metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28⋊2Q8, Dic7.7D8, C28⋊Q8⋊7C2, C4.7(Q8×D7), C2.D8⋊8D7, C2.15(D7×D8), C7⋊3(D4⋊Q8), (C2×C8).31D14, C14.31(C2×D8), C28.23(C2×Q8), Dic7⋊C8⋊25C2, C4⋊C4.173D14, D28⋊C4.8C2, C14.D8.8C2, C4.84(C4○D28), C28.Q8⋊23C2, (C2×Dic7).51D4, C22.235(D4×D7), C2.D56.10C2, C28.172(C4○D4), (C2×C56).245C22, (C2×C28).306C23, (C2×D28).86C22, C14.41(C22⋊Q8), C2.18(D14⋊Q8), C2.25(Q16⋊D7), C14.74(C8.C22), C4⋊Dic7.128C22, (C4×Dic7).38C22, (C7×C2.D8)⋊15C2, (C2×C7⋊C8).75C22, (C2×C14).311(C2×D4), (C7×C4⋊C4).99C22, (C2×C4).409(C22×D7), SmallGroup(448,424)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28⋊2Q8
G = < a,b,c,d | a28=b2=c4=1, d2=c2, bab=cac-1=a-1, dad-1=a13, cbc-1=a5b, dbd-1=a12b, 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, C2.D8, C2.D8, C4×D4, C4⋊Q8, C7⋊C8, C56, Dic14, C4×D7, D28, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, D4⋊Q8, C2×C7⋊C8, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C7×C4⋊C4, C2×C56, C2×Dic14, C2×C4×D7, C2×D28, C28.Q8, C14.D8, Dic7⋊C8, C2.D56, C7×C2.D8, C28⋊Q8, D28⋊C4, D28⋊2Q8
Quotients: C1, C2, C22, D4, Q8, C23, D7, D8, C2×D4, C2×Q8, C4○D4, D14, C22⋊Q8, C2×D8, C8.C22, C22×D7, D4⋊Q8, C4○D28, D4×D7, Q8×D7, D14⋊Q8, D7×D8, Q16⋊D7, D28⋊2Q8
►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 73)(2 72)(3 71)(4 70)(5 69)(6 68)(7 67)(8 66)(9 65)(10 64)(11 63)(12 62)(13 61)(14 60)(15 59)(16 58)(17 57)(18 84)(19 83)(20 82)(21 81)(22 80)(23 79)(24 78)(25 77)(26 76)(27 75)(28 74)(29 215)(30 214)(31 213)(32 212)(33 211)(34 210)(35 209)(36 208)(37 207)(38 206)(39 205)(40 204)(41 203)(42 202)(43 201)(44 200)(45 199)(46 198)(47 197)(48 224)(49 223)(50 222)(51 221)(52 220)(53 219)(54 218)(55 217)(56 216)(85 120)(86 119)(87 118)(88 117)(89 116)(90 115)(91 114)(92 113)(93 140)(94 139)(95 138)(96 137)(97 136)(98 135)(99 134)(100 133)(101 132)(102 131)(103 130)(104 129)(105 128)(106 127)(107 126)(108 125)(109 124)(110 123)(111 122)(112 121)(141 179)(142 178)(143 177)(144 176)(145 175)(146 174)(147 173)(148 172)(149 171)(150 170)(151 169)(152 196)(153 195)(154 194)(155 193)(156 192)(157 191)(158 190)(159 189)(160 188)(161 187)(162 186)(163 185)(164 184)(165 183)(166 182)(167 181)(168 180)
(1 189 67 160)(2 188 68 159)(3 187 69 158)(4 186 70 157)(5 185 71 156)(6 184 72 155)(7 183 73 154)(8 182 74 153)(9 181 75 152)(10 180 76 151)(11 179 77 150)(12 178 78 149)(13 177 79 148)(14 176 80 147)(15 175 81 146)(16 174 82 145)(17 173 83 144)(18 172 84 143)(19 171 57 142)(20 170 58 141)(21 169 59 168)(22 196 60 167)(23 195 61 166)(24 194 62 165)(25 193 63 164)(26 192 64 163)(27 191 65 162)(28 190 66 161)(29 113 207 95)(30 140 208 94)(31 139 209 93)(32 138 210 92)(33 137 211 91)(34 136 212 90)(35 135 213 89)(36 134 214 88)(37 133 215 87)(38 132 216 86)(39 131 217 85)(40 130 218 112)(41 129 219 111)(42 128 220 110)(43 127 221 109)(44 126 222 108)(45 125 223 107)(46 124 224 106)(47 123 197 105)(48 122 198 104)(49 121 199 103)(50 120 200 102)(51 119 201 101)(52 118 202 100)(53 117 203 99)(54 116 204 98)(55 115 205 97)(56 114 206 96)
(1 30 67 208)(2 43 68 221)(3 56 69 206)(4 41 70 219)(5 54 71 204)(6 39 72 217)(7 52 73 202)(8 37 74 215)(9 50 75 200)(10 35 76 213)(11 48 77 198)(12 33 78 211)(13 46 79 224)(14 31 80 209)(15 44 81 222)(16 29 82 207)(17 42 83 220)(18 55 84 205)(19 40 57 218)(20 53 58 203)(21 38 59 216)(22 51 60 201)(23 36 61 214)(24 49 62 199)(25 34 63 212)(26 47 64 197)(27 32 65 210)(28 45 66 223)(85 155 131 184)(86 168 132 169)(87 153 133 182)(88 166 134 195)(89 151 135 180)(90 164 136 193)(91 149 137 178)(92 162 138 191)(93 147 139 176)(94 160 140 189)(95 145 113 174)(96 158 114 187)(97 143 115 172)(98 156 116 185)(99 141 117 170)(100 154 118 183)(101 167 119 196)(102 152 120 181)(103 165 121 194)(104 150 122 179)(105 163 123 192)(106 148 124 177)(107 161 125 190)(108 146 126 175)(109 159 127 188)(110 144 128 173)(111 157 129 186)(112 142 130 171)
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), (1,73)(2,72)(3,71)(4,70)(5,69)(6,68)(7,67)(8,66)(9,65)(10,64)(11,63)(12,62)(13,61)(14,60)(15,59)(16,58)(17,57)(18,84)(19,83)(20,82)(21,81)(22,80)(23,79)(24,78)(25,77)(26,76)(27,75)(28,74)(29,215)(30,214)(31,213)(32,212)(33,211)(34,210)(35,209)(36,208)(37,207)(38,206)(39,205)(40,204)(41,203)(42,202)(43,201)(44,200)(45,199)(46,198)(47,197)(48,224)(49,223)(50,222)(51,221)(52,220)(53,219)(54,218)(55,217)(56,216)(85,120)(86,119)(87,118)(88,117)(89,116)(90,115)(91,114)(92,113)(93,140)(94,139)(95,138)(96,137)(97,136)(98,135)(99,134)(100,133)(101,132)(102,131)(103,130)(104,129)(105,128)(106,127)(107,126)(108,125)(109,124)(110,123)(111,122)(112,121)(141,179)(142,178)(143,177)(144,176)(145,175)(146,174)(147,173)(148,172)(149,171)(150,170)(151,169)(152,196)(153,195)(154,194)(155,193)(156,192)(157,191)(158,190)(159,189)(160,188)(161,187)(162,186)(163,185)(164,184)(165,183)(166,182)(167,181)(168,180), (1,189,67,160)(2,188,68,159)(3,187,69,158)(4,186,70,157)(5,185,71,156)(6,184,72,155)(7,183,73,154)(8,182,74,153)(9,181,75,152)(10,180,76,151)(11,179,77,150)(12,178,78,149)(13,177,79,148)(14,176,80,147)(15,175,81,146)(16,174,82,145)(17,173,83,144)(18,172,84,143)(19,171,57,142)(20,170,58,141)(21,169,59,168)(22,196,60,167)(23,195,61,166)(24,194,62,165)(25,193,63,164)(26,192,64,163)(27,191,65,162)(28,190,66,161)(29,113,207,95)(30,140,208,94)(31,139,209,93)(32,138,210,92)(33,137,211,91)(34,136,212,90)(35,135,213,89)(36,134,214,88)(37,133,215,87)(38,132,216,86)(39,131,217,85)(40,130,218,112)(41,129,219,111)(42,128,220,110)(43,127,221,109)(44,126,222,108)(45,125,223,107)(46,124,224,106)(47,123,197,105)(48,122,198,104)(49,121,199,103)(50,120,200,102)(51,119,201,101)(52,118,202,100)(53,117,203,99)(54,116,204,98)(55,115,205,97)(56,114,206,96), (1,30,67,208)(2,43,68,221)(3,56,69,206)(4,41,70,219)(5,54,71,204)(6,39,72,217)(7,52,73,202)(8,37,74,215)(9,50,75,200)(10,35,76,213)(11,48,77,198)(12,33,78,211)(13,46,79,224)(14,31,80,209)(15,44,81,222)(16,29,82,207)(17,42,83,220)(18,55,84,205)(19,40,57,218)(20,53,58,203)(21,38,59,216)(22,51,60,201)(23,36,61,214)(24,49,62,199)(25,34,63,212)(26,47,64,197)(27,32,65,210)(28,45,66,223)(85,155,131,184)(86,168,132,169)(87,153,133,182)(88,166,134,195)(89,151,135,180)(90,164,136,193)(91,149,137,178)(92,162,138,191)(93,147,139,176)(94,160,140,189)(95,145,113,174)(96,158,114,187)(97,143,115,172)(98,156,116,185)(99,141,117,170)(100,154,118,183)(101,167,119,196)(102,152,120,181)(103,165,121,194)(104,150,122,179)(105,163,123,192)(106,148,124,177)(107,161,125,190)(108,146,126,175)(109,159,127,188)(110,144,128,173)(111,157,129,186)(112,142,130,171)>;
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), (1,73)(2,72)(3,71)(4,70)(5,69)(6,68)(7,67)(8,66)(9,65)(10,64)(11,63)(12,62)(13,61)(14,60)(15,59)(16,58)(17,57)(18,84)(19,83)(20,82)(21,81)(22,80)(23,79)(24,78)(25,77)(26,76)(27,75)(28,74)(29,215)(30,214)(31,213)(32,212)(33,211)(34,210)(35,209)(36,208)(37,207)(38,206)(39,205)(40,204)(41,203)(42,202)(43,201)(44,200)(45,199)(46,198)(47,197)(48,224)(49,223)(50,222)(51,221)(52,220)(53,219)(54,218)(55,217)(56,216)(85,120)(86,119)(87,118)(88,117)(89,116)(90,115)(91,114)(92,113)(93,140)(94,139)(95,138)(96,137)(97,136)(98,135)(99,134)(100,133)(101,132)(102,131)(103,130)(104,129)(105,128)(106,127)(107,126)(108,125)(109,124)(110,123)(111,122)(112,121)(141,179)(142,178)(143,177)(144,176)(145,175)(146,174)(147,173)(148,172)(149,171)(150,170)(151,169)(152,196)(153,195)(154,194)(155,193)(156,192)(157,191)(158,190)(159,189)(160,188)(161,187)(162,186)(163,185)(164,184)(165,183)(166,182)(167,181)(168,180), (1,189,67,160)(2,188,68,159)(3,187,69,158)(4,186,70,157)(5,185,71,156)(6,184,72,155)(7,183,73,154)(8,182,74,153)(9,181,75,152)(10,180,76,151)(11,179,77,150)(12,178,78,149)(13,177,79,148)(14,176,80,147)(15,175,81,146)(16,174,82,145)(17,173,83,144)(18,172,84,143)(19,171,57,142)(20,170,58,141)(21,169,59,168)(22,196,60,167)(23,195,61,166)(24,194,62,165)(25,193,63,164)(26,192,64,163)(27,191,65,162)(28,190,66,161)(29,113,207,95)(30,140,208,94)(31,139,209,93)(32,138,210,92)(33,137,211,91)(34,136,212,90)(35,135,213,89)(36,134,214,88)(37,133,215,87)(38,132,216,86)(39,131,217,85)(40,130,218,112)(41,129,219,111)(42,128,220,110)(43,127,221,109)(44,126,222,108)(45,125,223,107)(46,124,224,106)(47,123,197,105)(48,122,198,104)(49,121,199,103)(50,120,200,102)(51,119,201,101)(52,118,202,100)(53,117,203,99)(54,116,204,98)(55,115,205,97)(56,114,206,96), (1,30,67,208)(2,43,68,221)(3,56,69,206)(4,41,70,219)(5,54,71,204)(6,39,72,217)(7,52,73,202)(8,37,74,215)(9,50,75,200)(10,35,76,213)(11,48,77,198)(12,33,78,211)(13,46,79,224)(14,31,80,209)(15,44,81,222)(16,29,82,207)(17,42,83,220)(18,55,84,205)(19,40,57,218)(20,53,58,203)(21,38,59,216)(22,51,60,201)(23,36,61,214)(24,49,62,199)(25,34,63,212)(26,47,64,197)(27,32,65,210)(28,45,66,223)(85,155,131,184)(86,168,132,169)(87,153,133,182)(88,166,134,195)(89,151,135,180)(90,164,136,193)(91,149,137,178)(92,162,138,191)(93,147,139,176)(94,160,140,189)(95,145,113,174)(96,158,114,187)(97,143,115,172)(98,156,116,185)(99,141,117,170)(100,154,118,183)(101,167,119,196)(102,152,120,181)(103,165,121,194)(104,150,122,179)(105,163,123,192)(106,148,124,177)(107,161,125,190)(108,146,126,175)(109,159,127,188)(110,144,128,173)(111,157,129,186)(112,142,130,171) );
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)], [(1,73),(2,72),(3,71),(4,70),(5,69),(6,68),(7,67),(8,66),(9,65),(10,64),(11,63),(12,62),(13,61),(14,60),(15,59),(16,58),(17,57),(18,84),(19,83),(20,82),(21,81),(22,80),(23,79),(24,78),(25,77),(26,76),(27,75),(28,74),(29,215),(30,214),(31,213),(32,212),(33,211),(34,210),(35,209),(36,208),(37,207),(38,206),(39,205),(40,204),(41,203),(42,202),(43,201),(44,200),(45,199),(46,198),(47,197),(48,224),(49,223),(50,222),(51,221),(52,220),(53,219),(54,218),(55,217),(56,216),(85,120),(86,119),(87,118),(88,117),(89,116),(90,115),(91,114),(92,113),(93,140),(94,139),(95,138),(96,137),(97,136),(98,135),(99,134),(100,133),(101,132),(102,131),(103,130),(104,129),(105,128),(106,127),(107,126),(108,125),(109,124),(110,123),(111,122),(112,121),(141,179),(142,178),(143,177),(144,176),(145,175),(146,174),(147,173),(148,172),(149,171),(150,170),(151,169),(152,196),(153,195),(154,194),(155,193),(156,192),(157,191),(158,190),(159,189),(160,188),(161,187),(162,186),(163,185),(164,184),(165,183),(166,182),(167,181),(168,180)], [(1,189,67,160),(2,188,68,159),(3,187,69,158),(4,186,70,157),(5,185,71,156),(6,184,72,155),(7,183,73,154),(8,182,74,153),(9,181,75,152),(10,180,76,151),(11,179,77,150),(12,178,78,149),(13,177,79,148),(14,176,80,147),(15,175,81,146),(16,174,82,145),(17,173,83,144),(18,172,84,143),(19,171,57,142),(20,170,58,141),(21,169,59,168),(22,196,60,167),(23,195,61,166),(24,194,62,165),(25,193,63,164),(26,192,64,163),(27,191,65,162),(28,190,66,161),(29,113,207,95),(30,140,208,94),(31,139,209,93),(32,138,210,92),(33,137,211,91),(34,136,212,90),(35,135,213,89),(36,134,214,88),(37,133,215,87),(38,132,216,86),(39,131,217,85),(40,130,218,112),(41,129,219,111),(42,128,220,110),(43,127,221,109),(44,126,222,108),(45,125,223,107),(46,124,224,106),(47,123,197,105),(48,122,198,104),(49,121,199,103),(50,120,200,102),(51,119,201,101),(52,118,202,100),(53,117,203,99),(54,116,204,98),(55,115,205,97),(56,114,206,96)], [(1,30,67,208),(2,43,68,221),(3,56,69,206),(4,41,70,219),(5,54,71,204),(6,39,72,217),(7,52,73,202),(8,37,74,215),(9,50,75,200),(10,35,76,213),(11,48,77,198),(12,33,78,211),(13,46,79,224),(14,31,80,209),(15,44,81,222),(16,29,82,207),(17,42,83,220),(18,55,84,205),(19,40,57,218),(20,53,58,203),(21,38,59,216),(22,51,60,201),(23,36,61,214),(24,49,62,199),(25,34,63,212),(26,47,64,197),(27,32,65,210),(28,45,66,223),(85,155,131,184),(86,168,132,169),(87,153,133,182),(88,166,134,195),(89,151,135,180),(90,164,136,193),(91,149,137,178),(92,162,138,191),(93,147,139,176),(94,160,140,189),(95,145,113,174),(96,158,114,187),(97,143,115,172),(98,156,116,185),(99,141,117,170),(100,154,118,183),(101,167,119,196),(102,152,120,181),(103,165,121,194),(104,150,122,179),(105,163,123,192),(106,148,124,177),(107,161,125,190),(108,146,126,175),(109,159,127,188),(110,144,128,173),(111,157,129,186),(112,142,130,171)]])
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 | D8 | C4○D4 | D14 | D14 | C4○D28 | C8.C22 | Q8×D7 | D4×D7 | D7×D8 | Q16⋊D7 |
| kernel | D28⋊2Q8 | C28.Q8 | C14.D8 | Dic7⋊C8 | C2.D56 | C7×C2.D8 | C28⋊Q8 | D28⋊C4 | D28 | C2×Dic7 | C2.D8 | 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⋊2Q8 ►in GL4(𝔽113) generated by
| 1 | 9 | 0 | 0 |
| 104 | 33 | 0 | 0 |
| 0 | 0 | 1 | 72 |
| 0 | 0 | 91 | 112 |
| 33 | 80 | 0 | 0 |
| 9 | 80 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 22 | 1 |
| 79 | 28 | 0 | 0 |
| 108 | 34 | 0 | 0 |
| 0 | 0 | 51 | 28 |
| 0 | 0 | 4 | 62 |
| 15 | 22 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
G:=sub<GL(4,GF(113))| [1,104,0,0,9,33,0,0,0,0,1,91,0,0,72,112],[33,9,0,0,80,80,0,0,0,0,112,22,0,0,0,1],[79,108,0,0,28,34,0,0,0,0,51,4,0,0,28,62],[15,0,0,0,22,98,0,0,0,0,112,0,0,0,0,112] >;
D28⋊2Q8 in GAP, Magma, Sage, TeX
D_{28}\rtimes_2Q_8 % in TeX
G:=Group("D28:2Q8"); // GroupNames label
G:=SmallGroup(448,424);
// by ID
G=gap.SmallGroup(448,424);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,64,590,219,268,1684,851,102,18822]);
// 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^5*b,d*b*d^-1=a^12*b,d*c*d^-1=c^-1>;
// generators/relations