D28.2Q8 in GAP, Magma, Sage, TeX
D_{28}._2Q_8 % in TeX
G:=Group("D28.2Q8"); // GroupNames label
G:=SmallGroup(448,425);
// by ID
G=gap.SmallGroup(448,425);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,64,590,555,100,1684,851,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=b^2=1,c^4=a^14,d^2=a^7*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=a^14*c^3>;
// generators/relations