metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28⋊4Q8, C28.13D8, C4.13D56, C42.37D14, C4⋊C8⋊4D7, C14.8(C2×D8), C4.44(Q8×D7), C56⋊1C4⋊12C2, C7⋊2(D4⋊Q8), (C2×C8).22D14, C2.10(C2×D56), C28⋊2Q8⋊13C2, (C4×D28).12C2, (C2×C28).123D4, (C2×C4).134D28, C28.103(C2×Q8), C2.D56.3C2, (C2×C56).25C22, (C4×C28).72C22, C28.287(C4○D4), (C2×C28).756C23, C22.119(C2×D28), C14.31(C22⋊Q8), C4⋊Dic7.19C22, C4.111(D4⋊2D7), C2.12(D14⋊2Q8), C2.19(C8.D14), (C2×D28).196C22, C14.16(C8.C22), (C7×C4⋊C8)⋊6C2, (C2×C14).139(C2×D4), (C2×C4).701(C22×D7), SmallGroup(448,380)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28⋊4Q8
G = < a,b,c,d | a28=b2=c4=1, d2=c2, bab=cac-1=a-1, ad=da, cbc-1=a19b, bd=db, dcd-1=c-1 >
Subgroups: 676 in 108 conjugacy classes, 45 normal (29 characteristic)
C1, C2, C2, C4, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C22⋊C4, C4⋊C4, C2×C8, C22×C4, C2×D4, C2×Q8, Dic7, C28, C28, C28, D14, C2×C14, D4⋊C4, C4⋊C8, C2.D8, C4×D4, C4⋊Q8, C56, Dic14, C4×D7, D28, D28, C2×Dic7, C2×C28, C22×D7, D4⋊Q8, C4⋊Dic7, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C4×C28, C2×C56, C2×Dic14, C2×C4×D7, C2×D28, C56⋊1C4, C2.D56, C7×C4⋊C8, C28⋊2Q8, C4×D28, D28⋊4Q8
Quotients: C1, C2, C22, D4, Q8, C23, D7, D8, C2×D4, C2×Q8, C4○D4, D14, C22⋊Q8, C2×D8, C8.C22, D28, C22×D7, D4⋊Q8, D56, C2×D28, D4⋊2D7, Q8×D7, D14⋊2Q8, C2×D56, C8.D14, D28⋊4Q8
►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 44)(30 43)(31 42)(32 41)(33 40)(34 39)(35 38)(36 37)(45 56)(46 55)(47 54)(48 53)(49 52)(50 51)(57 71)(58 70)(59 69)(60 68)(61 67)(62 66)(63 65)(72 84)(73 83)(74 82)(75 81)(76 80)(77 79)(85 103)(86 102)(87 101)(88 100)(89 99)(90 98)(91 97)(92 96)(93 95)(104 112)(105 111)(106 110)(107 109)(113 118)(114 117)(115 116)(119 140)(120 139)(121 138)(122 137)(123 136)(124 135)(125 134)(126 133)(127 132)(128 131)(129 130)(142 168)(143 167)(144 166)(145 165)(146 164)(147 163)(148 162)(149 161)(150 160)(151 159)(152 158)(153 157)(154 156)(169 176)(170 175)(171 174)(172 173)(177 196)(178 195)(179 194)(180 193)(181 192)(182 191)(183 190)(184 189)(185 188)(186 187)(197 213)(198 212)(199 211)(200 210)(201 209)(202 208)(203 207)(204 206)(214 224)(215 223)(216 222)(217 221)(218 220)
(1 159 116 82)(2 158 117 81)(3 157 118 80)(4 156 119 79)(5 155 120 78)(6 154 121 77)(7 153 122 76)(8 152 123 75)(9 151 124 74)(10 150 125 73)(11 149 126 72)(12 148 127 71)(13 147 128 70)(14 146 129 69)(15 145 130 68)(16 144 131 67)(17 143 132 66)(18 142 133 65)(19 141 134 64)(20 168 135 63)(21 167 136 62)(22 166 137 61)(23 165 138 60)(24 164 139 59)(25 163 140 58)(26 162 113 57)(27 161 114 84)(28 160 115 83)(29 217 179 92)(30 216 180 91)(31 215 181 90)(32 214 182 89)(33 213 183 88)(34 212 184 87)(35 211 185 86)(36 210 186 85)(37 209 187 112)(38 208 188 111)(39 207 189 110)(40 206 190 109)(41 205 191 108)(42 204 192 107)(43 203 193 106)(44 202 194 105)(45 201 195 104)(46 200 196 103)(47 199 169 102)(48 198 170 101)(49 197 171 100)(50 224 172 99)(51 223 173 98)(52 222 174 97)(53 221 175 96)(54 220 176 95)(55 219 177 94)(56 218 178 93)
(1 51 116 173)(2 52 117 174)(3 53 118 175)(4 54 119 176)(5 55 120 177)(6 56 121 178)(7 29 122 179)(8 30 123 180)(9 31 124 181)(10 32 125 182)(11 33 126 183)(12 34 127 184)(13 35 128 185)(14 36 129 186)(15 37 130 187)(16 38 131 188)(17 39 132 189)(18 40 133 190)(19 41 134 191)(20 42 135 192)(21 43 136 193)(22 44 137 194)(23 45 138 195)(24 46 139 196)(25 47 140 169)(26 48 113 170)(27 49 114 171)(28 50 115 172)(57 198 162 101)(58 199 163 102)(59 200 164 103)(60 201 165 104)(61 202 166 105)(62 203 167 106)(63 204 168 107)(64 205 141 108)(65 206 142 109)(66 207 143 110)(67 208 144 111)(68 209 145 112)(69 210 146 85)(70 211 147 86)(71 212 148 87)(72 213 149 88)(73 214 150 89)(74 215 151 90)(75 216 152 91)(76 217 153 92)(77 218 154 93)(78 219 155 94)(79 220 156 95)(80 221 157 96)(81 222 158 97)(82 223 159 98)(83 224 160 99)(84 197 161 100)
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)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)(57,71)(58,70)(59,69)(60,68)(61,67)(62,66)(63,65)(72,84)(73,83)(74,82)(75,81)(76,80)(77,79)(85,103)(86,102)(87,101)(88,100)(89,99)(90,98)(91,97)(92,96)(93,95)(104,112)(105,111)(106,110)(107,109)(113,118)(114,117)(115,116)(119,140)(120,139)(121,138)(122,137)(123,136)(124,135)(125,134)(126,133)(127,132)(128,131)(129,130)(142,168)(143,167)(144,166)(145,165)(146,164)(147,163)(148,162)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)(169,176)(170,175)(171,174)(172,173)(177,196)(178,195)(179,194)(180,193)(181,192)(182,191)(183,190)(184,189)(185,188)(186,187)(197,213)(198,212)(199,211)(200,210)(201,209)(202,208)(203,207)(204,206)(214,224)(215,223)(216,222)(217,221)(218,220), (1,159,116,82)(2,158,117,81)(3,157,118,80)(4,156,119,79)(5,155,120,78)(6,154,121,77)(7,153,122,76)(8,152,123,75)(9,151,124,74)(10,150,125,73)(11,149,126,72)(12,148,127,71)(13,147,128,70)(14,146,129,69)(15,145,130,68)(16,144,131,67)(17,143,132,66)(18,142,133,65)(19,141,134,64)(20,168,135,63)(21,167,136,62)(22,166,137,61)(23,165,138,60)(24,164,139,59)(25,163,140,58)(26,162,113,57)(27,161,114,84)(28,160,115,83)(29,217,179,92)(30,216,180,91)(31,215,181,90)(32,214,182,89)(33,213,183,88)(34,212,184,87)(35,211,185,86)(36,210,186,85)(37,209,187,112)(38,208,188,111)(39,207,189,110)(40,206,190,109)(41,205,191,108)(42,204,192,107)(43,203,193,106)(44,202,194,105)(45,201,195,104)(46,200,196,103)(47,199,169,102)(48,198,170,101)(49,197,171,100)(50,224,172,99)(51,223,173,98)(52,222,174,97)(53,221,175,96)(54,220,176,95)(55,219,177,94)(56,218,178,93), (1,51,116,173)(2,52,117,174)(3,53,118,175)(4,54,119,176)(5,55,120,177)(6,56,121,178)(7,29,122,179)(8,30,123,180)(9,31,124,181)(10,32,125,182)(11,33,126,183)(12,34,127,184)(13,35,128,185)(14,36,129,186)(15,37,130,187)(16,38,131,188)(17,39,132,189)(18,40,133,190)(19,41,134,191)(20,42,135,192)(21,43,136,193)(22,44,137,194)(23,45,138,195)(24,46,139,196)(25,47,140,169)(26,48,113,170)(27,49,114,171)(28,50,115,172)(57,198,162,101)(58,199,163,102)(59,200,164,103)(60,201,165,104)(61,202,166,105)(62,203,167,106)(63,204,168,107)(64,205,141,108)(65,206,142,109)(66,207,143,110)(67,208,144,111)(68,209,145,112)(69,210,146,85)(70,211,147,86)(71,212,148,87)(72,213,149,88)(73,214,150,89)(74,215,151,90)(75,216,152,91)(76,217,153,92)(77,218,154,93)(78,219,155,94)(79,220,156,95)(80,221,157,96)(81,222,158,97)(82,223,159,98)(83,224,160,99)(84,197,161,100)>;
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)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)(57,71)(58,70)(59,69)(60,68)(61,67)(62,66)(63,65)(72,84)(73,83)(74,82)(75,81)(76,80)(77,79)(85,103)(86,102)(87,101)(88,100)(89,99)(90,98)(91,97)(92,96)(93,95)(104,112)(105,111)(106,110)(107,109)(113,118)(114,117)(115,116)(119,140)(120,139)(121,138)(122,137)(123,136)(124,135)(125,134)(126,133)(127,132)(128,131)(129,130)(142,168)(143,167)(144,166)(145,165)(146,164)(147,163)(148,162)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)(169,176)(170,175)(171,174)(172,173)(177,196)(178,195)(179,194)(180,193)(181,192)(182,191)(183,190)(184,189)(185,188)(186,187)(197,213)(198,212)(199,211)(200,210)(201,209)(202,208)(203,207)(204,206)(214,224)(215,223)(216,222)(217,221)(218,220), (1,159,116,82)(2,158,117,81)(3,157,118,80)(4,156,119,79)(5,155,120,78)(6,154,121,77)(7,153,122,76)(8,152,123,75)(9,151,124,74)(10,150,125,73)(11,149,126,72)(12,148,127,71)(13,147,128,70)(14,146,129,69)(15,145,130,68)(16,144,131,67)(17,143,132,66)(18,142,133,65)(19,141,134,64)(20,168,135,63)(21,167,136,62)(22,166,137,61)(23,165,138,60)(24,164,139,59)(25,163,140,58)(26,162,113,57)(27,161,114,84)(28,160,115,83)(29,217,179,92)(30,216,180,91)(31,215,181,90)(32,214,182,89)(33,213,183,88)(34,212,184,87)(35,211,185,86)(36,210,186,85)(37,209,187,112)(38,208,188,111)(39,207,189,110)(40,206,190,109)(41,205,191,108)(42,204,192,107)(43,203,193,106)(44,202,194,105)(45,201,195,104)(46,200,196,103)(47,199,169,102)(48,198,170,101)(49,197,171,100)(50,224,172,99)(51,223,173,98)(52,222,174,97)(53,221,175,96)(54,220,176,95)(55,219,177,94)(56,218,178,93), (1,51,116,173)(2,52,117,174)(3,53,118,175)(4,54,119,176)(5,55,120,177)(6,56,121,178)(7,29,122,179)(8,30,123,180)(9,31,124,181)(10,32,125,182)(11,33,126,183)(12,34,127,184)(13,35,128,185)(14,36,129,186)(15,37,130,187)(16,38,131,188)(17,39,132,189)(18,40,133,190)(19,41,134,191)(20,42,135,192)(21,43,136,193)(22,44,137,194)(23,45,138,195)(24,46,139,196)(25,47,140,169)(26,48,113,170)(27,49,114,171)(28,50,115,172)(57,198,162,101)(58,199,163,102)(59,200,164,103)(60,201,165,104)(61,202,166,105)(62,203,167,106)(63,204,168,107)(64,205,141,108)(65,206,142,109)(66,207,143,110)(67,208,144,111)(68,209,145,112)(69,210,146,85)(70,211,147,86)(71,212,148,87)(72,213,149,88)(73,214,150,89)(74,215,151,90)(75,216,152,91)(76,217,153,92)(77,218,154,93)(78,219,155,94)(79,220,156,95)(80,221,157,96)(81,222,158,97)(82,223,159,98)(83,224,160,99)(84,197,161,100) );
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),(29,44),(30,43),(31,42),(32,41),(33,40),(34,39),(35,38),(36,37),(45,56),(46,55),(47,54),(48,53),(49,52),(50,51),(57,71),(58,70),(59,69),(60,68),(61,67),(62,66),(63,65),(72,84),(73,83),(74,82),(75,81),(76,80),(77,79),(85,103),(86,102),(87,101),(88,100),(89,99),(90,98),(91,97),(92,96),(93,95),(104,112),(105,111),(106,110),(107,109),(113,118),(114,117),(115,116),(119,140),(120,139),(121,138),(122,137),(123,136),(124,135),(125,134),(126,133),(127,132),(128,131),(129,130),(142,168),(143,167),(144,166),(145,165),(146,164),(147,163),(148,162),(149,161),(150,160),(151,159),(152,158),(153,157),(154,156),(169,176),(170,175),(171,174),(172,173),(177,196),(178,195),(179,194),(180,193),(181,192),(182,191),(183,190),(184,189),(185,188),(186,187),(197,213),(198,212),(199,211),(200,210),(201,209),(202,208),(203,207),(204,206),(214,224),(215,223),(216,222),(217,221),(218,220)], [(1,159,116,82),(2,158,117,81),(3,157,118,80),(4,156,119,79),(5,155,120,78),(6,154,121,77),(7,153,122,76),(8,152,123,75),(9,151,124,74),(10,150,125,73),(11,149,126,72),(12,148,127,71),(13,147,128,70),(14,146,129,69),(15,145,130,68),(16,144,131,67),(17,143,132,66),(18,142,133,65),(19,141,134,64),(20,168,135,63),(21,167,136,62),(22,166,137,61),(23,165,138,60),(24,164,139,59),(25,163,140,58),(26,162,113,57),(27,161,114,84),(28,160,115,83),(29,217,179,92),(30,216,180,91),(31,215,181,90),(32,214,182,89),(33,213,183,88),(34,212,184,87),(35,211,185,86),(36,210,186,85),(37,209,187,112),(38,208,188,111),(39,207,189,110),(40,206,190,109),(41,205,191,108),(42,204,192,107),(43,203,193,106),(44,202,194,105),(45,201,195,104),(46,200,196,103),(47,199,169,102),(48,198,170,101),(49,197,171,100),(50,224,172,99),(51,223,173,98),(52,222,174,97),(53,221,175,96),(54,220,176,95),(55,219,177,94),(56,218,178,93)], [(1,51,116,173),(2,52,117,174),(3,53,118,175),(4,54,119,176),(5,55,120,177),(6,56,121,178),(7,29,122,179),(8,30,123,180),(9,31,124,181),(10,32,125,182),(11,33,126,183),(12,34,127,184),(13,35,128,185),(14,36,129,186),(15,37,130,187),(16,38,131,188),(17,39,132,189),(18,40,133,190),(19,41,134,191),(20,42,135,192),(21,43,136,193),(22,44,137,194),(23,45,138,195),(24,46,139,196),(25,47,140,169),(26,48,113,170),(27,49,114,171),(28,50,115,172),(57,198,162,101),(58,199,163,102),(59,200,164,103),(60,201,165,104),(61,202,166,105),(62,203,167,106),(63,204,168,107),(64,205,141,108),(65,206,142,109),(66,207,143,110),(67,208,144,111),(68,209,145,112),(69,210,146,85),(70,211,147,86),(71,212,148,87),(72,213,149,88),(73,214,150,89),(74,215,151,90),(75,216,152,91),(76,217,153,92),(77,218,154,93),(78,219,155,94),(79,220,156,95),(80,221,157,96),(81,222,158,97),(82,223,159,98),(83,224,160,99),(84,197,161,100)]])
79 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 | ··· | 28L | 28M | ··· | 28X | 56A | ··· | 56X |
| 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 | 2 | 2 | 4 | 28 | 28 | 56 | 56 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
79 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | - | + | + | + | + | + | + | + | - | - | - | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | Q8 | D4 | D7 | D8 | C4○D4 | D14 | D14 | D28 | D56 | C8.C22 | D4⋊2D7 | Q8×D7 | C8.D14 |
| kernel | D28⋊4Q8 | C56⋊1C4 | C2.D56 | C7×C4⋊C8 | C28⋊2Q8 | C4×D28 | D28 | C2×C28 | C4⋊C8 | C28 | C28 | C42 | C2×C8 | C2×C4 | C4 | C14 | C4 | C4 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 2 | 2 | 3 | 4 | 2 | 3 | 6 | 12 | 24 | 1 | 3 | 3 | 6 |
Matrix representation of D28⋊4Q8 ►in GL4(𝔽113) generated by
| 94 | 13 | 0 | 0 |
| 100 | 104 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 94 | 13 | 0 | 0 |
| 94 | 19 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 49 | 1 |
| 84 | 43 | 0 | 0 |
| 12 | 29 | 0 | 0 |
| 0 | 0 | 81 | 1 |
| 0 | 0 | 105 | 32 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 15 | 0 |
| 0 | 0 | 56 | 98 |
G:=sub<GL(4,GF(113))| [94,100,0,0,13,104,0,0,0,0,112,0,0,0,0,112],[94,94,0,0,13,19,0,0,0,0,112,49,0,0,0,1],[84,12,0,0,43,29,0,0,0,0,81,105,0,0,1,32],[1,0,0,0,0,1,0,0,0,0,15,56,0,0,0,98] >;
D28⋊4Q8 in GAP, Magma, Sage, TeX
D_{28}\rtimes_4Q_8 % in TeX
G:=Group("D28:4Q8"); // GroupNames label
G:=SmallGroup(448,380);
// by ID
G=gap.SmallGroup(448,380);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,254,219,310,1123,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=b^2=c^4=1,d^2=c^2,b*a*b=c*a*c^-1=a^-1,a*d=d*a,c*b*c^-1=a^19*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations