metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28⋊10Q8, C42.130D14, C14.1112+ 1+4, (C4×Q8)⋊12D7, C4.50(Q8×D7), (Q8×C28)⋊14C2, C7⋊4(D4⋊3Q8), D14.8(C2×Q8), C4⋊C4.326D14, D14⋊3Q8⋊8C2, C28⋊2Q8⋊28C2, (C4×D28).21C2, C28.108(C2×Q8), D14⋊Q8⋊11C2, C4.67(C4○D28), (C2×Q8).178D14, C28.6Q8⋊18C2, C28.118(C4○D4), C14.31(C22×Q8), (C2×C28).590C23, (C4×C28).175C22, (C2×C14).123C24, C2.23(D4⋊8D14), D14⋊C4.103C22, (C2×D28).289C22, Dic7⋊C4.69C22, C4⋊Dic7.202C22, (Q8×C14).223C22, (C2×Dic7).55C23, C22.144(C23×D7), (C2×Dic14).31C22, (C22×D7).180C23, (D7×C4⋊C4)⋊18C2, C2.14(C2×Q8×D7), C2.62(C2×C4○D28), C14.55(C2×C4○D4), (C2×C4×D7).74C22, (C7×C4⋊C4).351C22, (C2×C4).169(C22×D7), SmallGroup(448,1032)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28⋊10Q8
G = < a,b,c,d | a28=b2=c4=1, d2=c2, bab=a-1, ac=ca, ad=da, cbc-1=a14b, bd=db, dcd-1=c-1 >
Subgroups: 1028 in 228 conjugacy classes, 107 normal (29 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C2×Q8, Dic7, C28, C28, D14, D14, C2×C14, C2×C4⋊C4, C4×D4, C4×Q8, C22⋊Q8, C42.C2, C4⋊Q8, Dic14, C4×D7, D28, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, D4⋊3Q8, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C4×C28, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, Q8×C14, C28⋊2Q8, C28.6Q8, C4×D28, C4×D28, D7×C4⋊C4, D14⋊Q8, D14⋊3Q8, Q8×C28, D28⋊10Q8
Quotients: C1, C2, C22, Q8, C23, D7, C2×Q8, C4○D4, C24, D14, C22×Q8, C2×C4○D4, 2+ 1+4, C22×D7, D4⋊3Q8, C4○D28, Q8×D7, C23×D7, C2×C4○D28, C2×Q8×D7, D4⋊8D14, D28⋊10Q8
►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 29)(2 56)(3 55)(4 54)(5 53)(6 52)(7 51)(8 50)(9 49)(10 48)(11 47)(12 46)(13 45)(14 44)(15 43)(16 42)(17 41)(18 40)(19 39)(20 38)(21 37)(22 36)(23 35)(24 34)(25 33)(26 32)(27 31)(28 30)(57 125)(58 124)(59 123)(60 122)(61 121)(62 120)(63 119)(64 118)(65 117)(66 116)(67 115)(68 114)(69 113)(70 140)(71 139)(72 138)(73 137)(74 136)(75 135)(76 134)(77 133)(78 132)(79 131)(80 130)(81 129)(82 128)(83 127)(84 126)(85 175)(86 174)(87 173)(88 172)(89 171)(90 170)(91 169)(92 196)(93 195)(94 194)(95 193)(96 192)(97 191)(98 190)(99 189)(100 188)(101 187)(102 186)(103 185)(104 184)(105 183)(106 182)(107 181)(108 180)(109 179)(110 178)(111 177)(112 176)(141 208)(142 207)(143 206)(144 205)(145 204)(146 203)(147 202)(148 201)(149 200)(150 199)(151 198)(152 197)(153 224)(154 223)(155 222)(156 221)(157 220)(158 219)(159 218)(160 217)(161 216)(162 215)(163 214)(164 213)(165 212)(166 211)(167 210)(168 209)
(1 208 51 149)(2 209 52 150)(3 210 53 151)(4 211 54 152)(5 212 55 153)(6 213 56 154)(7 214 29 155)(8 215 30 156)(9 216 31 157)(10 217 32 158)(11 218 33 159)(12 219 34 160)(13 220 35 161)(14 221 36 162)(15 222 37 163)(16 223 38 164)(17 224 39 165)(18 197 40 166)(19 198 41 167)(20 199 42 168)(21 200 43 141)(22 201 44 142)(23 202 45 143)(24 203 46 144)(25 204 47 145)(26 205 48 146)(27 206 49 147)(28 207 50 148)(57 106 139 182)(58 107 140 183)(59 108 113 184)(60 109 114 185)(61 110 115 186)(62 111 116 187)(63 112 117 188)(64 85 118 189)(65 86 119 190)(66 87 120 191)(67 88 121 192)(68 89 122 193)(69 90 123 194)(70 91 124 195)(71 92 125 196)(72 93 126 169)(73 94 127 170)(74 95 128 171)(75 96 129 172)(76 97 130 173)(77 98 131 174)(78 99 132 175)(79 100 133 176)(80 101 134 177)(81 102 135 178)(82 103 136 179)(83 104 137 180)(84 105 138 181)
(1 115 51 61)(2 116 52 62)(3 117 53 63)(4 118 54 64)(5 119 55 65)(6 120 56 66)(7 121 29 67)(8 122 30 68)(9 123 31 69)(10 124 32 70)(11 125 33 71)(12 126 34 72)(13 127 35 73)(14 128 36 74)(15 129 37 75)(16 130 38 76)(17 131 39 77)(18 132 40 78)(19 133 41 79)(20 134 42 80)(21 135 43 81)(22 136 44 82)(23 137 45 83)(24 138 46 84)(25 139 47 57)(26 140 48 58)(27 113 49 59)(28 114 50 60)(85 152 189 211)(86 153 190 212)(87 154 191 213)(88 155 192 214)(89 156 193 215)(90 157 194 216)(91 158 195 217)(92 159 196 218)(93 160 169 219)(94 161 170 220)(95 162 171 221)(96 163 172 222)(97 164 173 223)(98 165 174 224)(99 166 175 197)(100 167 176 198)(101 168 177 199)(102 141 178 200)(103 142 179 201)(104 143 180 202)(105 144 181 203)(106 145 182 204)(107 146 183 205)(108 147 184 206)(109 148 185 207)(110 149 186 208)(111 150 187 209)(112 151 188 210)
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), (1,29)(2,56)(3,55)(4,54)(5,53)(6,52)(7,51)(8,50)(9,49)(10,48)(11,47)(12,46)(13,45)(14,44)(15,43)(16,42)(17,41)(18,40)(19,39)(20,38)(21,37)(22,36)(23,35)(24,34)(25,33)(26,32)(27,31)(28,30)(57,125)(58,124)(59,123)(60,122)(61,121)(62,120)(63,119)(64,118)(65,117)(66,116)(67,115)(68,114)(69,113)(70,140)(71,139)(72,138)(73,137)(74,136)(75,135)(76,134)(77,133)(78,132)(79,131)(80,130)(81,129)(82,128)(83,127)(84,126)(85,175)(86,174)(87,173)(88,172)(89,171)(90,170)(91,169)(92,196)(93,195)(94,194)(95,193)(96,192)(97,191)(98,190)(99,189)(100,188)(101,187)(102,186)(103,185)(104,184)(105,183)(106,182)(107,181)(108,180)(109,179)(110,178)(111,177)(112,176)(141,208)(142,207)(143,206)(144,205)(145,204)(146,203)(147,202)(148,201)(149,200)(150,199)(151,198)(152,197)(153,224)(154,223)(155,222)(156,221)(157,220)(158,219)(159,218)(160,217)(161,216)(162,215)(163,214)(164,213)(165,212)(166,211)(167,210)(168,209), (1,208,51,149)(2,209,52,150)(3,210,53,151)(4,211,54,152)(5,212,55,153)(6,213,56,154)(7,214,29,155)(8,215,30,156)(9,216,31,157)(10,217,32,158)(11,218,33,159)(12,219,34,160)(13,220,35,161)(14,221,36,162)(15,222,37,163)(16,223,38,164)(17,224,39,165)(18,197,40,166)(19,198,41,167)(20,199,42,168)(21,200,43,141)(22,201,44,142)(23,202,45,143)(24,203,46,144)(25,204,47,145)(26,205,48,146)(27,206,49,147)(28,207,50,148)(57,106,139,182)(58,107,140,183)(59,108,113,184)(60,109,114,185)(61,110,115,186)(62,111,116,187)(63,112,117,188)(64,85,118,189)(65,86,119,190)(66,87,120,191)(67,88,121,192)(68,89,122,193)(69,90,123,194)(70,91,124,195)(71,92,125,196)(72,93,126,169)(73,94,127,170)(74,95,128,171)(75,96,129,172)(76,97,130,173)(77,98,131,174)(78,99,132,175)(79,100,133,176)(80,101,134,177)(81,102,135,178)(82,103,136,179)(83,104,137,180)(84,105,138,181), (1,115,51,61)(2,116,52,62)(3,117,53,63)(4,118,54,64)(5,119,55,65)(6,120,56,66)(7,121,29,67)(8,122,30,68)(9,123,31,69)(10,124,32,70)(11,125,33,71)(12,126,34,72)(13,127,35,73)(14,128,36,74)(15,129,37,75)(16,130,38,76)(17,131,39,77)(18,132,40,78)(19,133,41,79)(20,134,42,80)(21,135,43,81)(22,136,44,82)(23,137,45,83)(24,138,46,84)(25,139,47,57)(26,140,48,58)(27,113,49,59)(28,114,50,60)(85,152,189,211)(86,153,190,212)(87,154,191,213)(88,155,192,214)(89,156,193,215)(90,157,194,216)(91,158,195,217)(92,159,196,218)(93,160,169,219)(94,161,170,220)(95,162,171,221)(96,163,172,222)(97,164,173,223)(98,165,174,224)(99,166,175,197)(100,167,176,198)(101,168,177,199)(102,141,178,200)(103,142,179,201)(104,143,180,202)(105,144,181,203)(106,145,182,204)(107,146,183,205)(108,147,184,206)(109,148,185,207)(110,149,186,208)(111,150,187,209)(112,151,188,210)>;
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), (1,29)(2,56)(3,55)(4,54)(5,53)(6,52)(7,51)(8,50)(9,49)(10,48)(11,47)(12,46)(13,45)(14,44)(15,43)(16,42)(17,41)(18,40)(19,39)(20,38)(21,37)(22,36)(23,35)(24,34)(25,33)(26,32)(27,31)(28,30)(57,125)(58,124)(59,123)(60,122)(61,121)(62,120)(63,119)(64,118)(65,117)(66,116)(67,115)(68,114)(69,113)(70,140)(71,139)(72,138)(73,137)(74,136)(75,135)(76,134)(77,133)(78,132)(79,131)(80,130)(81,129)(82,128)(83,127)(84,126)(85,175)(86,174)(87,173)(88,172)(89,171)(90,170)(91,169)(92,196)(93,195)(94,194)(95,193)(96,192)(97,191)(98,190)(99,189)(100,188)(101,187)(102,186)(103,185)(104,184)(105,183)(106,182)(107,181)(108,180)(109,179)(110,178)(111,177)(112,176)(141,208)(142,207)(143,206)(144,205)(145,204)(146,203)(147,202)(148,201)(149,200)(150,199)(151,198)(152,197)(153,224)(154,223)(155,222)(156,221)(157,220)(158,219)(159,218)(160,217)(161,216)(162,215)(163,214)(164,213)(165,212)(166,211)(167,210)(168,209), (1,208,51,149)(2,209,52,150)(3,210,53,151)(4,211,54,152)(5,212,55,153)(6,213,56,154)(7,214,29,155)(8,215,30,156)(9,216,31,157)(10,217,32,158)(11,218,33,159)(12,219,34,160)(13,220,35,161)(14,221,36,162)(15,222,37,163)(16,223,38,164)(17,224,39,165)(18,197,40,166)(19,198,41,167)(20,199,42,168)(21,200,43,141)(22,201,44,142)(23,202,45,143)(24,203,46,144)(25,204,47,145)(26,205,48,146)(27,206,49,147)(28,207,50,148)(57,106,139,182)(58,107,140,183)(59,108,113,184)(60,109,114,185)(61,110,115,186)(62,111,116,187)(63,112,117,188)(64,85,118,189)(65,86,119,190)(66,87,120,191)(67,88,121,192)(68,89,122,193)(69,90,123,194)(70,91,124,195)(71,92,125,196)(72,93,126,169)(73,94,127,170)(74,95,128,171)(75,96,129,172)(76,97,130,173)(77,98,131,174)(78,99,132,175)(79,100,133,176)(80,101,134,177)(81,102,135,178)(82,103,136,179)(83,104,137,180)(84,105,138,181), (1,115,51,61)(2,116,52,62)(3,117,53,63)(4,118,54,64)(5,119,55,65)(6,120,56,66)(7,121,29,67)(8,122,30,68)(9,123,31,69)(10,124,32,70)(11,125,33,71)(12,126,34,72)(13,127,35,73)(14,128,36,74)(15,129,37,75)(16,130,38,76)(17,131,39,77)(18,132,40,78)(19,133,41,79)(20,134,42,80)(21,135,43,81)(22,136,44,82)(23,137,45,83)(24,138,46,84)(25,139,47,57)(26,140,48,58)(27,113,49,59)(28,114,50,60)(85,152,189,211)(86,153,190,212)(87,154,191,213)(88,155,192,214)(89,156,193,215)(90,157,194,216)(91,158,195,217)(92,159,196,218)(93,160,169,219)(94,161,170,220)(95,162,171,221)(96,163,172,222)(97,164,173,223)(98,165,174,224)(99,166,175,197)(100,167,176,198)(101,168,177,199)(102,141,178,200)(103,142,179,201)(104,143,180,202)(105,144,181,203)(106,145,182,204)(107,146,183,205)(108,147,184,206)(109,148,185,207)(110,149,186,208)(111,150,187,209)(112,151,188,210) );
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)], [(1,29),(2,56),(3,55),(4,54),(5,53),(6,52),(7,51),(8,50),(9,49),(10,48),(11,47),(12,46),(13,45),(14,44),(15,43),(16,42),(17,41),(18,40),(19,39),(20,38),(21,37),(22,36),(23,35),(24,34),(25,33),(26,32),(27,31),(28,30),(57,125),(58,124),(59,123),(60,122),(61,121),(62,120),(63,119),(64,118),(65,117),(66,116),(67,115),(68,114),(69,113),(70,140),(71,139),(72,138),(73,137),(74,136),(75,135),(76,134),(77,133),(78,132),(79,131),(80,130),(81,129),(82,128),(83,127),(84,126),(85,175),(86,174),(87,173),(88,172),(89,171),(90,170),(91,169),(92,196),(93,195),(94,194),(95,193),(96,192),(97,191),(98,190),(99,189),(100,188),(101,187),(102,186),(103,185),(104,184),(105,183),(106,182),(107,181),(108,180),(109,179),(110,178),(111,177),(112,176),(141,208),(142,207),(143,206),(144,205),(145,204),(146,203),(147,202),(148,201),(149,200),(150,199),(151,198),(152,197),(153,224),(154,223),(155,222),(156,221),(157,220),(158,219),(159,218),(160,217),(161,216),(162,215),(163,214),(164,213),(165,212),(166,211),(167,210),(168,209)], [(1,208,51,149),(2,209,52,150),(3,210,53,151),(4,211,54,152),(5,212,55,153),(6,213,56,154),(7,214,29,155),(8,215,30,156),(9,216,31,157),(10,217,32,158),(11,218,33,159),(12,219,34,160),(13,220,35,161),(14,221,36,162),(15,222,37,163),(16,223,38,164),(17,224,39,165),(18,197,40,166),(19,198,41,167),(20,199,42,168),(21,200,43,141),(22,201,44,142),(23,202,45,143),(24,203,46,144),(25,204,47,145),(26,205,48,146),(27,206,49,147),(28,207,50,148),(57,106,139,182),(58,107,140,183),(59,108,113,184),(60,109,114,185),(61,110,115,186),(62,111,116,187),(63,112,117,188),(64,85,118,189),(65,86,119,190),(66,87,120,191),(67,88,121,192),(68,89,122,193),(69,90,123,194),(70,91,124,195),(71,92,125,196),(72,93,126,169),(73,94,127,170),(74,95,128,171),(75,96,129,172),(76,97,130,173),(77,98,131,174),(78,99,132,175),(79,100,133,176),(80,101,134,177),(81,102,135,178),(82,103,136,179),(83,104,137,180),(84,105,138,181)], [(1,115,51,61),(2,116,52,62),(3,117,53,63),(4,118,54,64),(5,119,55,65),(6,120,56,66),(7,121,29,67),(8,122,30,68),(9,123,31,69),(10,124,32,70),(11,125,33,71),(12,126,34,72),(13,127,35,73),(14,128,36,74),(15,129,37,75),(16,130,38,76),(17,131,39,77),(18,132,40,78),(19,133,41,79),(20,134,42,80),(21,135,43,81),(22,136,44,82),(23,137,45,83),(24,138,46,84),(25,139,47,57),(26,140,48,58),(27,113,49,59),(28,114,50,60),(85,152,189,211),(86,153,190,212),(87,154,191,213),(88,155,192,214),(89,156,193,215),(90,157,194,216),(91,158,195,217),(92,159,196,218),(93,160,169,219),(94,161,170,220),(95,162,171,221),(96,163,172,222),(97,164,173,223),(98,165,174,224),(99,166,175,197),(100,167,176,198),(101,168,177,199),(102,141,178,200),(103,142,179,201),(104,143,180,202),(105,144,181,203),(106,145,182,204),(107,146,183,205),(108,147,184,206),(109,148,185,207),(110,149,186,208),(111,150,187,209),(112,151,188,210)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | ··· | 4H | 4I | 4J | 4K | 4L | ··· | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 14 | 14 | 2 | ··· | 2 | 4 | 4 | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | + | + | + | + | + | - | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | Q8 | D7 | C4○D4 | D14 | D14 | D14 | C4○D28 | 2+ 1+4 | Q8×D7 | D4⋊8D14 |
| kernel | D28⋊10Q8 | C28⋊2Q8 | C28.6Q8 | C4×D28 | D7×C4⋊C4 | D14⋊Q8 | D14⋊3Q8 | Q8×C28 | D28 | C4×Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | C4 | C14 | C4 | C2 |
| # reps | 1 | 1 | 2 | 3 | 2 | 4 | 2 | 1 | 4 | 3 | 4 | 9 | 9 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of D28⋊10Q8 ►in GL4(𝔽29) generated by
| 5 | 25 | 0 | 0 |
| 6 | 7 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 28 |
| 1 | 10 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 28 |
| 18 | 14 | 0 | 0 |
| 8 | 11 | 0 | 0 |
| 0 | 0 | 0 | 28 |
| 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 14 | 21 |
| 0 | 0 | 21 | 15 |
G:=sub<GL(4,GF(29))| [5,6,0,0,25,7,0,0,0,0,28,0,0,0,0,28],[1,0,0,0,10,28,0,0,0,0,28,0,0,0,0,28],[18,8,0,0,14,11,0,0,0,0,0,1,0,0,28,0],[1,0,0,0,0,1,0,0,0,0,14,21,0,0,21,15] >;
D28⋊10Q8 in GAP, Magma, Sage, TeX
D_{28}\rtimes_{10}Q_8 % in TeX
G:=Group("D28:10Q8"); // GroupNames label
G:=SmallGroup(448,1032);
// by ID
G=gap.SmallGroup(448,1032);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,232,100,185,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=b^2=c^4=1,d^2=c^2,b*a*b=a^-1,a*c=c*a,a*d=d*a,c*b*c^-1=a^14*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations