metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28⋊7Q8, C42.149D14, C14.1312+ 1+4, C28⋊Q8⋊36C2, C4.16(Q8×D7), C7⋊7(D4⋊3Q8), C42.C2⋊5D7, C28.51(C2×Q8), C4⋊C4.205D14, (C4×D28).24C2, D14.11(C2×Q8), D14⋊Q8⋊34C2, D14⋊2Q8⋊35C2, (C4×Dic14)⋊47C2, (C2×C28).88C23, C28.3Q8⋊34C2, D28⋊C4.11C2, C14.43(C22×Q8), (C2×C14).234C24, (C4×C28).194C22, D14⋊C4.40C22, C2.56(D4⋊8D14), Dic7.29(C4○D4), (C2×D28).267C22, C4⋊Dic7.379C22, C22.255(C23×D7), Dic7⋊C4.144C22, (C4×Dic7).141C22, (C2×Dic7).122C23, (C22×D7).221C23, (C2×Dic14).251C22, (D7×C4⋊C4)⋊35C2, C2.26(C2×Q8×D7), C2.85(D7×C4○D4), (C7×C42.C2)⋊7C2, C14.196(C2×C4○D4), (C2×C4×D7).217C22, (C2×C4).78(C22×D7), (C7×C4⋊C4).189C22, SmallGroup(448,1143)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28⋊7Q8
G = < a,b,c,d | a28=b2=c4=1, d2=c2, bab=a-1, ac=ca, dad-1=a13, cbc-1=a14b, dbd-1=a26b, dcd-1=c-1 >
Subgroups: 1052 in 228 conjugacy classes, 105 normal (43 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, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C4⋊C4, C4×D4, C4×Q8, C22⋊Q8, C42.C2, C42.C2, C4⋊Q8, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, D4⋊3Q8, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C2×C4×D7, C2×D28, C4×Dic14, C4×D28, C28⋊Q8, C28.3Q8, D7×C4⋊C4, D28⋊C4, D14⋊Q8, D14⋊2Q8, C7×C42.C2, D28⋊7Q8
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, Q8×D7, C23×D7, C2×Q8×D7, D7×C4○D4, D4⋊8D14, D28⋊7Q8
►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 78)(2 77)(3 76)(4 75)(5 74)(6 73)(7 72)(8 71)(9 70)(10 69)(11 68)(12 67)(13 66)(14 65)(15 64)(16 63)(17 62)(18 61)(19 60)(20 59)(21 58)(22 57)(23 84)(24 83)(25 82)(26 81)(27 80)(28 79)(29 167)(30 166)(31 165)(32 164)(33 163)(34 162)(35 161)(36 160)(37 159)(38 158)(39 157)(40 156)(41 155)(42 154)(43 153)(44 152)(45 151)(46 150)(47 149)(48 148)(49 147)(50 146)(51 145)(52 144)(53 143)(54 142)(55 141)(56 168)(85 176)(86 175)(87 174)(88 173)(89 172)(90 171)(91 170)(92 169)(93 196)(94 195)(95 194)(96 193)(97 192)(98 191)(99 190)(100 189)(101 188)(102 187)(103 186)(104 185)(105 184)(106 183)(107 182)(108 181)(109 180)(110 179)(111 178)(112 177)(113 222)(114 221)(115 220)(116 219)(117 218)(118 217)(119 216)(120 215)(121 214)(122 213)(123 212)(124 211)(125 210)(126 209)(127 208)(128 207)(129 206)(130 205)(131 204)(132 203)(133 202)(134 201)(135 200)(136 199)(137 198)(138 197)(139 224)(140 223)
(1 135 58 222)(2 136 59 223)(3 137 60 224)(4 138 61 197)(5 139 62 198)(6 140 63 199)(7 113 64 200)(8 114 65 201)(9 115 66 202)(10 116 67 203)(11 117 68 204)(12 118 69 205)(13 119 70 206)(14 120 71 207)(15 121 72 208)(16 122 73 209)(17 123 74 210)(18 124 75 211)(19 125 76 212)(20 126 77 213)(21 127 78 214)(22 128 79 215)(23 129 80 216)(24 130 81 217)(25 131 82 218)(26 132 83 219)(27 133 84 220)(28 134 57 221)(29 107 167 196)(30 108 168 169)(31 109 141 170)(32 110 142 171)(33 111 143 172)(34 112 144 173)(35 85 145 174)(36 86 146 175)(37 87 147 176)(38 88 148 177)(39 89 149 178)(40 90 150 179)(41 91 151 180)(42 92 152 181)(43 93 153 182)(44 94 154 183)(45 95 155 184)(46 96 156 185)(47 97 157 186)(48 98 158 187)(49 99 159 188)(50 100 160 189)(51 101 161 190)(52 102 162 191)(53 103 163 192)(54 104 164 193)(55 105 165 194)(56 106 166 195)
(1 186 58 97)(2 171 59 110)(3 184 60 95)(4 169 61 108)(5 182 62 93)(6 195 63 106)(7 180 64 91)(8 193 65 104)(9 178 66 89)(10 191 67 102)(11 176 68 87)(12 189 69 100)(13 174 70 85)(14 187 71 98)(15 172 72 111)(16 185 73 96)(17 170 74 109)(18 183 75 94)(19 196 76 107)(20 181 77 92)(21 194 78 105)(22 179 79 90)(23 192 80 103)(24 177 81 88)(25 190 82 101)(26 175 83 86)(27 188 84 99)(28 173 57 112)(29 125 167 212)(30 138 168 197)(31 123 141 210)(32 136 142 223)(33 121 143 208)(34 134 144 221)(35 119 145 206)(36 132 146 219)(37 117 147 204)(38 130 148 217)(39 115 149 202)(40 128 150 215)(41 113 151 200)(42 126 152 213)(43 139 153 198)(44 124 154 211)(45 137 155 224)(46 122 156 209)(47 135 157 222)(48 120 158 207)(49 133 159 220)(50 118 160 205)(51 131 161 218)(52 116 162 203)(53 129 163 216)(54 114 164 201)(55 127 165 214)(56 140 166 199)
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), (1,78)(2,77)(3,76)(4,75)(5,74)(6,73)(7,72)(8,71)(9,70)(10,69)(11,68)(12,67)(13,66)(14,65)(15,64)(16,63)(17,62)(18,61)(19,60)(20,59)(21,58)(22,57)(23,84)(24,83)(25,82)(26,81)(27,80)(28,79)(29,167)(30,166)(31,165)(32,164)(33,163)(34,162)(35,161)(36,160)(37,159)(38,158)(39,157)(40,156)(41,155)(42,154)(43,153)(44,152)(45,151)(46,150)(47,149)(48,148)(49,147)(50,146)(51,145)(52,144)(53,143)(54,142)(55,141)(56,168)(85,176)(86,175)(87,174)(88,173)(89,172)(90,171)(91,170)(92,169)(93,196)(94,195)(95,194)(96,193)(97,192)(98,191)(99,190)(100,189)(101,188)(102,187)(103,186)(104,185)(105,184)(106,183)(107,182)(108,181)(109,180)(110,179)(111,178)(112,177)(113,222)(114,221)(115,220)(116,219)(117,218)(118,217)(119,216)(120,215)(121,214)(122,213)(123,212)(124,211)(125,210)(126,209)(127,208)(128,207)(129,206)(130,205)(131,204)(132,203)(133,202)(134,201)(135,200)(136,199)(137,198)(138,197)(139,224)(140,223), (1,135,58,222)(2,136,59,223)(3,137,60,224)(4,138,61,197)(5,139,62,198)(6,140,63,199)(7,113,64,200)(8,114,65,201)(9,115,66,202)(10,116,67,203)(11,117,68,204)(12,118,69,205)(13,119,70,206)(14,120,71,207)(15,121,72,208)(16,122,73,209)(17,123,74,210)(18,124,75,211)(19,125,76,212)(20,126,77,213)(21,127,78,214)(22,128,79,215)(23,129,80,216)(24,130,81,217)(25,131,82,218)(26,132,83,219)(27,133,84,220)(28,134,57,221)(29,107,167,196)(30,108,168,169)(31,109,141,170)(32,110,142,171)(33,111,143,172)(34,112,144,173)(35,85,145,174)(36,86,146,175)(37,87,147,176)(38,88,148,177)(39,89,149,178)(40,90,150,179)(41,91,151,180)(42,92,152,181)(43,93,153,182)(44,94,154,183)(45,95,155,184)(46,96,156,185)(47,97,157,186)(48,98,158,187)(49,99,159,188)(50,100,160,189)(51,101,161,190)(52,102,162,191)(53,103,163,192)(54,104,164,193)(55,105,165,194)(56,106,166,195), (1,186,58,97)(2,171,59,110)(3,184,60,95)(4,169,61,108)(5,182,62,93)(6,195,63,106)(7,180,64,91)(8,193,65,104)(9,178,66,89)(10,191,67,102)(11,176,68,87)(12,189,69,100)(13,174,70,85)(14,187,71,98)(15,172,72,111)(16,185,73,96)(17,170,74,109)(18,183,75,94)(19,196,76,107)(20,181,77,92)(21,194,78,105)(22,179,79,90)(23,192,80,103)(24,177,81,88)(25,190,82,101)(26,175,83,86)(27,188,84,99)(28,173,57,112)(29,125,167,212)(30,138,168,197)(31,123,141,210)(32,136,142,223)(33,121,143,208)(34,134,144,221)(35,119,145,206)(36,132,146,219)(37,117,147,204)(38,130,148,217)(39,115,149,202)(40,128,150,215)(41,113,151,200)(42,126,152,213)(43,139,153,198)(44,124,154,211)(45,137,155,224)(46,122,156,209)(47,135,157,222)(48,120,158,207)(49,133,159,220)(50,118,160,205)(51,131,161,218)(52,116,162,203)(53,129,163,216)(54,114,164,201)(55,127,165,214)(56,140,166,199)>;
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), (1,78)(2,77)(3,76)(4,75)(5,74)(6,73)(7,72)(8,71)(9,70)(10,69)(11,68)(12,67)(13,66)(14,65)(15,64)(16,63)(17,62)(18,61)(19,60)(20,59)(21,58)(22,57)(23,84)(24,83)(25,82)(26,81)(27,80)(28,79)(29,167)(30,166)(31,165)(32,164)(33,163)(34,162)(35,161)(36,160)(37,159)(38,158)(39,157)(40,156)(41,155)(42,154)(43,153)(44,152)(45,151)(46,150)(47,149)(48,148)(49,147)(50,146)(51,145)(52,144)(53,143)(54,142)(55,141)(56,168)(85,176)(86,175)(87,174)(88,173)(89,172)(90,171)(91,170)(92,169)(93,196)(94,195)(95,194)(96,193)(97,192)(98,191)(99,190)(100,189)(101,188)(102,187)(103,186)(104,185)(105,184)(106,183)(107,182)(108,181)(109,180)(110,179)(111,178)(112,177)(113,222)(114,221)(115,220)(116,219)(117,218)(118,217)(119,216)(120,215)(121,214)(122,213)(123,212)(124,211)(125,210)(126,209)(127,208)(128,207)(129,206)(130,205)(131,204)(132,203)(133,202)(134,201)(135,200)(136,199)(137,198)(138,197)(139,224)(140,223), (1,135,58,222)(2,136,59,223)(3,137,60,224)(4,138,61,197)(5,139,62,198)(6,140,63,199)(7,113,64,200)(8,114,65,201)(9,115,66,202)(10,116,67,203)(11,117,68,204)(12,118,69,205)(13,119,70,206)(14,120,71,207)(15,121,72,208)(16,122,73,209)(17,123,74,210)(18,124,75,211)(19,125,76,212)(20,126,77,213)(21,127,78,214)(22,128,79,215)(23,129,80,216)(24,130,81,217)(25,131,82,218)(26,132,83,219)(27,133,84,220)(28,134,57,221)(29,107,167,196)(30,108,168,169)(31,109,141,170)(32,110,142,171)(33,111,143,172)(34,112,144,173)(35,85,145,174)(36,86,146,175)(37,87,147,176)(38,88,148,177)(39,89,149,178)(40,90,150,179)(41,91,151,180)(42,92,152,181)(43,93,153,182)(44,94,154,183)(45,95,155,184)(46,96,156,185)(47,97,157,186)(48,98,158,187)(49,99,159,188)(50,100,160,189)(51,101,161,190)(52,102,162,191)(53,103,163,192)(54,104,164,193)(55,105,165,194)(56,106,166,195), (1,186,58,97)(2,171,59,110)(3,184,60,95)(4,169,61,108)(5,182,62,93)(6,195,63,106)(7,180,64,91)(8,193,65,104)(9,178,66,89)(10,191,67,102)(11,176,68,87)(12,189,69,100)(13,174,70,85)(14,187,71,98)(15,172,72,111)(16,185,73,96)(17,170,74,109)(18,183,75,94)(19,196,76,107)(20,181,77,92)(21,194,78,105)(22,179,79,90)(23,192,80,103)(24,177,81,88)(25,190,82,101)(26,175,83,86)(27,188,84,99)(28,173,57,112)(29,125,167,212)(30,138,168,197)(31,123,141,210)(32,136,142,223)(33,121,143,208)(34,134,144,221)(35,119,145,206)(36,132,146,219)(37,117,147,204)(38,130,148,217)(39,115,149,202)(40,128,150,215)(41,113,151,200)(42,126,152,213)(43,139,153,198)(44,124,154,211)(45,137,155,224)(46,122,156,209)(47,135,157,222)(48,120,158,207)(49,133,159,220)(50,118,160,205)(51,131,161,218)(52,116,162,203)(53,129,163,216)(54,114,164,201)(55,127,165,214)(56,140,166,199) );
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)], [(1,78),(2,77),(3,76),(4,75),(5,74),(6,73),(7,72),(8,71),(9,70),(10,69),(11,68),(12,67),(13,66),(14,65),(15,64),(16,63),(17,62),(18,61),(19,60),(20,59),(21,58),(22,57),(23,84),(24,83),(25,82),(26,81),(27,80),(28,79),(29,167),(30,166),(31,165),(32,164),(33,163),(34,162),(35,161),(36,160),(37,159),(38,158),(39,157),(40,156),(41,155),(42,154),(43,153),(44,152),(45,151),(46,150),(47,149),(48,148),(49,147),(50,146),(51,145),(52,144),(53,143),(54,142),(55,141),(56,168),(85,176),(86,175),(87,174),(88,173),(89,172),(90,171),(91,170),(92,169),(93,196),(94,195),(95,194),(96,193),(97,192),(98,191),(99,190),(100,189),(101,188),(102,187),(103,186),(104,185),(105,184),(106,183),(107,182),(108,181),(109,180),(110,179),(111,178),(112,177),(113,222),(114,221),(115,220),(116,219),(117,218),(118,217),(119,216),(120,215),(121,214),(122,213),(123,212),(124,211),(125,210),(126,209),(127,208),(128,207),(129,206),(130,205),(131,204),(132,203),(133,202),(134,201),(135,200),(136,199),(137,198),(138,197),(139,224),(140,223)], [(1,135,58,222),(2,136,59,223),(3,137,60,224),(4,138,61,197),(5,139,62,198),(6,140,63,199),(7,113,64,200),(8,114,65,201),(9,115,66,202),(10,116,67,203),(11,117,68,204),(12,118,69,205),(13,119,70,206),(14,120,71,207),(15,121,72,208),(16,122,73,209),(17,123,74,210),(18,124,75,211),(19,125,76,212),(20,126,77,213),(21,127,78,214),(22,128,79,215),(23,129,80,216),(24,130,81,217),(25,131,82,218),(26,132,83,219),(27,133,84,220),(28,134,57,221),(29,107,167,196),(30,108,168,169),(31,109,141,170),(32,110,142,171),(33,111,143,172),(34,112,144,173),(35,85,145,174),(36,86,146,175),(37,87,147,176),(38,88,148,177),(39,89,149,178),(40,90,150,179),(41,91,151,180),(42,92,152,181),(43,93,153,182),(44,94,154,183),(45,95,155,184),(46,96,156,185),(47,97,157,186),(48,98,158,187),(49,99,159,188),(50,100,160,189),(51,101,161,190),(52,102,162,191),(53,103,163,192),(54,104,164,193),(55,105,165,194),(56,106,166,195)], [(1,186,58,97),(2,171,59,110),(3,184,60,95),(4,169,61,108),(5,182,62,93),(6,195,63,106),(7,180,64,91),(8,193,65,104),(9,178,66,89),(10,191,67,102),(11,176,68,87),(12,189,69,100),(13,174,70,85),(14,187,71,98),(15,172,72,111),(16,185,73,96),(17,170,74,109),(18,183,75,94),(19,196,76,107),(20,181,77,92),(21,194,78,105),(22,179,79,90),(23,192,80,103),(24,177,81,88),(25,190,82,101),(26,175,83,86),(27,188,84,99),(28,173,57,112),(29,125,167,212),(30,138,168,197),(31,123,141,210),(32,136,142,223),(33,121,143,208),(34,134,144,221),(35,119,145,206),(36,132,146,219),(37,117,147,204),(38,130,148,217),(39,115,149,202),(40,128,150,215),(41,113,151,200),(42,126,152,213),(43,139,153,198),(44,124,154,211),(45,137,155,224),(46,122,156,209),(47,135,157,222),(48,120,158,207),(49,133,159,220),(50,118,160,205),(51,131,161,218),(52,116,162,203),(53,129,163,216),(54,114,164,201),(55,127,165,214),(56,140,166,199)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | ··· | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 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 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | + | + | + | + | - | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | Q8 | D7 | C4○D4 | D14 | D14 | 2+ 1+4 | Q8×D7 | D7×C4○D4 | D4⋊8D14 |
| kernel | D28⋊7Q8 | C4×Dic14 | C4×D28 | C28⋊Q8 | C28.3Q8 | D7×C4⋊C4 | D28⋊C4 | D14⋊Q8 | D14⋊2Q8 | C7×C42.C2 | D28 | C42.C2 | Dic7 | C42 | C4⋊C4 | C14 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 2 | 1 | 4 | 3 | 4 | 3 | 18 | 1 | 6 | 6 | 6 |
Matrix representation of D28⋊7Q8 ►in GL6(𝔽29)
| 0 | 12 | 0 | 0 | 0 | 0 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 26 | 0 | 0 |
| 0 | 0 | 3 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 26 | 0 | 0 |
| 0 | 0 | 21 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 28 |
| 0 | 0 | 0 | 0 | 24 | 9 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 3 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 14 |
| 0 | 0 | 0 | 0 | 10 | 27 |
G:=sub<GL(6,GF(29))| [0,12,0,0,0,0,12,0,0,0,0,0,0,0,8,3,0,0,0,0,26,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,28,0,0,0,0,0,0,8,21,0,0,0,0,26,21,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,20,24,0,0,0,0,28,9],[0,28,0,0,0,0,28,0,0,0,0,0,0,0,1,3,0,0,0,0,0,28,0,0,0,0,0,0,2,10,0,0,0,0,14,27] >;
D28⋊7Q8 in GAP, Magma, Sage, TeX
D_{28}\rtimes_7Q_8 % in TeX
G:=Group("D28:7Q8"); // GroupNames label
G:=SmallGroup(448,1143);
// by ID
G=gap.SmallGroup(448,1143);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,219,184,1571,297,80,18822]);
// 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,d*a*d^-1=a^13,c*b*c^-1=a^14*b,d*b*d^-1=a^26*b,d*c*d^-1=c^-1>;
// generators/relations