metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28.37D4, Dic14.36D4, C22⋊Q8⋊2D7, C4⋊C4.66D14, C4.102(D4×D7), (C2×C28).266D4, C28.153(C2×D4), C7⋊4(D4.7D4), (C2×Q8).28D14, C14.D8⋊38C2, C14.48C22≀C2, C14.Q16⋊37C2, (C22×C14).93D4, C14.100(C4○D8), C28.55D4⋊14C2, (C2×C28).366C23, (C22×C4).128D14, C23.27(C7⋊D4), (Q8×C14).46C22, C2.16(C23⋊D14), (C2×D28).243C22, C14.90(C8.C22), C2.19(D4.8D14), C2.11(C28.C23), (C22×C28).170C22, (C2×Dic14).270C22, (C2×Q8⋊D7)⋊9C2, (C2×C7⋊Q16)⋊8C2, (C7×C22⋊Q8)⋊2C2, (C2×C4○D28).10C2, (C2×C14).497(C2×D4), (C2×C7⋊C8).115C22, (C2×C4).173(C7⋊D4), (C7×C4⋊C4).113C22, (C2×C4).466(C22×D7), C22.172(C2×C7⋊D4), SmallGroup(448,581)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28.37D4
G = < a,b,c,d | a28=b2=c4=1, d2=a14, bab=a-1, cac-1=a15, ad=da, cbc-1=a7b, bd=db, dcd-1=c-1 >
Subgroups: 796 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, C4⋊C4, C2×C8, SD16, Q16, C22×C4, C22×C4, C2×D4, C2×Q8, 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, C7⋊C8, Dic14, Dic14, C4×D7, D28, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×Q8, C22×D7, C22×C14, D4.7D4, C2×C7⋊C8, Q8⋊D7, C7⋊Q16, C7×C22⋊C4, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C4○D28, C2×C7⋊D4, C22×C28, Q8×C14, C14.D8, C14.Q16, C28.55D4, C2×Q8⋊D7, C2×C7⋊Q16, C7×C22⋊Q8, C2×C4○D28, D28.37D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, D14, C22≀C2, C4○D8, C8.C22, C7⋊D4, C22×D7, D4.7D4, D4×D7, C2×C7⋊D4, C23⋊D14, C28.C23, D4.8D14, D28.37D4
►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 33)(30 32)(34 56)(35 55)(36 54)(37 53)(38 52)(39 51)(40 50)(41 49)(42 48)(43 47)(44 46)(57 68)(58 67)(59 66)(60 65)(61 64)(62 63)(69 84)(70 83)(71 82)(72 81)(73 80)(74 79)(75 78)(76 77)(85 112)(86 111)(87 110)(88 109)(89 108)(90 107)(91 106)(92 105)(93 104)(94 103)(95 102)(96 101)(97 100)(98 99)(113 114)(115 140)(116 139)(117 138)(118 137)(119 136)(120 135)(121 134)(122 133)(123 132)(124 131)(125 130)(126 129)(127 128)(141 149)(142 148)(143 147)(144 146)(150 168)(151 167)(152 166)(153 165)(154 164)(155 163)(156 162)(157 161)(158 160)(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)(197 201)(198 200)(202 224)(203 223)(204 222)(205 221)(206 220)(207 219)(208 218)(209 217)(210 216)(211 215)(212 214)
(1 203 85 188)(2 218 86 175)(3 205 87 190)(4 220 88 177)(5 207 89 192)(6 222 90 179)(7 209 91 194)(8 224 92 181)(9 211 93 196)(10 198 94 183)(11 213 95 170)(12 200 96 185)(13 215 97 172)(14 202 98 187)(15 217 99 174)(16 204 100 189)(17 219 101 176)(18 206 102 191)(19 221 103 178)(20 208 104 193)(21 223 105 180)(22 210 106 195)(23 197 107 182)(24 212 108 169)(25 199 109 184)(26 214 110 171)(27 201 111 186)(28 216 112 173)(29 71 143 136)(30 58 144 123)(31 73 145 138)(32 60 146 125)(33 75 147 140)(34 62 148 127)(35 77 149 114)(36 64 150 129)(37 79 151 116)(38 66 152 131)(39 81 153 118)(40 68 154 133)(41 83 155 120)(42 70 156 135)(43 57 157 122)(44 72 158 137)(45 59 159 124)(46 74 160 139)(47 61 161 126)(48 76 162 113)(49 63 163 128)(50 78 164 115)(51 65 165 130)(52 80 166 117)(53 67 167 132)(54 82 168 119)(55 69 141 134)(56 84 142 121)
(1 63 15 77)(2 64 16 78)(3 65 17 79)(4 66 18 80)(5 67 19 81)(6 68 20 82)(7 69 21 83)(8 70 22 84)(9 71 23 57)(10 72 24 58)(11 73 25 59)(12 74 26 60)(13 75 27 61)(14 76 28 62)(29 197 43 211)(30 198 44 212)(31 199 45 213)(32 200 46 214)(33 201 47 215)(34 202 48 216)(35 203 49 217)(36 204 50 218)(37 205 51 219)(38 206 52 220)(39 207 53 221)(40 208 54 222)(41 209 55 223)(42 210 56 224)(85 128 99 114)(86 129 100 115)(87 130 101 116)(88 131 102 117)(89 132 103 118)(90 133 104 119)(91 134 105 120)(92 135 106 121)(93 136 107 122)(94 137 108 123)(95 138 109 124)(96 139 110 125)(97 140 111 126)(98 113 112 127)(141 180 155 194)(142 181 156 195)(143 182 157 196)(144 183 158 169)(145 184 159 170)(146 185 160 171)(147 186 161 172)(148 187 162 173)(149 188 163 174)(150 189 164 175)(151 190 165 176)(152 191 166 177)(153 192 167 178)(154 193 168 179)
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)(29,33)(30,32)(34,56)(35,55)(36,54)(37,53)(38,52)(39,51)(40,50)(41,49)(42,48)(43,47)(44,46)(57,68)(58,67)(59,66)(60,65)(61,64)(62,63)(69,84)(70,83)(71,82)(72,81)(73,80)(74,79)(75,78)(76,77)(85,112)(86,111)(87,110)(88,109)(89,108)(90,107)(91,106)(92,105)(93,104)(94,103)(95,102)(96,101)(97,100)(98,99)(113,114)(115,140)(116,139)(117,138)(118,137)(119,136)(120,135)(121,134)(122,133)(123,132)(124,131)(125,130)(126,129)(127,128)(141,149)(142,148)(143,147)(144,146)(150,168)(151,167)(152,166)(153,165)(154,164)(155,163)(156,162)(157,161)(158,160)(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)(197,201)(198,200)(202,224)(203,223)(204,222)(205,221)(206,220)(207,219)(208,218)(209,217)(210,216)(211,215)(212,214), (1,203,85,188)(2,218,86,175)(3,205,87,190)(4,220,88,177)(5,207,89,192)(6,222,90,179)(7,209,91,194)(8,224,92,181)(9,211,93,196)(10,198,94,183)(11,213,95,170)(12,200,96,185)(13,215,97,172)(14,202,98,187)(15,217,99,174)(16,204,100,189)(17,219,101,176)(18,206,102,191)(19,221,103,178)(20,208,104,193)(21,223,105,180)(22,210,106,195)(23,197,107,182)(24,212,108,169)(25,199,109,184)(26,214,110,171)(27,201,111,186)(28,216,112,173)(29,71,143,136)(30,58,144,123)(31,73,145,138)(32,60,146,125)(33,75,147,140)(34,62,148,127)(35,77,149,114)(36,64,150,129)(37,79,151,116)(38,66,152,131)(39,81,153,118)(40,68,154,133)(41,83,155,120)(42,70,156,135)(43,57,157,122)(44,72,158,137)(45,59,159,124)(46,74,160,139)(47,61,161,126)(48,76,162,113)(49,63,163,128)(50,78,164,115)(51,65,165,130)(52,80,166,117)(53,67,167,132)(54,82,168,119)(55,69,141,134)(56,84,142,121), (1,63,15,77)(2,64,16,78)(3,65,17,79)(4,66,18,80)(5,67,19,81)(6,68,20,82)(7,69,21,83)(8,70,22,84)(9,71,23,57)(10,72,24,58)(11,73,25,59)(12,74,26,60)(13,75,27,61)(14,76,28,62)(29,197,43,211)(30,198,44,212)(31,199,45,213)(32,200,46,214)(33,201,47,215)(34,202,48,216)(35,203,49,217)(36,204,50,218)(37,205,51,219)(38,206,52,220)(39,207,53,221)(40,208,54,222)(41,209,55,223)(42,210,56,224)(85,128,99,114)(86,129,100,115)(87,130,101,116)(88,131,102,117)(89,132,103,118)(90,133,104,119)(91,134,105,120)(92,135,106,121)(93,136,107,122)(94,137,108,123)(95,138,109,124)(96,139,110,125)(97,140,111,126)(98,113,112,127)(141,180,155,194)(142,181,156,195)(143,182,157,196)(144,183,158,169)(145,184,159,170)(146,185,160,171)(147,186,161,172)(148,187,162,173)(149,188,163,174)(150,189,164,175)(151,190,165,176)(152,191,166,177)(153,192,167,178)(154,193,168,179)>;
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)(29,33)(30,32)(34,56)(35,55)(36,54)(37,53)(38,52)(39,51)(40,50)(41,49)(42,48)(43,47)(44,46)(57,68)(58,67)(59,66)(60,65)(61,64)(62,63)(69,84)(70,83)(71,82)(72,81)(73,80)(74,79)(75,78)(76,77)(85,112)(86,111)(87,110)(88,109)(89,108)(90,107)(91,106)(92,105)(93,104)(94,103)(95,102)(96,101)(97,100)(98,99)(113,114)(115,140)(116,139)(117,138)(118,137)(119,136)(120,135)(121,134)(122,133)(123,132)(124,131)(125,130)(126,129)(127,128)(141,149)(142,148)(143,147)(144,146)(150,168)(151,167)(152,166)(153,165)(154,164)(155,163)(156,162)(157,161)(158,160)(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)(197,201)(198,200)(202,224)(203,223)(204,222)(205,221)(206,220)(207,219)(208,218)(209,217)(210,216)(211,215)(212,214), (1,203,85,188)(2,218,86,175)(3,205,87,190)(4,220,88,177)(5,207,89,192)(6,222,90,179)(7,209,91,194)(8,224,92,181)(9,211,93,196)(10,198,94,183)(11,213,95,170)(12,200,96,185)(13,215,97,172)(14,202,98,187)(15,217,99,174)(16,204,100,189)(17,219,101,176)(18,206,102,191)(19,221,103,178)(20,208,104,193)(21,223,105,180)(22,210,106,195)(23,197,107,182)(24,212,108,169)(25,199,109,184)(26,214,110,171)(27,201,111,186)(28,216,112,173)(29,71,143,136)(30,58,144,123)(31,73,145,138)(32,60,146,125)(33,75,147,140)(34,62,148,127)(35,77,149,114)(36,64,150,129)(37,79,151,116)(38,66,152,131)(39,81,153,118)(40,68,154,133)(41,83,155,120)(42,70,156,135)(43,57,157,122)(44,72,158,137)(45,59,159,124)(46,74,160,139)(47,61,161,126)(48,76,162,113)(49,63,163,128)(50,78,164,115)(51,65,165,130)(52,80,166,117)(53,67,167,132)(54,82,168,119)(55,69,141,134)(56,84,142,121), (1,63,15,77)(2,64,16,78)(3,65,17,79)(4,66,18,80)(5,67,19,81)(6,68,20,82)(7,69,21,83)(8,70,22,84)(9,71,23,57)(10,72,24,58)(11,73,25,59)(12,74,26,60)(13,75,27,61)(14,76,28,62)(29,197,43,211)(30,198,44,212)(31,199,45,213)(32,200,46,214)(33,201,47,215)(34,202,48,216)(35,203,49,217)(36,204,50,218)(37,205,51,219)(38,206,52,220)(39,207,53,221)(40,208,54,222)(41,209,55,223)(42,210,56,224)(85,128,99,114)(86,129,100,115)(87,130,101,116)(88,131,102,117)(89,132,103,118)(90,133,104,119)(91,134,105,120)(92,135,106,121)(93,136,107,122)(94,137,108,123)(95,138,109,124)(96,139,110,125)(97,140,111,126)(98,113,112,127)(141,180,155,194)(142,181,156,195)(143,182,157,196)(144,183,158,169)(145,184,159,170)(146,185,160,171)(147,186,161,172)(148,187,162,173)(149,188,163,174)(150,189,164,175)(151,190,165,176)(152,191,166,177)(153,192,167,178)(154,193,168,179) );
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),(29,33),(30,32),(34,56),(35,55),(36,54),(37,53),(38,52),(39,51),(40,50),(41,49),(42,48),(43,47),(44,46),(57,68),(58,67),(59,66),(60,65),(61,64),(62,63),(69,84),(70,83),(71,82),(72,81),(73,80),(74,79),(75,78),(76,77),(85,112),(86,111),(87,110),(88,109),(89,108),(90,107),(91,106),(92,105),(93,104),(94,103),(95,102),(96,101),(97,100),(98,99),(113,114),(115,140),(116,139),(117,138),(118,137),(119,136),(120,135),(121,134),(122,133),(123,132),(124,131),(125,130),(126,129),(127,128),(141,149),(142,148),(143,147),(144,146),(150,168),(151,167),(152,166),(153,165),(154,164),(155,163),(156,162),(157,161),(158,160),(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),(197,201),(198,200),(202,224),(203,223),(204,222),(205,221),(206,220),(207,219),(208,218),(209,217),(210,216),(211,215),(212,214)], [(1,203,85,188),(2,218,86,175),(3,205,87,190),(4,220,88,177),(5,207,89,192),(6,222,90,179),(7,209,91,194),(8,224,92,181),(9,211,93,196),(10,198,94,183),(11,213,95,170),(12,200,96,185),(13,215,97,172),(14,202,98,187),(15,217,99,174),(16,204,100,189),(17,219,101,176),(18,206,102,191),(19,221,103,178),(20,208,104,193),(21,223,105,180),(22,210,106,195),(23,197,107,182),(24,212,108,169),(25,199,109,184),(26,214,110,171),(27,201,111,186),(28,216,112,173),(29,71,143,136),(30,58,144,123),(31,73,145,138),(32,60,146,125),(33,75,147,140),(34,62,148,127),(35,77,149,114),(36,64,150,129),(37,79,151,116),(38,66,152,131),(39,81,153,118),(40,68,154,133),(41,83,155,120),(42,70,156,135),(43,57,157,122),(44,72,158,137),(45,59,159,124),(46,74,160,139),(47,61,161,126),(48,76,162,113),(49,63,163,128),(50,78,164,115),(51,65,165,130),(52,80,166,117),(53,67,167,132),(54,82,168,119),(55,69,141,134),(56,84,142,121)], [(1,63,15,77),(2,64,16,78),(3,65,17,79),(4,66,18,80),(5,67,19,81),(6,68,20,82),(7,69,21,83),(8,70,22,84),(9,71,23,57),(10,72,24,58),(11,73,25,59),(12,74,26,60),(13,75,27,61),(14,76,28,62),(29,197,43,211),(30,198,44,212),(31,199,45,213),(32,200,46,214),(33,201,47,215),(34,202,48,216),(35,203,49,217),(36,204,50,218),(37,205,51,219),(38,206,52,220),(39,207,53,221),(40,208,54,222),(41,209,55,223),(42,210,56,224),(85,128,99,114),(86,129,100,115),(87,130,101,116),(88,131,102,117),(89,132,103,118),(90,133,104,119),(91,134,105,120),(92,135,106,121),(93,136,107,122),(94,137,108,123),(95,138,109,124),(96,139,110,125),(97,140,111,126),(98,113,112,127),(141,180,155,194),(142,181,156,195),(143,182,157,196),(144,183,158,169),(145,184,159,170),(146,185,160,171),(147,186,161,172),(148,187,162,173),(149,188,163,174),(150,189,164,175),(151,190,165,176),(152,191,166,177),(153,192,167,178),(154,193,168,179)]])
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 | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28X |
| 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 |
| size | 1 | 1 | 1 | 1 | 4 | 28 | 28 | 2 | 2 | 2 | 2 | 8 | 8 | 28 | 28 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 8 | ··· | 8 |
61 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 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D4 | D7 | D14 | D14 | D14 | C4○D8 | C7⋊D4 | C7⋊D4 | C8.C22 | D4×D7 | C28.C23 | D4.8D14 |
| kernel | D28.37D4 | C14.D8 | C14.Q16 | C28.55D4 | C2×Q8⋊D7 | C2×C7⋊Q16 | C7×C22⋊Q8 | C2×C4○D28 | Dic14 | D28 | C2×C28 | C22×C14 | C22⋊Q8 | C4⋊C4 | C22×C4 | C2×Q8 | C14 | C2×C4 | C23 | C14 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 3 | 3 | 3 | 3 | 4 | 6 | 6 | 1 | 6 | 6 | 6 |
Matrix representation of D28.37D4 ►in GL6(𝔽113)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 89 | 0 | 0 |
| 0 | 0 | 24 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 87 |
| 0 | 0 | 0 | 0 | 87 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 89 | 0 | 0 |
| 0 | 0 | 103 | 103 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 87 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 80 | 104 | 0 | 0 | 0 | 0 |
| 96 | 33 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 15 |
| 0 | 0 | 0 | 0 | 98 | 0 |
| 33 | 49 | 0 | 0 | 0 | 0 |
| 17 | 80 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 98 | 0 |
| 0 | 0 | 0 | 0 | 0 | 98 |
G:=sub<GL(6,GF(113))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,10,24,0,0,0,0,89,112,0,0,0,0,0,0,112,87,0,0,0,0,87,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,10,103,0,0,0,0,89,103,0,0,0,0,0,0,112,0,0,0,0,0,87,1],[80,96,0,0,0,0,104,33,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,98,0,0,0,0,15,0],[33,17,0,0,0,0,49,80,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,98,0,0,0,0,0,0,98] >;
D28.37D4 in GAP, Magma, Sage, TeX
D_{28}._{37}D_4 % in TeX
G:=Group("D28.37D4"); // GroupNames label
G:=SmallGroup(448,581);
// by ID
G=gap.SmallGroup(448,581);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,254,219,184,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=b^2=c^4=1,d^2=a^14,b*a*b=a^-1,c*a*c^-1=a^15,a*d=d*a,c*b*c^-1=a^7*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations