metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28.3Q8, C42.38D14, C4⋊C8⋊7D7, C7⋊3(D4.Q8), C4.45(Q8×D7), C56⋊1C4⋊13C2, C8⋊Dic7⋊17C2, (C2×C4).40D28, (C4×D28).13C2, (C2×C8).132D14, (C2×C28).246D4, C28.104(C2×Q8), C2.D56.4C2, C14.14(C4○D8), (C4×C28).73C22, (C2×C56).26C22, C28.6Q8⋊10C2, C28.288(C4○D4), C2.19(C8⋊D14), C14.16(C8⋊C22), (C2×C28).757C23, C22.120(C2×D28), C14.32(C22⋊Q8), C4⋊Dic7.20C22, C4.112(D4⋊2D7), C2.16(D56⋊7C2), C2.13(D14⋊2Q8), (C2×D28).197C22, (C7×C4⋊C8)⋊9C2, (C2×C14).140(C2×D4), (C2×C4).702(C22×D7), SmallGroup(448,381)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28.3Q8
G = < a,b,c,d | a28=b2=1, c4=a14, d2=a21c2, bab=a-1, ac=ca, ad=da, cbc-1=a7b, bd=db, dcd-1=a7c3 >
Subgroups: 612 in 102 conjugacy classes, 41 normal (39 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, C23, D7, C14, C42, C22⋊C4, C4⋊C4, C2×C8, C22×C4, C2×D4, Dic7, C28, C28, D14, C2×C14, D4⋊C4, C4⋊C8, C4.Q8, C2.D8, C4×D4, C42.C2, C56, C4×D7, D28, D28, C2×Dic7, C2×C28, C22×D7, D4.Q8, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C4×C28, C2×C56, C2×C4×D7, C2×D28, C8⋊Dic7, C56⋊1C4, C2.D56, C7×C4⋊C8, C28.6Q8, C4×D28, D28.3Q8
Quotients: C1, C2, C22, D4, Q8, C23, D7, C2×D4, C2×Q8, C4○D4, D14, C22⋊Q8, C4○D8, C8⋊C22, D28, C22×D7, D4.Q8, C2×D28, D4⋊2D7, Q8×D7, D14⋊2Q8, D56⋊7C2, C8⋊D14, D28.3Q8
►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 14)(2 13)(3 12)(4 11)(5 10)(6 9)(7 8)(15 28)(16 27)(17 26)(18 25)(19 24)(20 23)(21 22)(29 39)(30 38)(31 37)(32 36)(33 35)(40 56)(41 55)(42 54)(43 53)(44 52)(45 51)(46 50)(47 49)(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 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)(113 140)(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)(141 148)(142 147)(143 146)(144 145)(149 168)(150 167)(151 166)(152 165)(153 164)(154 163)(155 162)(156 161)(157 160)(158 159)(169 179)(170 178)(171 177)(172 176)(173 175)(180 196)(181 195)(182 194)(183 193)(184 192)(185 191)(186 190)(187 189)(197 199)(200 224)(201 223)(202 222)(203 221)(204 220)(205 219)(206 218)(207 217)(208 216)(209 215)(210 214)(211 213)
(1 223 127 192 15 209 113 178)(2 224 128 193 16 210 114 179)(3 197 129 194 17 211 115 180)(4 198 130 195 18 212 116 181)(5 199 131 196 19 213 117 182)(6 200 132 169 20 214 118 183)(7 201 133 170 21 215 119 184)(8 202 134 171 22 216 120 185)(9 203 135 172 23 217 121 186)(10 204 136 173 24 218 122 187)(11 205 137 174 25 219 123 188)(12 206 138 175 26 220 124 189)(13 207 139 176 27 221 125 190)(14 208 140 177 28 222 126 191)(29 157 81 94 43 143 67 108)(30 158 82 95 44 144 68 109)(31 159 83 96 45 145 69 110)(32 160 84 97 46 146 70 111)(33 161 57 98 47 147 71 112)(34 162 58 99 48 148 72 85)(35 163 59 100 49 149 73 86)(36 164 60 101 50 150 74 87)(37 165 61 102 51 151 75 88)(38 166 62 103 52 152 76 89)(39 167 63 104 53 153 77 90)(40 168 64 105 54 154 78 91)(41 141 65 106 55 155 79 92)(42 142 66 107 56 156 80 93)
(1 152 120 110)(2 153 121 111)(3 154 122 112)(4 155 123 85)(5 156 124 86)(6 157 125 87)(7 158 126 88)(8 159 127 89)(9 160 128 90)(10 161 129 91)(11 162 130 92)(12 163 131 93)(13 164 132 94)(14 165 133 95)(15 166 134 96)(16 167 135 97)(17 168 136 98)(18 141 137 99)(19 142 138 100)(20 143 139 101)(21 144 140 102)(22 145 113 103)(23 146 114 104)(24 147 115 105)(25 148 116 106)(26 149 117 107)(27 150 118 108)(28 151 119 109)(29 169 74 207)(30 170 75 208)(31 171 76 209)(32 172 77 210)(33 173 78 211)(34 174 79 212)(35 175 80 213)(36 176 81 214)(37 177 82 215)(38 178 83 216)(39 179 84 217)(40 180 57 218)(41 181 58 219)(42 182 59 220)(43 183 60 221)(44 184 61 222)(45 185 62 223)(46 186 63 224)(47 187 64 197)(48 188 65 198)(49 189 66 199)(50 190 67 200)(51 191 68 201)(52 192 69 202)(53 193 70 203)(54 194 71 204)(55 195 72 205)(56 196 73 206)
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), (1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(29,39)(30,38)(31,37)(32,36)(33,35)(40,56)(41,55)(42,54)(43,53)(44,52)(45,51)(46,50)(47,49)(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)(85,92)(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)(113,140)(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)(141,148)(142,147)(143,146)(144,145)(149,168)(150,167)(151,166)(152,165)(153,164)(154,163)(155,162)(156,161)(157,160)(158,159)(169,179)(170,178)(171,177)(172,176)(173,175)(180,196)(181,195)(182,194)(183,193)(184,192)(185,191)(186,190)(187,189)(197,199)(200,224)(201,223)(202,222)(203,221)(204,220)(205,219)(206,218)(207,217)(208,216)(209,215)(210,214)(211,213), (1,223,127,192,15,209,113,178)(2,224,128,193,16,210,114,179)(3,197,129,194,17,211,115,180)(4,198,130,195,18,212,116,181)(5,199,131,196,19,213,117,182)(6,200,132,169,20,214,118,183)(7,201,133,170,21,215,119,184)(8,202,134,171,22,216,120,185)(9,203,135,172,23,217,121,186)(10,204,136,173,24,218,122,187)(11,205,137,174,25,219,123,188)(12,206,138,175,26,220,124,189)(13,207,139,176,27,221,125,190)(14,208,140,177,28,222,126,191)(29,157,81,94,43,143,67,108)(30,158,82,95,44,144,68,109)(31,159,83,96,45,145,69,110)(32,160,84,97,46,146,70,111)(33,161,57,98,47,147,71,112)(34,162,58,99,48,148,72,85)(35,163,59,100,49,149,73,86)(36,164,60,101,50,150,74,87)(37,165,61,102,51,151,75,88)(38,166,62,103,52,152,76,89)(39,167,63,104,53,153,77,90)(40,168,64,105,54,154,78,91)(41,141,65,106,55,155,79,92)(42,142,66,107,56,156,80,93), (1,152,120,110)(2,153,121,111)(3,154,122,112)(4,155,123,85)(5,156,124,86)(6,157,125,87)(7,158,126,88)(8,159,127,89)(9,160,128,90)(10,161,129,91)(11,162,130,92)(12,163,131,93)(13,164,132,94)(14,165,133,95)(15,166,134,96)(16,167,135,97)(17,168,136,98)(18,141,137,99)(19,142,138,100)(20,143,139,101)(21,144,140,102)(22,145,113,103)(23,146,114,104)(24,147,115,105)(25,148,116,106)(26,149,117,107)(27,150,118,108)(28,151,119,109)(29,169,74,207)(30,170,75,208)(31,171,76,209)(32,172,77,210)(33,173,78,211)(34,174,79,212)(35,175,80,213)(36,176,81,214)(37,177,82,215)(38,178,83,216)(39,179,84,217)(40,180,57,218)(41,181,58,219)(42,182,59,220)(43,183,60,221)(44,184,61,222)(45,185,62,223)(46,186,63,224)(47,187,64,197)(48,188,65,198)(49,189,66,199)(50,190,67,200)(51,191,68,201)(52,192,69,202)(53,193,70,203)(54,194,71,204)(55,195,72,205)(56,196,73,206)>;
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), (1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(29,39)(30,38)(31,37)(32,36)(33,35)(40,56)(41,55)(42,54)(43,53)(44,52)(45,51)(46,50)(47,49)(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)(85,92)(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)(113,140)(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)(141,148)(142,147)(143,146)(144,145)(149,168)(150,167)(151,166)(152,165)(153,164)(154,163)(155,162)(156,161)(157,160)(158,159)(169,179)(170,178)(171,177)(172,176)(173,175)(180,196)(181,195)(182,194)(183,193)(184,192)(185,191)(186,190)(187,189)(197,199)(200,224)(201,223)(202,222)(203,221)(204,220)(205,219)(206,218)(207,217)(208,216)(209,215)(210,214)(211,213), (1,223,127,192,15,209,113,178)(2,224,128,193,16,210,114,179)(3,197,129,194,17,211,115,180)(4,198,130,195,18,212,116,181)(5,199,131,196,19,213,117,182)(6,200,132,169,20,214,118,183)(7,201,133,170,21,215,119,184)(8,202,134,171,22,216,120,185)(9,203,135,172,23,217,121,186)(10,204,136,173,24,218,122,187)(11,205,137,174,25,219,123,188)(12,206,138,175,26,220,124,189)(13,207,139,176,27,221,125,190)(14,208,140,177,28,222,126,191)(29,157,81,94,43,143,67,108)(30,158,82,95,44,144,68,109)(31,159,83,96,45,145,69,110)(32,160,84,97,46,146,70,111)(33,161,57,98,47,147,71,112)(34,162,58,99,48,148,72,85)(35,163,59,100,49,149,73,86)(36,164,60,101,50,150,74,87)(37,165,61,102,51,151,75,88)(38,166,62,103,52,152,76,89)(39,167,63,104,53,153,77,90)(40,168,64,105,54,154,78,91)(41,141,65,106,55,155,79,92)(42,142,66,107,56,156,80,93), (1,152,120,110)(2,153,121,111)(3,154,122,112)(4,155,123,85)(5,156,124,86)(6,157,125,87)(7,158,126,88)(8,159,127,89)(9,160,128,90)(10,161,129,91)(11,162,130,92)(12,163,131,93)(13,164,132,94)(14,165,133,95)(15,166,134,96)(16,167,135,97)(17,168,136,98)(18,141,137,99)(19,142,138,100)(20,143,139,101)(21,144,140,102)(22,145,113,103)(23,146,114,104)(24,147,115,105)(25,148,116,106)(26,149,117,107)(27,150,118,108)(28,151,119,109)(29,169,74,207)(30,170,75,208)(31,171,76,209)(32,172,77,210)(33,173,78,211)(34,174,79,212)(35,175,80,213)(36,176,81,214)(37,177,82,215)(38,178,83,216)(39,179,84,217)(40,180,57,218)(41,181,58,219)(42,182,59,220)(43,183,60,221)(44,184,61,222)(45,185,62,223)(46,186,63,224)(47,187,64,197)(48,188,65,198)(49,189,66,199)(50,190,67,200)(51,191,68,201)(52,192,69,202)(53,193,70,203)(54,194,71,204)(55,195,72,205)(56,196,73,206) );
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)], [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,28),(16,27),(17,26),(18,25),(19,24),(20,23),(21,22),(29,39),(30,38),(31,37),(32,36),(33,35),(40,56),(41,55),(42,54),(43,53),(44,52),(45,51),(46,50),(47,49),(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),(85,92),(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),(113,140),(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),(141,148),(142,147),(143,146),(144,145),(149,168),(150,167),(151,166),(152,165),(153,164),(154,163),(155,162),(156,161),(157,160),(158,159),(169,179),(170,178),(171,177),(172,176),(173,175),(180,196),(181,195),(182,194),(183,193),(184,192),(185,191),(186,190),(187,189),(197,199),(200,224),(201,223),(202,222),(203,221),(204,220),(205,219),(206,218),(207,217),(208,216),(209,215),(210,214),(211,213)], [(1,223,127,192,15,209,113,178),(2,224,128,193,16,210,114,179),(3,197,129,194,17,211,115,180),(4,198,130,195,18,212,116,181),(5,199,131,196,19,213,117,182),(6,200,132,169,20,214,118,183),(7,201,133,170,21,215,119,184),(8,202,134,171,22,216,120,185),(9,203,135,172,23,217,121,186),(10,204,136,173,24,218,122,187),(11,205,137,174,25,219,123,188),(12,206,138,175,26,220,124,189),(13,207,139,176,27,221,125,190),(14,208,140,177,28,222,126,191),(29,157,81,94,43,143,67,108),(30,158,82,95,44,144,68,109),(31,159,83,96,45,145,69,110),(32,160,84,97,46,146,70,111),(33,161,57,98,47,147,71,112),(34,162,58,99,48,148,72,85),(35,163,59,100,49,149,73,86),(36,164,60,101,50,150,74,87),(37,165,61,102,51,151,75,88),(38,166,62,103,52,152,76,89),(39,167,63,104,53,153,77,90),(40,168,64,105,54,154,78,91),(41,141,65,106,55,155,79,92),(42,142,66,107,56,156,80,93)], [(1,152,120,110),(2,153,121,111),(3,154,122,112),(4,155,123,85),(5,156,124,86),(6,157,125,87),(7,158,126,88),(8,159,127,89),(9,160,128,90),(10,161,129,91),(11,162,130,92),(12,163,131,93),(13,164,132,94),(14,165,133,95),(15,166,134,96),(16,167,135,97),(17,168,136,98),(18,141,137,99),(19,142,138,100),(20,143,139,101),(21,144,140,102),(22,145,113,103),(23,146,114,104),(24,147,115,105),(25,148,116,106),(26,149,117,107),(27,150,118,108),(28,151,119,109),(29,169,74,207),(30,170,75,208),(31,171,76,209),(32,172,77,210),(33,173,78,211),(34,174,79,212),(35,175,80,213),(36,176,81,214),(37,177,82,215),(38,178,83,216),(39,179,84,217),(40,180,57,218),(41,181,58,219),(42,182,59,220),(43,183,60,221),(44,184,61,222),(45,185,62,223),(46,186,63,224),(47,187,64,197),(48,188,65,198),(49,189,66,199),(50,190,67,200),(51,191,68,201),(52,192,69,202),(53,193,70,203),(54,194,71,204),(55,195,72,205),(56,196,73,206)]])
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 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | + | + | + | + | + | + | - | - | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | Q8 | D4 | D7 | C4○D4 | D14 | D14 | C4○D8 | D28 | D56⋊7C2 | C8⋊C22 | D4⋊2D7 | Q8×D7 | C8⋊D14 |
| kernel | D28.3Q8 | C8⋊Dic7 | C56⋊1C4 | C2.D56 | C7×C4⋊C8 | C28.6Q8 | C4×D28 | D28 | C2×C28 | C4⋊C8 | C28 | C42 | C2×C8 | C14 | C2×C4 | C2 | C14 | C4 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 2 | 3 | 2 | 3 | 6 | 4 | 12 | 24 | 1 | 3 | 3 | 6 |
Matrix representation of D28.3Q8 ►in GL4(𝔽113) generated by
| 23 | 36 | 0 | 0 |
| 77 | 96 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 90 | 77 | 0 | 0 |
| 90 | 23 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 87 | 1 |
| 18 | 9 | 0 | 0 |
| 104 | 8 | 0 | 0 |
| 0 | 0 | 26 | 111 |
| 0 | 0 | 55 | 87 |
| 15 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 |
| 0 | 0 | 15 | 0 |
| 0 | 0 | 51 | 98 |
G:=sub<GL(4,GF(113))| [23,77,0,0,36,96,0,0,0,0,112,0,0,0,0,112],[90,90,0,0,77,23,0,0,0,0,112,87,0,0,0,1],[18,104,0,0,9,8,0,0,0,0,26,55,0,0,111,87],[15,0,0,0,0,15,0,0,0,0,15,51,0,0,0,98] >;
D28.3Q8 in GAP, Magma, Sage, TeX
D_{28}._3Q_8 % in TeX
G:=Group("D28.3Q8"); // GroupNames label
G:=SmallGroup(448,381);
// by ID
G=gap.SmallGroup(448,381);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,344,254,219,142,1123,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=b^2=1,c^4=a^14,d^2=a^21*c^2,b*a*b=a^-1,a*c=c*a,a*d=d*a,c*b*c^-1=a^7*b,b*d=d*b,d*c*d^-1=a^7*c^3>;
// generators/relations