metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28.17D4, (C2×Q16)⋊4D7, C4.68(D4×D7), D14⋊C8⋊29C2, (C2×C8).39D14, C28.53(C2×D4), (C7×Q8).10D4, (C14×Q16)⋊14C2, D14⋊3Q8⋊7C2, C7⋊6(D4.7D4), (C2×Q8).63D14, Q8.9(C7⋊D4), C2.D56⋊30C2, C14.62C22≀C2, C14.80(C4○D8), Q8⋊Dic7⋊34C2, (C22×D7).40D4, C22.278(D4×D7), (C2×C56).253C22, (C2×C28).461C23, (C2×Dic7).188D4, (Q8×C14).90C22, C2.17(Q8.D14), C2.30(C23⋊D14), C2.29(Q16⋊D7), (C2×D28).125C22, C14.79(C8.C22), C4⋊Dic7.184C22, (C2×Q8⋊D7)⋊20C2, C4.49(C2×C7⋊D4), (C2×C4×D7).53C22, (C2×C14).372(C2×D4), (C2×C7⋊C8).166C22, (C2×Q8⋊2D7).5C2, (C2×C4).549(C22×D7), SmallGroup(448,721)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28.17D4
G = < a,b,c,d | a28=b2=c4=1, d2=a14, bab=cac-1=a-1, dad-1=a15, cbc-1=a19b, dbd-1=a21b, dcd-1=a14c-1 >
Subgroups: 868 in 152 conjugacy classes, 43 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, Q8, C23, D7, C14, C22⋊C4, C4⋊C4, C2×C8, C2×C8, SD16, Q16, C22×C4, C2×D4, C2×Q8, C4○D4, Dic7, C28, C28, D14, C2×C14, C22⋊C8, D4⋊C4, Q8⋊C4, C22⋊Q8, C2×SD16, C2×Q16, C2×C4○D4, C7⋊C8, C56, C4×D7, D28, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C7×Q8, C22×D7, C22×D7, D4.7D4, C2×C7⋊C8, Dic7⋊C4, C4⋊Dic7, D14⋊C4, Q8⋊D7, C2×C56, C7×Q16, C2×C4×D7, C2×C4×D7, C2×D28, C2×D28, Q8⋊2D7, Q8×C14, D14⋊C8, C2.D56, Q8⋊Dic7, C2×Q8⋊D7, D14⋊3Q8, C14×Q16, C2×Q8⋊2D7, D28.17D4
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, Q16⋊D7, Q8.D14, C23⋊D14, D28.17D4
►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 52)(30 51)(31 50)(32 49)(33 48)(34 47)(35 46)(36 45)(37 44)(38 43)(39 42)(40 41)(53 56)(54 55)(57 61)(58 60)(62 84)(63 83)(64 82)(65 81)(66 80)(67 79)(68 78)(69 77)(70 76)(71 75)(72 74)(85 89)(86 88)(90 112)(91 111)(92 110)(93 109)(94 108)(95 107)(96 106)(97 105)(98 104)(99 103)(100 102)(113 140)(114 139)(115 138)(116 137)(117 136)(118 135)(119 134)(120 133)(121 132)(122 131)(123 130)(124 129)(125 128)(126 127)(141 154)(142 153)(143 152)(144 151)(145 150)(146 149)(147 148)(155 168)(156 167)(157 166)(158 165)(159 164)(160 163)(161 162)(169 187)(170 186)(171 185)(172 184)(173 183)(174 182)(175 181)(176 180)(177 179)(188 196)(189 195)(190 194)(191 193)(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)
(1 203 127 63)(2 202 128 62)(3 201 129 61)(4 200 130 60)(5 199 131 59)(6 198 132 58)(7 197 133 57)(8 224 134 84)(9 223 135 83)(10 222 136 82)(11 221 137 81)(12 220 138 80)(13 219 139 79)(14 218 140 78)(15 217 113 77)(16 216 114 76)(17 215 115 75)(18 214 116 74)(19 213 117 73)(20 212 118 72)(21 211 119 71)(22 210 120 70)(23 209 121 69)(24 208 122 68)(25 207 123 67)(26 206 124 66)(27 205 125 65)(28 204 126 64)(29 194 150 103)(30 193 151 102)(31 192 152 101)(32 191 153 100)(33 190 154 99)(34 189 155 98)(35 188 156 97)(36 187 157 96)(37 186 158 95)(38 185 159 94)(39 184 160 93)(40 183 161 92)(41 182 162 91)(42 181 163 90)(43 180 164 89)(44 179 165 88)(45 178 166 87)(46 177 167 86)(47 176 168 85)(48 175 141 112)(49 174 142 111)(50 173 143 110)(51 172 144 109)(52 171 145 108)(53 170 146 107)(54 169 147 106)(55 196 148 105)(56 195 149 104)
(1 98 15 112)(2 85 16 99)(3 100 17 86)(4 87 18 101)(5 102 19 88)(6 89 20 103)(7 104 21 90)(8 91 22 105)(9 106 23 92)(10 93 24 107)(11 108 25 94)(12 95 26 109)(13 110 27 96)(14 97 28 111)(29 72 43 58)(30 59 44 73)(31 74 45 60)(32 61 46 75)(33 76 47 62)(34 63 48 77)(35 78 49 64)(36 65 50 79)(37 80 51 66)(38 67 52 81)(39 82 53 68)(40 69 54 83)(41 84 55 70)(42 71 56 57)(113 175 127 189)(114 190 128 176)(115 177 129 191)(116 192 130 178)(117 179 131 193)(118 194 132 180)(119 181 133 195)(120 196 134 182)(121 183 135 169)(122 170 136 184)(123 185 137 171)(124 172 138 186)(125 187 139 173)(126 174 140 188)(141 217 155 203)(142 204 156 218)(143 219 157 205)(144 206 158 220)(145 221 159 207)(146 208 160 222)(147 223 161 209)(148 210 162 224)(149 197 163 211)(150 212 164 198)(151 199 165 213)(152 214 166 200)(153 201 167 215)(154 216 168 202)
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)(29,52)(30,51)(31,50)(32,49)(33,48)(34,47)(35,46)(36,45)(37,44)(38,43)(39,42)(40,41)(53,56)(54,55)(57,61)(58,60)(62,84)(63,83)(64,82)(65,81)(66,80)(67,79)(68,78)(69,77)(70,76)(71,75)(72,74)(85,89)(86,88)(90,112)(91,111)(92,110)(93,109)(94,108)(95,107)(96,106)(97,105)(98,104)(99,103)(100,102)(113,140)(114,139)(115,138)(116,137)(117,136)(118,135)(119,134)(120,133)(121,132)(122,131)(123,130)(124,129)(125,128)(126,127)(141,154)(142,153)(143,152)(144,151)(145,150)(146,149)(147,148)(155,168)(156,167)(157,166)(158,165)(159,164)(160,163)(161,162)(169,187)(170,186)(171,185)(172,184)(173,183)(174,182)(175,181)(176,180)(177,179)(188,196)(189,195)(190,194)(191,193)(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), (1,203,127,63)(2,202,128,62)(3,201,129,61)(4,200,130,60)(5,199,131,59)(6,198,132,58)(7,197,133,57)(8,224,134,84)(9,223,135,83)(10,222,136,82)(11,221,137,81)(12,220,138,80)(13,219,139,79)(14,218,140,78)(15,217,113,77)(16,216,114,76)(17,215,115,75)(18,214,116,74)(19,213,117,73)(20,212,118,72)(21,211,119,71)(22,210,120,70)(23,209,121,69)(24,208,122,68)(25,207,123,67)(26,206,124,66)(27,205,125,65)(28,204,126,64)(29,194,150,103)(30,193,151,102)(31,192,152,101)(32,191,153,100)(33,190,154,99)(34,189,155,98)(35,188,156,97)(36,187,157,96)(37,186,158,95)(38,185,159,94)(39,184,160,93)(40,183,161,92)(41,182,162,91)(42,181,163,90)(43,180,164,89)(44,179,165,88)(45,178,166,87)(46,177,167,86)(47,176,168,85)(48,175,141,112)(49,174,142,111)(50,173,143,110)(51,172,144,109)(52,171,145,108)(53,170,146,107)(54,169,147,106)(55,196,148,105)(56,195,149,104), (1,98,15,112)(2,85,16,99)(3,100,17,86)(4,87,18,101)(5,102,19,88)(6,89,20,103)(7,104,21,90)(8,91,22,105)(9,106,23,92)(10,93,24,107)(11,108,25,94)(12,95,26,109)(13,110,27,96)(14,97,28,111)(29,72,43,58)(30,59,44,73)(31,74,45,60)(32,61,46,75)(33,76,47,62)(34,63,48,77)(35,78,49,64)(36,65,50,79)(37,80,51,66)(38,67,52,81)(39,82,53,68)(40,69,54,83)(41,84,55,70)(42,71,56,57)(113,175,127,189)(114,190,128,176)(115,177,129,191)(116,192,130,178)(117,179,131,193)(118,194,132,180)(119,181,133,195)(120,196,134,182)(121,183,135,169)(122,170,136,184)(123,185,137,171)(124,172,138,186)(125,187,139,173)(126,174,140,188)(141,217,155,203)(142,204,156,218)(143,219,157,205)(144,206,158,220)(145,221,159,207)(146,208,160,222)(147,223,161,209)(148,210,162,224)(149,197,163,211)(150,212,164,198)(151,199,165,213)(152,214,166,200)(153,201,167,215)(154,216,168,202)>;
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)(29,52)(30,51)(31,50)(32,49)(33,48)(34,47)(35,46)(36,45)(37,44)(38,43)(39,42)(40,41)(53,56)(54,55)(57,61)(58,60)(62,84)(63,83)(64,82)(65,81)(66,80)(67,79)(68,78)(69,77)(70,76)(71,75)(72,74)(85,89)(86,88)(90,112)(91,111)(92,110)(93,109)(94,108)(95,107)(96,106)(97,105)(98,104)(99,103)(100,102)(113,140)(114,139)(115,138)(116,137)(117,136)(118,135)(119,134)(120,133)(121,132)(122,131)(123,130)(124,129)(125,128)(126,127)(141,154)(142,153)(143,152)(144,151)(145,150)(146,149)(147,148)(155,168)(156,167)(157,166)(158,165)(159,164)(160,163)(161,162)(169,187)(170,186)(171,185)(172,184)(173,183)(174,182)(175,181)(176,180)(177,179)(188,196)(189,195)(190,194)(191,193)(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), (1,203,127,63)(2,202,128,62)(3,201,129,61)(4,200,130,60)(5,199,131,59)(6,198,132,58)(7,197,133,57)(8,224,134,84)(9,223,135,83)(10,222,136,82)(11,221,137,81)(12,220,138,80)(13,219,139,79)(14,218,140,78)(15,217,113,77)(16,216,114,76)(17,215,115,75)(18,214,116,74)(19,213,117,73)(20,212,118,72)(21,211,119,71)(22,210,120,70)(23,209,121,69)(24,208,122,68)(25,207,123,67)(26,206,124,66)(27,205,125,65)(28,204,126,64)(29,194,150,103)(30,193,151,102)(31,192,152,101)(32,191,153,100)(33,190,154,99)(34,189,155,98)(35,188,156,97)(36,187,157,96)(37,186,158,95)(38,185,159,94)(39,184,160,93)(40,183,161,92)(41,182,162,91)(42,181,163,90)(43,180,164,89)(44,179,165,88)(45,178,166,87)(46,177,167,86)(47,176,168,85)(48,175,141,112)(49,174,142,111)(50,173,143,110)(51,172,144,109)(52,171,145,108)(53,170,146,107)(54,169,147,106)(55,196,148,105)(56,195,149,104), (1,98,15,112)(2,85,16,99)(3,100,17,86)(4,87,18,101)(5,102,19,88)(6,89,20,103)(7,104,21,90)(8,91,22,105)(9,106,23,92)(10,93,24,107)(11,108,25,94)(12,95,26,109)(13,110,27,96)(14,97,28,111)(29,72,43,58)(30,59,44,73)(31,74,45,60)(32,61,46,75)(33,76,47,62)(34,63,48,77)(35,78,49,64)(36,65,50,79)(37,80,51,66)(38,67,52,81)(39,82,53,68)(40,69,54,83)(41,84,55,70)(42,71,56,57)(113,175,127,189)(114,190,128,176)(115,177,129,191)(116,192,130,178)(117,179,131,193)(118,194,132,180)(119,181,133,195)(120,196,134,182)(121,183,135,169)(122,170,136,184)(123,185,137,171)(124,172,138,186)(125,187,139,173)(126,174,140,188)(141,217,155,203)(142,204,156,218)(143,219,157,205)(144,206,158,220)(145,221,159,207)(146,208,160,222)(147,223,161,209)(148,210,162,224)(149,197,163,211)(150,212,164,198)(151,199,165,213)(152,214,166,200)(153,201,167,215)(154,216,168,202) );
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),(29,52),(30,51),(31,50),(32,49),(33,48),(34,47),(35,46),(36,45),(37,44),(38,43),(39,42),(40,41),(53,56),(54,55),(57,61),(58,60),(62,84),(63,83),(64,82),(65,81),(66,80),(67,79),(68,78),(69,77),(70,76),(71,75),(72,74),(85,89),(86,88),(90,112),(91,111),(92,110),(93,109),(94,108),(95,107),(96,106),(97,105),(98,104),(99,103),(100,102),(113,140),(114,139),(115,138),(116,137),(117,136),(118,135),(119,134),(120,133),(121,132),(122,131),(123,130),(124,129),(125,128),(126,127),(141,154),(142,153),(143,152),(144,151),(145,150),(146,149),(147,148),(155,168),(156,167),(157,166),(158,165),(159,164),(160,163),(161,162),(169,187),(170,186),(171,185),(172,184),(173,183),(174,182),(175,181),(176,180),(177,179),(188,196),(189,195),(190,194),(191,193),(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)], [(1,203,127,63),(2,202,128,62),(3,201,129,61),(4,200,130,60),(5,199,131,59),(6,198,132,58),(7,197,133,57),(8,224,134,84),(9,223,135,83),(10,222,136,82),(11,221,137,81),(12,220,138,80),(13,219,139,79),(14,218,140,78),(15,217,113,77),(16,216,114,76),(17,215,115,75),(18,214,116,74),(19,213,117,73),(20,212,118,72),(21,211,119,71),(22,210,120,70),(23,209,121,69),(24,208,122,68),(25,207,123,67),(26,206,124,66),(27,205,125,65),(28,204,126,64),(29,194,150,103),(30,193,151,102),(31,192,152,101),(32,191,153,100),(33,190,154,99),(34,189,155,98),(35,188,156,97),(36,187,157,96),(37,186,158,95),(38,185,159,94),(39,184,160,93),(40,183,161,92),(41,182,162,91),(42,181,163,90),(43,180,164,89),(44,179,165,88),(45,178,166,87),(46,177,167,86),(47,176,168,85),(48,175,141,112),(49,174,142,111),(50,173,143,110),(51,172,144,109),(52,171,145,108),(53,170,146,107),(54,169,147,106),(55,196,148,105),(56,195,149,104)], [(1,98,15,112),(2,85,16,99),(3,100,17,86),(4,87,18,101),(5,102,19,88),(6,89,20,103),(7,104,21,90),(8,91,22,105),(9,106,23,92),(10,93,24,107),(11,108,25,94),(12,95,26,109),(13,110,27,96),(14,97,28,111),(29,72,43,58),(30,59,44,73),(31,74,45,60),(32,61,46,75),(33,76,47,62),(34,63,48,77),(35,78,49,64),(36,65,50,79),(37,80,51,66),(38,67,52,81),(39,82,53,68),(40,69,54,83),(41,84,55,70),(42,71,56,57),(113,175,127,189),(114,190,128,176),(115,177,129,191),(116,192,130,178),(117,179,131,193),(118,194,132,180),(119,181,133,195),(120,196,134,182),(121,183,135,169),(122,170,136,184),(123,185,137,171),(124,172,138,186),(125,187,139,173),(126,174,140,188),(141,217,155,203),(142,204,156,218),(143,219,157,205),(144,206,158,220),(145,221,159,207),(146,208,160,222),(147,223,161,209),(148,210,162,224),(149,197,163,211),(150,212,164,198),(151,199,165,213),(152,214,166,200),(153,201,167,215),(154,216,168,202)]])
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 | 28 | 2 | 2 | 4 | 4 | 8 | 14 | 14 | 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 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D4 | D7 | D14 | D14 | C4○D8 | C7⋊D4 | C8.C22 | D4×D7 | D4×D7 | Q16⋊D7 | Q8.D14 |
| kernel | D28.17D4 | D14⋊C8 | C2.D56 | Q8⋊Dic7 | C2×Q8⋊D7 | D14⋊3Q8 | C14×Q16 | C2×Q8⋊2D7 | D28 | C2×Dic7 | C7×Q8 | C22×D7 | C2×Q16 | C2×C8 | C2×Q8 | C14 | Q8 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 2 | 1 | 3 | 3 | 6 | 4 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of D28.17D4 ►in GL4(𝔽113) generated by
| 0 | 1 | 0 | 0 |
| 112 | 0 | 0 | 0 |
| 0 | 0 | 34 | 9 |
| 0 | 0 | 25 | 0 |
| 112 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 9 |
| 0 | 0 | 88 | 0 |
| 31 | 82 | 0 | 0 |
| 82 | 82 | 0 | 0 |
| 0 | 0 | 91 | 53 |
| 0 | 0 | 74 | 22 |
| 13 | 13 | 0 | 0 |
| 13 | 100 | 0 | 0 |
| 0 | 0 | 22 | 5 |
| 0 | 0 | 39 | 91 |
G:=sub<GL(4,GF(113))| [0,112,0,0,1,0,0,0,0,0,34,25,0,0,9,0],[112,0,0,0,0,1,0,0,0,0,0,88,0,0,9,0],[31,82,0,0,82,82,0,0,0,0,91,74,0,0,53,22],[13,13,0,0,13,100,0,0,0,0,22,39,0,0,5,91] >;
D28.17D4 in GAP, Magma, Sage, TeX
D_{28}._{17}D_4 % in TeX
G:=Group("D28.17D4"); // GroupNames label
G:=SmallGroup(448,721);
// by ID
G=gap.SmallGroup(448,721);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,232,758,135,184,570,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=b^2=c^4=1,d^2=a^14,b*a*b=c*a*c^-1=a^-1,d*a*d^-1=a^15,c*b*c^-1=a^19*b,d*b*d^-1=a^21*b,d*c*d^-1=a^14*c^-1>;
// generators/relations