metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28.12D4, C4.97(D4×D7), Dic7⋊C8⋊8C2, Q8⋊C4⋊8D7, (C2×D56).3C2, (C2×C8).20D14, D28⋊C4⋊5C2, C4⋊C4.157D14, C4.8(C4○D28), C28.129(C2×D4), C7⋊2(D4.2D4), (C2×Q8).24D14, C14.D8⋊13C2, C28.24(C4○D4), C14.72(C4○D8), C28.23D4⋊2C2, (C2×C56).20C22, (C2×Dic7).36D4, C22.208(D4×D7), C2.19(D56⋊C2), C14.28(C4⋊D4), C14.66(C8⋊C22), (C2×C28).259C23, (C2×D28).69C22, (Q8×C14).42C22, C2.31(D14⋊D4), C2.11(Q8.D14), (C4×Dic7).26C22, (C2×Q8⋊D7)⋊6C2, (C7×Q8⋊C4)⋊8C2, (C2×C7⋊C8).49C22, (C2×C14).272(C2×D4), (C7×C4⋊C4).60C22, (C2×C4).366(C22×D7), SmallGroup(448,353)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28.12D4
G = < a,b,c,d | a28=b2=c4=1, d2=a7, bab=a-1, cac-1=a15, ad=da, bc=cb, dbd-1=a7b, dcd-1=a21c-1 >
Subgroups: 820 in 124 conjugacy classes, 39 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C22⋊C4, C4⋊C4, C2×C8, C2×C8, D8, SD16, C22×C4, C2×D4, C2×Q8, Dic7, C28, C28, D14, C2×C14, D4⋊C4, Q8⋊C4, C4⋊C8, C4×D4, C4.4D4, C2×D8, C2×SD16, C7⋊C8, C56, C4×D7, D28, D28, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, D4.2D4, D56, C2×C7⋊C8, C4×Dic7, D14⋊C4, Q8⋊D7, C7×C4⋊C4, C2×C56, C2×C4×D7, C2×D28, Q8×C14, C14.D8, Dic7⋊C8, C7×Q8⋊C4, D28⋊C4, C2×D56, C2×Q8⋊D7, C28.23D4, D28.12D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4⋊D4, C4○D8, C8⋊C22, C22×D7, D4.2D4, C4○D28, D4×D7, D14⋊D4, D56⋊C2, Q8.D14, D28.12D4
►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 50)(30 49)(31 48)(32 47)(33 46)(34 45)(35 44)(36 43)(37 42)(38 41)(39 40)(51 56)(52 55)(53 54)(57 73)(58 72)(59 71)(60 70)(61 69)(62 68)(63 67)(64 66)(74 84)(75 83)(76 82)(77 81)(78 80)(85 111)(86 110)(87 109)(88 108)(89 107)(90 106)(91 105)(92 104)(93 103)(94 102)(95 101)(96 100)(97 99)(113 116)(114 115)(117 140)(118 139)(119 138)(120 137)(121 136)(122 135)(123 134)(124 133)(125 132)(126 131)(127 130)(128 129)(141 161)(142 160)(143 159)(144 158)(145 157)(146 156)(147 155)(148 154)(149 153)(150 152)(162 168)(163 167)(164 166)(169 183)(170 182)(171 181)(172 180)(173 179)(174 178)(175 177)(184 196)(185 195)(186 194)(187 193)(188 192)(189 191)(197 224)(198 223)(199 222)(200 221)(201 220)(202 219)(203 218)(204 217)(205 216)(206 215)(207 214)(208 213)(209 212)(210 211)
(1 122 54 218)(2 137 55 205)(3 124 56 220)(4 139 29 207)(5 126 30 222)(6 113 31 209)(7 128 32 224)(8 115 33 211)(9 130 34 198)(10 117 35 213)(11 132 36 200)(12 119 37 215)(13 134 38 202)(14 121 39 217)(15 136 40 204)(16 123 41 219)(17 138 42 206)(18 125 43 221)(19 140 44 208)(20 127 45 223)(21 114 46 210)(22 129 47 197)(23 116 48 212)(24 131 49 199)(25 118 50 214)(26 133 51 201)(27 120 52 216)(28 135 53 203)(57 143 90 182)(58 158 91 169)(59 145 92 184)(60 160 93 171)(61 147 94 186)(62 162 95 173)(63 149 96 188)(64 164 97 175)(65 151 98 190)(66 166 99 177)(67 153 100 192)(68 168 101 179)(69 155 102 194)(70 142 103 181)(71 157 104 196)(72 144 105 183)(73 159 106 170)(74 146 107 185)(75 161 108 172)(76 148 109 187)(77 163 110 174)(78 150 111 189)(79 165 112 176)(80 152 85 191)(81 167 86 178)(82 154 87 193)(83 141 88 180)(84 156 89 195)
(1 141 8 148 15 155 22 162)(2 142 9 149 16 156 23 163)(3 143 10 150 17 157 24 164)(4 144 11 151 18 158 25 165)(5 145 12 152 19 159 26 166)(6 146 13 153 20 160 27 167)(7 147 14 154 21 161 28 168)(29 183 36 190 43 169 50 176)(30 184 37 191 44 170 51 177)(31 185 38 192 45 171 52 178)(32 186 39 193 46 172 53 179)(33 187 40 194 47 173 54 180)(34 188 41 195 48 174 55 181)(35 189 42 196 49 175 56 182)(57 138 64 117 71 124 78 131)(58 139 65 118 72 125 79 132)(59 140 66 119 73 126 80 133)(60 113 67 120 74 127 81 134)(61 114 68 121 75 128 82 135)(62 115 69 122 76 129 83 136)(63 116 70 123 77 130 84 137)(85 201 92 208 99 215 106 222)(86 202 93 209 100 216 107 223)(87 203 94 210 101 217 108 224)(88 204 95 211 102 218 109 197)(89 205 96 212 103 219 110 198)(90 206 97 213 104 220 111 199)(91 207 98 214 105 221 112 200)
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)(29,50)(30,49)(31,48)(32,47)(33,46)(34,45)(35,44)(36,43)(37,42)(38,41)(39,40)(51,56)(52,55)(53,54)(57,73)(58,72)(59,71)(60,70)(61,69)(62,68)(63,67)(64,66)(74,84)(75,83)(76,82)(77,81)(78,80)(85,111)(86,110)(87,109)(88,108)(89,107)(90,106)(91,105)(92,104)(93,103)(94,102)(95,101)(96,100)(97,99)(113,116)(114,115)(117,140)(118,139)(119,138)(120,137)(121,136)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)(128,129)(141,161)(142,160)(143,159)(144,158)(145,157)(146,156)(147,155)(148,154)(149,153)(150,152)(162,168)(163,167)(164,166)(169,183)(170,182)(171,181)(172,180)(173,179)(174,178)(175,177)(184,196)(185,195)(186,194)(187,193)(188,192)(189,191)(197,224)(198,223)(199,222)(200,221)(201,220)(202,219)(203,218)(204,217)(205,216)(206,215)(207,214)(208,213)(209,212)(210,211), (1,122,54,218)(2,137,55,205)(3,124,56,220)(4,139,29,207)(5,126,30,222)(6,113,31,209)(7,128,32,224)(8,115,33,211)(9,130,34,198)(10,117,35,213)(11,132,36,200)(12,119,37,215)(13,134,38,202)(14,121,39,217)(15,136,40,204)(16,123,41,219)(17,138,42,206)(18,125,43,221)(19,140,44,208)(20,127,45,223)(21,114,46,210)(22,129,47,197)(23,116,48,212)(24,131,49,199)(25,118,50,214)(26,133,51,201)(27,120,52,216)(28,135,53,203)(57,143,90,182)(58,158,91,169)(59,145,92,184)(60,160,93,171)(61,147,94,186)(62,162,95,173)(63,149,96,188)(64,164,97,175)(65,151,98,190)(66,166,99,177)(67,153,100,192)(68,168,101,179)(69,155,102,194)(70,142,103,181)(71,157,104,196)(72,144,105,183)(73,159,106,170)(74,146,107,185)(75,161,108,172)(76,148,109,187)(77,163,110,174)(78,150,111,189)(79,165,112,176)(80,152,85,191)(81,167,86,178)(82,154,87,193)(83,141,88,180)(84,156,89,195), (1,141,8,148,15,155,22,162)(2,142,9,149,16,156,23,163)(3,143,10,150,17,157,24,164)(4,144,11,151,18,158,25,165)(5,145,12,152,19,159,26,166)(6,146,13,153,20,160,27,167)(7,147,14,154,21,161,28,168)(29,183,36,190,43,169,50,176)(30,184,37,191,44,170,51,177)(31,185,38,192,45,171,52,178)(32,186,39,193,46,172,53,179)(33,187,40,194,47,173,54,180)(34,188,41,195,48,174,55,181)(35,189,42,196,49,175,56,182)(57,138,64,117,71,124,78,131)(58,139,65,118,72,125,79,132)(59,140,66,119,73,126,80,133)(60,113,67,120,74,127,81,134)(61,114,68,121,75,128,82,135)(62,115,69,122,76,129,83,136)(63,116,70,123,77,130,84,137)(85,201,92,208,99,215,106,222)(86,202,93,209,100,216,107,223)(87,203,94,210,101,217,108,224)(88,204,95,211,102,218,109,197)(89,205,96,212,103,219,110,198)(90,206,97,213,104,220,111,199)(91,207,98,214,105,221,112,200)>;
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)(29,50)(30,49)(31,48)(32,47)(33,46)(34,45)(35,44)(36,43)(37,42)(38,41)(39,40)(51,56)(52,55)(53,54)(57,73)(58,72)(59,71)(60,70)(61,69)(62,68)(63,67)(64,66)(74,84)(75,83)(76,82)(77,81)(78,80)(85,111)(86,110)(87,109)(88,108)(89,107)(90,106)(91,105)(92,104)(93,103)(94,102)(95,101)(96,100)(97,99)(113,116)(114,115)(117,140)(118,139)(119,138)(120,137)(121,136)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)(128,129)(141,161)(142,160)(143,159)(144,158)(145,157)(146,156)(147,155)(148,154)(149,153)(150,152)(162,168)(163,167)(164,166)(169,183)(170,182)(171,181)(172,180)(173,179)(174,178)(175,177)(184,196)(185,195)(186,194)(187,193)(188,192)(189,191)(197,224)(198,223)(199,222)(200,221)(201,220)(202,219)(203,218)(204,217)(205,216)(206,215)(207,214)(208,213)(209,212)(210,211), (1,122,54,218)(2,137,55,205)(3,124,56,220)(4,139,29,207)(5,126,30,222)(6,113,31,209)(7,128,32,224)(8,115,33,211)(9,130,34,198)(10,117,35,213)(11,132,36,200)(12,119,37,215)(13,134,38,202)(14,121,39,217)(15,136,40,204)(16,123,41,219)(17,138,42,206)(18,125,43,221)(19,140,44,208)(20,127,45,223)(21,114,46,210)(22,129,47,197)(23,116,48,212)(24,131,49,199)(25,118,50,214)(26,133,51,201)(27,120,52,216)(28,135,53,203)(57,143,90,182)(58,158,91,169)(59,145,92,184)(60,160,93,171)(61,147,94,186)(62,162,95,173)(63,149,96,188)(64,164,97,175)(65,151,98,190)(66,166,99,177)(67,153,100,192)(68,168,101,179)(69,155,102,194)(70,142,103,181)(71,157,104,196)(72,144,105,183)(73,159,106,170)(74,146,107,185)(75,161,108,172)(76,148,109,187)(77,163,110,174)(78,150,111,189)(79,165,112,176)(80,152,85,191)(81,167,86,178)(82,154,87,193)(83,141,88,180)(84,156,89,195), (1,141,8,148,15,155,22,162)(2,142,9,149,16,156,23,163)(3,143,10,150,17,157,24,164)(4,144,11,151,18,158,25,165)(5,145,12,152,19,159,26,166)(6,146,13,153,20,160,27,167)(7,147,14,154,21,161,28,168)(29,183,36,190,43,169,50,176)(30,184,37,191,44,170,51,177)(31,185,38,192,45,171,52,178)(32,186,39,193,46,172,53,179)(33,187,40,194,47,173,54,180)(34,188,41,195,48,174,55,181)(35,189,42,196,49,175,56,182)(57,138,64,117,71,124,78,131)(58,139,65,118,72,125,79,132)(59,140,66,119,73,126,80,133)(60,113,67,120,74,127,81,134)(61,114,68,121,75,128,82,135)(62,115,69,122,76,129,83,136)(63,116,70,123,77,130,84,137)(85,201,92,208,99,215,106,222)(86,202,93,209,100,216,107,223)(87,203,94,210,101,217,108,224)(88,204,95,211,102,218,109,197)(89,205,96,212,103,219,110,198)(90,206,97,213,104,220,111,199)(91,207,98,214,105,221,112,200) );
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),(29,50),(30,49),(31,48),(32,47),(33,46),(34,45),(35,44),(36,43),(37,42),(38,41),(39,40),(51,56),(52,55),(53,54),(57,73),(58,72),(59,71),(60,70),(61,69),(62,68),(63,67),(64,66),(74,84),(75,83),(76,82),(77,81),(78,80),(85,111),(86,110),(87,109),(88,108),(89,107),(90,106),(91,105),(92,104),(93,103),(94,102),(95,101),(96,100),(97,99),(113,116),(114,115),(117,140),(118,139),(119,138),(120,137),(121,136),(122,135),(123,134),(124,133),(125,132),(126,131),(127,130),(128,129),(141,161),(142,160),(143,159),(144,158),(145,157),(146,156),(147,155),(148,154),(149,153),(150,152),(162,168),(163,167),(164,166),(169,183),(170,182),(171,181),(172,180),(173,179),(174,178),(175,177),(184,196),(185,195),(186,194),(187,193),(188,192),(189,191),(197,224),(198,223),(199,222),(200,221),(201,220),(202,219),(203,218),(204,217),(205,216),(206,215),(207,214),(208,213),(209,212),(210,211)], [(1,122,54,218),(2,137,55,205),(3,124,56,220),(4,139,29,207),(5,126,30,222),(6,113,31,209),(7,128,32,224),(8,115,33,211),(9,130,34,198),(10,117,35,213),(11,132,36,200),(12,119,37,215),(13,134,38,202),(14,121,39,217),(15,136,40,204),(16,123,41,219),(17,138,42,206),(18,125,43,221),(19,140,44,208),(20,127,45,223),(21,114,46,210),(22,129,47,197),(23,116,48,212),(24,131,49,199),(25,118,50,214),(26,133,51,201),(27,120,52,216),(28,135,53,203),(57,143,90,182),(58,158,91,169),(59,145,92,184),(60,160,93,171),(61,147,94,186),(62,162,95,173),(63,149,96,188),(64,164,97,175),(65,151,98,190),(66,166,99,177),(67,153,100,192),(68,168,101,179),(69,155,102,194),(70,142,103,181),(71,157,104,196),(72,144,105,183),(73,159,106,170),(74,146,107,185),(75,161,108,172),(76,148,109,187),(77,163,110,174),(78,150,111,189),(79,165,112,176),(80,152,85,191),(81,167,86,178),(82,154,87,193),(83,141,88,180),(84,156,89,195)], [(1,141,8,148,15,155,22,162),(2,142,9,149,16,156,23,163),(3,143,10,150,17,157,24,164),(4,144,11,151,18,158,25,165),(5,145,12,152,19,159,26,166),(6,146,13,153,20,160,27,167),(7,147,14,154,21,161,28,168),(29,183,36,190,43,169,50,176),(30,184,37,191,44,170,51,177),(31,185,38,192,45,171,52,178),(32,186,39,193,46,172,53,179),(33,187,40,194,47,173,54,180),(34,188,41,195,48,174,55,181),(35,189,42,196,49,175,56,182),(57,138,64,117,71,124,78,131),(58,139,65,118,72,125,79,132),(59,140,66,119,73,126,80,133),(60,113,67,120,74,127,81,134),(61,114,68,121,75,128,82,135),(62,115,69,122,76,129,83,136),(63,116,70,123,77,130,84,137),(85,201,92,208,99,215,106,222),(86,202,93,209,100,216,107,223),(87,203,94,210,101,217,108,224),(88,204,95,211,102,218,109,197),(89,205,96,212,103,219,110,198),(90,206,97,213,104,220,111,199),(91,207,98,214,105,221,112,200)]])
61 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 | 28A | ··· | 28F | 28G | ··· | 28R | 56A | ··· | 56L |
| 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 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 56 | 2 | 2 | 4 | 4 | 8 | 14 | 14 | 28 | 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 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | C4○D4 | D14 | D14 | D14 | C4○D8 | C4○D28 | C8⋊C22 | D4×D7 | D4×D7 | D56⋊C2 | Q8.D14 |
| kernel | D28.12D4 | C14.D8 | Dic7⋊C8 | C7×Q8⋊C4 | D28⋊C4 | C2×D56 | C2×Q8⋊D7 | C28.23D4 | D28 | C2×Dic7 | Q8⋊C4 | C28 | C4⋊C4 | C2×C8 | C2×Q8 | C14 | C4 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 3 | 2 | 3 | 3 | 3 | 4 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of D28.12D4 ►in GL6(𝔽113)
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 104 | 34 | 0 | 0 |
| 0 | 0 | 71 | 33 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 105 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 25 | 0 | 0 |
| 0 | 0 | 104 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 98 | 0 | 0 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 15 |
| 0 | 0 | 0 | 0 | 15 | 0 |
| 13 | 25 | 0 | 0 | 0 | 0 |
| 61 | 100 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 82 | 82 |
| 0 | 0 | 0 | 0 | 31 | 82 |
G:=sub<GL(6,GF(113))| [112,0,0,0,0,0,0,112,0,0,0,0,0,0,104,71,0,0,0,0,34,33,0,0,0,0,0,0,0,1,0,0,0,0,112,0],[112,105,0,0,0,0,0,1,0,0,0,0,0,0,0,104,0,0,0,0,25,0,0,0,0,0,0,0,0,112,0,0,0,0,112,0],[98,0,0,0,0,0,0,98,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,0,15,0,0,0,0,15,0],[13,61,0,0,0,0,25,100,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,82,31,0,0,0,0,82,82] >;
D28.12D4 in GAP, Magma, Sage, TeX
D_{28}._{12}D_4 % in TeX
G:=Group("D28.12D4"); // GroupNames label
G:=SmallGroup(448,353);
// by ID
G=gap.SmallGroup(448,353);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,64,590,555,184,1684,851,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=b^2=c^4=1,d^2=a^7,b*a*b=a^-1,c*a*c^-1=a^15,a*d=d*a,b*c=c*b,d*b*d^-1=a^7*b,d*c*d^-1=a^21*c^-1>;
// generators/relations