metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28⋊1Q8, Dic7.5SD16, C28⋊Q8⋊6C2, C4.3(Q8×D7), C4.Q8⋊11D7, C7⋊3(D4⋊2Q8), C28.15(C2×Q8), Dic7⋊C8⋊30C2, C4⋊C4.164D14, (C2×C8).141D14, C2.25(D7×SD16), C14.D8.5C2, D28⋊C4.5C2, C4.76(C4○D28), C4.Dic14⋊18C2, (C2×Dic7).44D4, C14.41(C2×SD16), C22.221(D4×D7), C2.D56.13C2, C28.168(C4○D4), C2.24(D56⋊C2), C14.73(C8⋊C22), (C2×C28).286C23, (C2×C56).288C22, (C2×D28).78C22, C14.37(C22⋊Q8), C2.14(D14⋊Q8), C4⋊Dic7.114C22, (C4×Dic7).32C22, (C7×C4.Q8)⋊19C2, (C2×C7⋊C8).63C22, (C2×C14).291(C2×D4), (C7×C4⋊C4).79C22, (C2×C4).389(C22×D7), SmallGroup(448,404)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28⋊Q8
G = < a,b,c,d | a28=b2=c4=1, d2=c2, bab=cac-1=a-1, dad-1=a13, cbc-1=a19b, dbd-1=a26b, dcd-1=c-1 >
Subgroups: 652 in 108 conjugacy classes, 41 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, C4⋊C4, C2×C8, C2×C8, C22×C4, C2×D4, C2×Q8, Dic7, Dic7, C28, C28, D14, C2×C14, D4⋊C4, C4⋊C8, C4.Q8, C4.Q8, C4×D4, C4⋊Q8, C7⋊C8, C56, Dic14, C4×D7, D28, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, D4⋊2Q8, C2×C7⋊C8, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C7×C4⋊C4, C2×C56, C2×Dic14, C2×C4×D7, C2×D28, C4.Dic14, C14.D8, Dic7⋊C8, C2.D56, C7×C4.Q8, C28⋊Q8, D28⋊C4, D28⋊Q8
Quotients: C1, C2, C22, D4, Q8, C23, D7, SD16, C2×D4, C2×Q8, C4○D4, D14, C22⋊Q8, C2×SD16, C8⋊C22, C22×D7, D4⋊2Q8, C4○D28, D4×D7, Q8×D7, D14⋊Q8, D7×SD16, D56⋊C2, D28⋊Q8
►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)
(1 186)(2 185)(3 184)(4 183)(5 182)(6 181)(7 180)(8 179)(9 178)(10 177)(11 176)(12 175)(13 174)(14 173)(15 172)(16 171)(17 170)(18 169)(19 196)(20 195)(21 194)(22 193)(23 192)(24 191)(25 190)(26 189)(27 188)(28 187)(29 141)(30 168)(31 167)(32 166)(33 165)(34 164)(35 163)(36 162)(37 161)(38 160)(39 159)(40 158)(41 157)(42 156)(43 155)(44 154)(45 153)(46 152)(47 151)(48 150)(49 149)(50 148)(51 147)(52 146)(53 145)(54 144)(55 143)(56 142)(57 208)(58 207)(59 206)(60 205)(61 204)(62 203)(63 202)(64 201)(65 200)(66 199)(67 198)(68 197)(69 224)(70 223)(71 222)(72 221)(73 220)(74 219)(75 218)(76 217)(77 216)(78 215)(79 214)(80 213)(81 212)(82 211)(83 210)(84 209)(85 117)(86 116)(87 115)(88 114)(89 113)(90 140)(91 139)(92 138)(93 137)(94 136)(95 135)(96 134)(97 133)(98 132)(99 131)(100 130)(101 129)(102 128)(103 127)(104 126)(105 125)(106 124)(107 123)(108 122)(109 121)(110 120)(111 119)(112 118)
(1 161 194 38)(2 160 195 37)(3 159 196 36)(4 158 169 35)(5 157 170 34)(6 156 171 33)(7 155 172 32)(8 154 173 31)(9 153 174 30)(10 152 175 29)(11 151 176 56)(12 150 177 55)(13 149 178 54)(14 148 179 53)(15 147 180 52)(16 146 181 51)(17 145 182 50)(18 144 183 49)(19 143 184 48)(20 142 185 47)(21 141 186 46)(22 168 187 45)(23 167 188 44)(24 166 189 43)(25 165 190 42)(26 164 191 41)(27 163 192 40)(28 162 193 39)(57 97 207 115)(58 96 208 114)(59 95 209 113)(60 94 210 140)(61 93 211 139)(62 92 212 138)(63 91 213 137)(64 90 214 136)(65 89 215 135)(66 88 216 134)(67 87 217 133)(68 86 218 132)(69 85 219 131)(70 112 220 130)(71 111 221 129)(72 110 222 128)(73 109 223 127)(74 108 224 126)(75 107 197 125)(76 106 198 124)(77 105 199 123)(78 104 200 122)(79 103 201 121)(80 102 202 120)(81 101 203 119)(82 100 204 118)(83 99 205 117)(84 98 206 116)
(1 135 194 89)(2 120 195 102)(3 133 196 87)(4 118 169 100)(5 131 170 85)(6 116 171 98)(7 129 172 111)(8 114 173 96)(9 127 174 109)(10 140 175 94)(11 125 176 107)(12 138 177 92)(13 123 178 105)(14 136 179 90)(15 121 180 103)(16 134 181 88)(17 119 182 101)(18 132 183 86)(19 117 184 99)(20 130 185 112)(21 115 186 97)(22 128 187 110)(23 113 188 95)(24 126 189 108)(25 139 190 93)(26 124 191 106)(27 137 192 91)(28 122 193 104)(29 60 152 210)(30 73 153 223)(31 58 154 208)(32 71 155 221)(33 84 156 206)(34 69 157 219)(35 82 158 204)(36 67 159 217)(37 80 160 202)(38 65 161 215)(39 78 162 200)(40 63 163 213)(41 76 164 198)(42 61 165 211)(43 74 166 224)(44 59 167 209)(45 72 168 222)(46 57 141 207)(47 70 142 220)(48 83 143 205)(49 68 144 218)(50 81 145 203)(51 66 146 216)(52 79 147 201)(53 64 148 214)(54 77 149 199)(55 62 150 212)(56 75 151 197)
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), (1,186)(2,185)(3,184)(4,183)(5,182)(6,181)(7,180)(8,179)(9,178)(10,177)(11,176)(12,175)(13,174)(14,173)(15,172)(16,171)(17,170)(18,169)(19,196)(20,195)(21,194)(22,193)(23,192)(24,191)(25,190)(26,189)(27,188)(28,187)(29,141)(30,168)(31,167)(32,166)(33,165)(34,164)(35,163)(36,162)(37,161)(38,160)(39,159)(40,158)(41,157)(42,156)(43,155)(44,154)(45,153)(46,152)(47,151)(48,150)(49,149)(50,148)(51,147)(52,146)(53,145)(54,144)(55,143)(56,142)(57,208)(58,207)(59,206)(60,205)(61,204)(62,203)(63,202)(64,201)(65,200)(66,199)(67,198)(68,197)(69,224)(70,223)(71,222)(72,221)(73,220)(74,219)(75,218)(76,217)(77,216)(78,215)(79,214)(80,213)(81,212)(82,211)(83,210)(84,209)(85,117)(86,116)(87,115)(88,114)(89,113)(90,140)(91,139)(92,138)(93,137)(94,136)(95,135)(96,134)(97,133)(98,132)(99,131)(100,130)(101,129)(102,128)(103,127)(104,126)(105,125)(106,124)(107,123)(108,122)(109,121)(110,120)(111,119)(112,118), (1,161,194,38)(2,160,195,37)(3,159,196,36)(4,158,169,35)(5,157,170,34)(6,156,171,33)(7,155,172,32)(8,154,173,31)(9,153,174,30)(10,152,175,29)(11,151,176,56)(12,150,177,55)(13,149,178,54)(14,148,179,53)(15,147,180,52)(16,146,181,51)(17,145,182,50)(18,144,183,49)(19,143,184,48)(20,142,185,47)(21,141,186,46)(22,168,187,45)(23,167,188,44)(24,166,189,43)(25,165,190,42)(26,164,191,41)(27,163,192,40)(28,162,193,39)(57,97,207,115)(58,96,208,114)(59,95,209,113)(60,94,210,140)(61,93,211,139)(62,92,212,138)(63,91,213,137)(64,90,214,136)(65,89,215,135)(66,88,216,134)(67,87,217,133)(68,86,218,132)(69,85,219,131)(70,112,220,130)(71,111,221,129)(72,110,222,128)(73,109,223,127)(74,108,224,126)(75,107,197,125)(76,106,198,124)(77,105,199,123)(78,104,200,122)(79,103,201,121)(80,102,202,120)(81,101,203,119)(82,100,204,118)(83,99,205,117)(84,98,206,116), (1,135,194,89)(2,120,195,102)(3,133,196,87)(4,118,169,100)(5,131,170,85)(6,116,171,98)(7,129,172,111)(8,114,173,96)(9,127,174,109)(10,140,175,94)(11,125,176,107)(12,138,177,92)(13,123,178,105)(14,136,179,90)(15,121,180,103)(16,134,181,88)(17,119,182,101)(18,132,183,86)(19,117,184,99)(20,130,185,112)(21,115,186,97)(22,128,187,110)(23,113,188,95)(24,126,189,108)(25,139,190,93)(26,124,191,106)(27,137,192,91)(28,122,193,104)(29,60,152,210)(30,73,153,223)(31,58,154,208)(32,71,155,221)(33,84,156,206)(34,69,157,219)(35,82,158,204)(36,67,159,217)(37,80,160,202)(38,65,161,215)(39,78,162,200)(40,63,163,213)(41,76,164,198)(42,61,165,211)(43,74,166,224)(44,59,167,209)(45,72,168,222)(46,57,141,207)(47,70,142,220)(48,83,143,205)(49,68,144,218)(50,81,145,203)(51,66,146,216)(52,79,147,201)(53,64,148,214)(54,77,149,199)(55,62,150,212)(56,75,151,197)>;
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), (1,186)(2,185)(3,184)(4,183)(5,182)(6,181)(7,180)(8,179)(9,178)(10,177)(11,176)(12,175)(13,174)(14,173)(15,172)(16,171)(17,170)(18,169)(19,196)(20,195)(21,194)(22,193)(23,192)(24,191)(25,190)(26,189)(27,188)(28,187)(29,141)(30,168)(31,167)(32,166)(33,165)(34,164)(35,163)(36,162)(37,161)(38,160)(39,159)(40,158)(41,157)(42,156)(43,155)(44,154)(45,153)(46,152)(47,151)(48,150)(49,149)(50,148)(51,147)(52,146)(53,145)(54,144)(55,143)(56,142)(57,208)(58,207)(59,206)(60,205)(61,204)(62,203)(63,202)(64,201)(65,200)(66,199)(67,198)(68,197)(69,224)(70,223)(71,222)(72,221)(73,220)(74,219)(75,218)(76,217)(77,216)(78,215)(79,214)(80,213)(81,212)(82,211)(83,210)(84,209)(85,117)(86,116)(87,115)(88,114)(89,113)(90,140)(91,139)(92,138)(93,137)(94,136)(95,135)(96,134)(97,133)(98,132)(99,131)(100,130)(101,129)(102,128)(103,127)(104,126)(105,125)(106,124)(107,123)(108,122)(109,121)(110,120)(111,119)(112,118), (1,161,194,38)(2,160,195,37)(3,159,196,36)(4,158,169,35)(5,157,170,34)(6,156,171,33)(7,155,172,32)(8,154,173,31)(9,153,174,30)(10,152,175,29)(11,151,176,56)(12,150,177,55)(13,149,178,54)(14,148,179,53)(15,147,180,52)(16,146,181,51)(17,145,182,50)(18,144,183,49)(19,143,184,48)(20,142,185,47)(21,141,186,46)(22,168,187,45)(23,167,188,44)(24,166,189,43)(25,165,190,42)(26,164,191,41)(27,163,192,40)(28,162,193,39)(57,97,207,115)(58,96,208,114)(59,95,209,113)(60,94,210,140)(61,93,211,139)(62,92,212,138)(63,91,213,137)(64,90,214,136)(65,89,215,135)(66,88,216,134)(67,87,217,133)(68,86,218,132)(69,85,219,131)(70,112,220,130)(71,111,221,129)(72,110,222,128)(73,109,223,127)(74,108,224,126)(75,107,197,125)(76,106,198,124)(77,105,199,123)(78,104,200,122)(79,103,201,121)(80,102,202,120)(81,101,203,119)(82,100,204,118)(83,99,205,117)(84,98,206,116), (1,135,194,89)(2,120,195,102)(3,133,196,87)(4,118,169,100)(5,131,170,85)(6,116,171,98)(7,129,172,111)(8,114,173,96)(9,127,174,109)(10,140,175,94)(11,125,176,107)(12,138,177,92)(13,123,178,105)(14,136,179,90)(15,121,180,103)(16,134,181,88)(17,119,182,101)(18,132,183,86)(19,117,184,99)(20,130,185,112)(21,115,186,97)(22,128,187,110)(23,113,188,95)(24,126,189,108)(25,139,190,93)(26,124,191,106)(27,137,192,91)(28,122,193,104)(29,60,152,210)(30,73,153,223)(31,58,154,208)(32,71,155,221)(33,84,156,206)(34,69,157,219)(35,82,158,204)(36,67,159,217)(37,80,160,202)(38,65,161,215)(39,78,162,200)(40,63,163,213)(41,76,164,198)(42,61,165,211)(43,74,166,224)(44,59,167,209)(45,72,168,222)(46,57,141,207)(47,70,142,220)(48,83,143,205)(49,68,144,218)(50,81,145,203)(51,66,146,216)(52,79,147,201)(53,64,148,214)(54,77,149,199)(55,62,150,212)(56,75,151,197) );
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)], [(1,186),(2,185),(3,184),(4,183),(5,182),(6,181),(7,180),(8,179),(9,178),(10,177),(11,176),(12,175),(13,174),(14,173),(15,172),(16,171),(17,170),(18,169),(19,196),(20,195),(21,194),(22,193),(23,192),(24,191),(25,190),(26,189),(27,188),(28,187),(29,141),(30,168),(31,167),(32,166),(33,165),(34,164),(35,163),(36,162),(37,161),(38,160),(39,159),(40,158),(41,157),(42,156),(43,155),(44,154),(45,153),(46,152),(47,151),(48,150),(49,149),(50,148),(51,147),(52,146),(53,145),(54,144),(55,143),(56,142),(57,208),(58,207),(59,206),(60,205),(61,204),(62,203),(63,202),(64,201),(65,200),(66,199),(67,198),(68,197),(69,224),(70,223),(71,222),(72,221),(73,220),(74,219),(75,218),(76,217),(77,216),(78,215),(79,214),(80,213),(81,212),(82,211),(83,210),(84,209),(85,117),(86,116),(87,115),(88,114),(89,113),(90,140),(91,139),(92,138),(93,137),(94,136),(95,135),(96,134),(97,133),(98,132),(99,131),(100,130),(101,129),(102,128),(103,127),(104,126),(105,125),(106,124),(107,123),(108,122),(109,121),(110,120),(111,119),(112,118)], [(1,161,194,38),(2,160,195,37),(3,159,196,36),(4,158,169,35),(5,157,170,34),(6,156,171,33),(7,155,172,32),(8,154,173,31),(9,153,174,30),(10,152,175,29),(11,151,176,56),(12,150,177,55),(13,149,178,54),(14,148,179,53),(15,147,180,52),(16,146,181,51),(17,145,182,50),(18,144,183,49),(19,143,184,48),(20,142,185,47),(21,141,186,46),(22,168,187,45),(23,167,188,44),(24,166,189,43),(25,165,190,42),(26,164,191,41),(27,163,192,40),(28,162,193,39),(57,97,207,115),(58,96,208,114),(59,95,209,113),(60,94,210,140),(61,93,211,139),(62,92,212,138),(63,91,213,137),(64,90,214,136),(65,89,215,135),(66,88,216,134),(67,87,217,133),(68,86,218,132),(69,85,219,131),(70,112,220,130),(71,111,221,129),(72,110,222,128),(73,109,223,127),(74,108,224,126),(75,107,197,125),(76,106,198,124),(77,105,199,123),(78,104,200,122),(79,103,201,121),(80,102,202,120),(81,101,203,119),(82,100,204,118),(83,99,205,117),(84,98,206,116)], [(1,135,194,89),(2,120,195,102),(3,133,196,87),(4,118,169,100),(5,131,170,85),(6,116,171,98),(7,129,172,111),(8,114,173,96),(9,127,174,109),(10,140,175,94),(11,125,176,107),(12,138,177,92),(13,123,178,105),(14,136,179,90),(15,121,180,103),(16,134,181,88),(17,119,182,101),(18,132,183,86),(19,117,184,99),(20,130,185,112),(21,115,186,97),(22,128,187,110),(23,113,188,95),(24,126,189,108),(25,139,190,93),(26,124,191,106),(27,137,192,91),(28,122,193,104),(29,60,152,210),(30,73,153,223),(31,58,154,208),(32,71,155,221),(33,84,156,206),(34,69,157,219),(35,82,158,204),(36,67,159,217),(37,80,160,202),(38,65,161,215),(39,78,162,200),(40,63,163,213),(41,76,164,198),(42,61,165,211),(43,74,166,224),(44,59,167,209),(45,72,168,222),(46,57,141,207),(47,70,142,220),(48,83,143,205),(49,68,144,218),(50,81,145,203),(51,66,146,216),(52,79,147,201),(53,64,148,214),(54,77,149,199),(55,62,150,212),(56,75,151,197)]])
61 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 | ··· | 28F | 28G | ··· | 28R | 56A | ··· | 56L |
| 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 | 4 | 4 | 8 | 14 | 14 | 28 | 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 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | + | + | + | + | + | - | + | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | Q8 | D4 | D7 | SD16 | C4○D4 | D14 | D14 | C4○D28 | C8⋊C22 | Q8×D7 | D4×D7 | D7×SD16 | D56⋊C2 |
| kernel | D28⋊Q8 | C4.Dic14 | C14.D8 | Dic7⋊C8 | C2.D56 | C7×C4.Q8 | C28⋊Q8 | D28⋊C4 | D28 | C2×Dic7 | C4.Q8 | Dic7 | C28 | C4⋊C4 | C2×C8 | C4 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 3 | 4 | 2 | 6 | 3 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of D28⋊Q8 ►in GL4(𝔽113) generated by
| 1 | 24 | 0 | 0 |
| 89 | 103 | 0 | 0 |
| 0 | 0 | 1 | 111 |
| 0 | 0 | 1 | 112 |
| 103 | 10 | 0 | 0 |
| 24 | 10 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 112 | 1 |
| 29 | 25 | 0 | 0 |
| 7 | 84 | 0 | 0 |
| 0 | 0 | 0 | 87 |
| 0 | 0 | 100 | 0 |
| 15 | 21 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 1 | 111 |
| 0 | 0 | 1 | 112 |
G:=sub<GL(4,GF(113))| [1,89,0,0,24,103,0,0,0,0,1,1,0,0,111,112],[103,24,0,0,10,10,0,0,0,0,112,112,0,0,0,1],[29,7,0,0,25,84,0,0,0,0,0,100,0,0,87,0],[15,0,0,0,21,98,0,0,0,0,1,1,0,0,111,112] >;
D28⋊Q8 in GAP, Magma, Sage, TeX
D_{28}\rtimes Q_8 % in TeX
G:=Group("D28:Q8"); // GroupNames label
G:=SmallGroup(448,404);
// by ID
G=gap.SmallGroup(448,404);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,64,590,219,100,1684,851,102,18822]);
// 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,d*a*d^-1=a^13,c*b*c^-1=a^19*b,d*b*d^-1=a^26*b,d*c*d^-1=c^-1>;
// generators/relations