metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Q8⋊6D28, C42.129D14, C14.1102+ 1+4, (C4×Q8)⋊10D7, (C7×Q8)⋊11D4, (C4×D28)⋊39C2, (Q8×C28)⋊12C2, C7⋊2(Q8⋊6D4), C28.58(C2×D4), C4.26(C2×D28), C28⋊17(C4○D4), C4⋊D28⋊18C2, C28⋊4D4⋊13C2, C4⋊C4.296D14, C4⋊3(Q8⋊2D7), (C2×Q8).205D14, C14.20(C22×D4), C2.22(C22×D28), (C4×C28).173C22, (C2×C14).121C24, (C2×C28).170C23, (C2×D28).28C22, C2.22(D4⋊8D14), D14⋊C4.101C22, C4⋊Dic7.399C22, (Q8×C14).221C22, (C22×D7).46C23, C22.142(C23×D7), (C2×Dic7).215C23, (C2×Q8⋊2D7)⋊4C2, (C2×C4×D7).73C22, C14.112(C2×C4○D4), C2.11(C2×Q8⋊2D7), (C7×C4⋊C4).349C22, (C2×C4).734(C22×D7), SmallGroup(448,1030)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Q8⋊6D28
G = < a,b,c,d | a4=c28=d2=1, b2=a2, bab-1=dad=a-1, ac=ca, bc=cb, bd=db, dcd=c-1 >
Subgroups: 1796 in 312 conjugacy classes, 115 normal (18 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic7, C28, C28, D14, C2×C14, C4×D4, C4×Q8, C4⋊D4, C4⋊1D4, C2×C4○D4, C4×D7, D28, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, Q8⋊6D4, C4⋊Dic7, D14⋊C4, C4×C28, C7×C4⋊C4, C2×C4×D7, C2×D28, Q8⋊2D7, Q8×C14, C4×D28, C28⋊4D4, C4⋊D28, Q8×C28, C2×Q8⋊2D7, Q8⋊6D28
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C22×D4, C2×C4○D4, 2+ 1+4, D28, C22×D7, Q8⋊6D4, C2×D28, Q8⋊2D7, C23×D7, C22×D28, C2×Q8⋊2D7, D4⋊8D14, Q8⋊6D28
►On 224 points
Generators in S224
(1 157 69 214)(2 158 70 215)(3 159 71 216)(4 160 72 217)(5 161 73 218)(6 162 74 219)(7 163 75 220)(8 164 76 221)(9 165 77 222)(10 166 78 223)(11 167 79 224)(12 168 80 197)(13 141 81 198)(14 142 82 199)(15 143 83 200)(16 144 84 201)(17 145 57 202)(18 146 58 203)(19 147 59 204)(20 148 60 205)(21 149 61 206)(22 150 62 207)(23 151 63 208)(24 152 64 209)(25 153 65 210)(26 154 66 211)(27 155 67 212)(28 156 68 213)(29 101 132 183)(30 102 133 184)(31 103 134 185)(32 104 135 186)(33 105 136 187)(34 106 137 188)(35 107 138 189)(36 108 139 190)(37 109 140 191)(38 110 113 192)(39 111 114 193)(40 112 115 194)(41 85 116 195)(42 86 117 196)(43 87 118 169)(44 88 119 170)(45 89 120 171)(46 90 121 172)(47 91 122 173)(48 92 123 174)(49 93 124 175)(50 94 125 176)(51 95 126 177)(52 96 127 178)(53 97 128 179)(54 98 129 180)(55 99 130 181)(56 100 131 182)
(1 126 69 51)(2 127 70 52)(3 128 71 53)(4 129 72 54)(5 130 73 55)(6 131 74 56)(7 132 75 29)(8 133 76 30)(9 134 77 31)(10 135 78 32)(11 136 79 33)(12 137 80 34)(13 138 81 35)(14 139 82 36)(15 140 83 37)(16 113 84 38)(17 114 57 39)(18 115 58 40)(19 116 59 41)(20 117 60 42)(21 118 61 43)(22 119 62 44)(23 120 63 45)(24 121 64 46)(25 122 65 47)(26 123 66 48)(27 124 67 49)(28 125 68 50)(85 204 195 147)(86 205 196 148)(87 206 169 149)(88 207 170 150)(89 208 171 151)(90 209 172 152)(91 210 173 153)(92 211 174 154)(93 212 175 155)(94 213 176 156)(95 214 177 157)(96 215 178 158)(97 216 179 159)(98 217 180 160)(99 218 181 161)(100 219 182 162)(101 220 183 163)(102 221 184 164)(103 222 185 165)(104 223 186 166)(105 224 187 167)(106 197 188 168)(107 198 189 141)(108 199 190 142)(109 200 191 143)(110 201 192 144)(111 202 193 145)(112 203 194 146)
(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)
(1 206)(2 205)(3 204)(4 203)(5 202)(6 201)(7 200)(8 199)(9 198)(10 197)(11 224)(12 223)(13 222)(14 221)(15 220)(16 219)(17 218)(18 217)(19 216)(20 215)(21 214)(22 213)(23 212)(24 211)(25 210)(26 209)(27 208)(28 207)(29 109)(30 108)(31 107)(32 106)(33 105)(34 104)(35 103)(36 102)(37 101)(38 100)(39 99)(40 98)(41 97)(42 96)(43 95)(44 94)(45 93)(46 92)(47 91)(48 90)(49 89)(50 88)(51 87)(52 86)(53 85)(54 112)(55 111)(56 110)(57 161)(58 160)(59 159)(60 158)(61 157)(62 156)(63 155)(64 154)(65 153)(66 152)(67 151)(68 150)(69 149)(70 148)(71 147)(72 146)(73 145)(74 144)(75 143)(76 142)(77 141)(78 168)(79 167)(80 166)(81 165)(82 164)(83 163)(84 162)(113 182)(114 181)(115 180)(116 179)(117 178)(118 177)(119 176)(120 175)(121 174)(122 173)(123 172)(124 171)(125 170)(126 169)(127 196)(128 195)(129 194)(130 193)(131 192)(132 191)(133 190)(134 189)(135 188)(136 187)(137 186)(138 185)(139 184)(140 183)
G:=sub<Sym(224)| (1,157,69,214)(2,158,70,215)(3,159,71,216)(4,160,72,217)(5,161,73,218)(6,162,74,219)(7,163,75,220)(8,164,76,221)(9,165,77,222)(10,166,78,223)(11,167,79,224)(12,168,80,197)(13,141,81,198)(14,142,82,199)(15,143,83,200)(16,144,84,201)(17,145,57,202)(18,146,58,203)(19,147,59,204)(20,148,60,205)(21,149,61,206)(22,150,62,207)(23,151,63,208)(24,152,64,209)(25,153,65,210)(26,154,66,211)(27,155,67,212)(28,156,68,213)(29,101,132,183)(30,102,133,184)(31,103,134,185)(32,104,135,186)(33,105,136,187)(34,106,137,188)(35,107,138,189)(36,108,139,190)(37,109,140,191)(38,110,113,192)(39,111,114,193)(40,112,115,194)(41,85,116,195)(42,86,117,196)(43,87,118,169)(44,88,119,170)(45,89,120,171)(46,90,121,172)(47,91,122,173)(48,92,123,174)(49,93,124,175)(50,94,125,176)(51,95,126,177)(52,96,127,178)(53,97,128,179)(54,98,129,180)(55,99,130,181)(56,100,131,182), (1,126,69,51)(2,127,70,52)(3,128,71,53)(4,129,72,54)(5,130,73,55)(6,131,74,56)(7,132,75,29)(8,133,76,30)(9,134,77,31)(10,135,78,32)(11,136,79,33)(12,137,80,34)(13,138,81,35)(14,139,82,36)(15,140,83,37)(16,113,84,38)(17,114,57,39)(18,115,58,40)(19,116,59,41)(20,117,60,42)(21,118,61,43)(22,119,62,44)(23,120,63,45)(24,121,64,46)(25,122,65,47)(26,123,66,48)(27,124,67,49)(28,125,68,50)(85,204,195,147)(86,205,196,148)(87,206,169,149)(88,207,170,150)(89,208,171,151)(90,209,172,152)(91,210,173,153)(92,211,174,154)(93,212,175,155)(94,213,176,156)(95,214,177,157)(96,215,178,158)(97,216,179,159)(98,217,180,160)(99,218,181,161)(100,219,182,162)(101,220,183,163)(102,221,184,164)(103,222,185,165)(104,223,186,166)(105,224,187,167)(106,197,188,168)(107,198,189,141)(108,199,190,142)(109,200,191,143)(110,201,192,144)(111,202,193,145)(112,203,194,146), (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), (1,206)(2,205)(3,204)(4,203)(5,202)(6,201)(7,200)(8,199)(9,198)(10,197)(11,224)(12,223)(13,222)(14,221)(15,220)(16,219)(17,218)(18,217)(19,216)(20,215)(21,214)(22,213)(23,212)(24,211)(25,210)(26,209)(27,208)(28,207)(29,109)(30,108)(31,107)(32,106)(33,105)(34,104)(35,103)(36,102)(37,101)(38,100)(39,99)(40,98)(41,97)(42,96)(43,95)(44,94)(45,93)(46,92)(47,91)(48,90)(49,89)(50,88)(51,87)(52,86)(53,85)(54,112)(55,111)(56,110)(57,161)(58,160)(59,159)(60,158)(61,157)(62,156)(63,155)(64,154)(65,153)(66,152)(67,151)(68,150)(69,149)(70,148)(71,147)(72,146)(73,145)(74,144)(75,143)(76,142)(77,141)(78,168)(79,167)(80,166)(81,165)(82,164)(83,163)(84,162)(113,182)(114,181)(115,180)(116,179)(117,178)(118,177)(119,176)(120,175)(121,174)(122,173)(123,172)(124,171)(125,170)(126,169)(127,196)(128,195)(129,194)(130,193)(131,192)(132,191)(133,190)(134,189)(135,188)(136,187)(137,186)(138,185)(139,184)(140,183)>;
G:=Group( (1,157,69,214)(2,158,70,215)(3,159,71,216)(4,160,72,217)(5,161,73,218)(6,162,74,219)(7,163,75,220)(8,164,76,221)(9,165,77,222)(10,166,78,223)(11,167,79,224)(12,168,80,197)(13,141,81,198)(14,142,82,199)(15,143,83,200)(16,144,84,201)(17,145,57,202)(18,146,58,203)(19,147,59,204)(20,148,60,205)(21,149,61,206)(22,150,62,207)(23,151,63,208)(24,152,64,209)(25,153,65,210)(26,154,66,211)(27,155,67,212)(28,156,68,213)(29,101,132,183)(30,102,133,184)(31,103,134,185)(32,104,135,186)(33,105,136,187)(34,106,137,188)(35,107,138,189)(36,108,139,190)(37,109,140,191)(38,110,113,192)(39,111,114,193)(40,112,115,194)(41,85,116,195)(42,86,117,196)(43,87,118,169)(44,88,119,170)(45,89,120,171)(46,90,121,172)(47,91,122,173)(48,92,123,174)(49,93,124,175)(50,94,125,176)(51,95,126,177)(52,96,127,178)(53,97,128,179)(54,98,129,180)(55,99,130,181)(56,100,131,182), (1,126,69,51)(2,127,70,52)(3,128,71,53)(4,129,72,54)(5,130,73,55)(6,131,74,56)(7,132,75,29)(8,133,76,30)(9,134,77,31)(10,135,78,32)(11,136,79,33)(12,137,80,34)(13,138,81,35)(14,139,82,36)(15,140,83,37)(16,113,84,38)(17,114,57,39)(18,115,58,40)(19,116,59,41)(20,117,60,42)(21,118,61,43)(22,119,62,44)(23,120,63,45)(24,121,64,46)(25,122,65,47)(26,123,66,48)(27,124,67,49)(28,125,68,50)(85,204,195,147)(86,205,196,148)(87,206,169,149)(88,207,170,150)(89,208,171,151)(90,209,172,152)(91,210,173,153)(92,211,174,154)(93,212,175,155)(94,213,176,156)(95,214,177,157)(96,215,178,158)(97,216,179,159)(98,217,180,160)(99,218,181,161)(100,219,182,162)(101,220,183,163)(102,221,184,164)(103,222,185,165)(104,223,186,166)(105,224,187,167)(106,197,188,168)(107,198,189,141)(108,199,190,142)(109,200,191,143)(110,201,192,144)(111,202,193,145)(112,203,194,146), (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), (1,206)(2,205)(3,204)(4,203)(5,202)(6,201)(7,200)(8,199)(9,198)(10,197)(11,224)(12,223)(13,222)(14,221)(15,220)(16,219)(17,218)(18,217)(19,216)(20,215)(21,214)(22,213)(23,212)(24,211)(25,210)(26,209)(27,208)(28,207)(29,109)(30,108)(31,107)(32,106)(33,105)(34,104)(35,103)(36,102)(37,101)(38,100)(39,99)(40,98)(41,97)(42,96)(43,95)(44,94)(45,93)(46,92)(47,91)(48,90)(49,89)(50,88)(51,87)(52,86)(53,85)(54,112)(55,111)(56,110)(57,161)(58,160)(59,159)(60,158)(61,157)(62,156)(63,155)(64,154)(65,153)(66,152)(67,151)(68,150)(69,149)(70,148)(71,147)(72,146)(73,145)(74,144)(75,143)(76,142)(77,141)(78,168)(79,167)(80,166)(81,165)(82,164)(83,163)(84,162)(113,182)(114,181)(115,180)(116,179)(117,178)(118,177)(119,176)(120,175)(121,174)(122,173)(123,172)(124,171)(125,170)(126,169)(127,196)(128,195)(129,194)(130,193)(131,192)(132,191)(133,190)(134,189)(135,188)(136,187)(137,186)(138,185)(139,184)(140,183) );
G=PermutationGroup([[(1,157,69,214),(2,158,70,215),(3,159,71,216),(4,160,72,217),(5,161,73,218),(6,162,74,219),(7,163,75,220),(8,164,76,221),(9,165,77,222),(10,166,78,223),(11,167,79,224),(12,168,80,197),(13,141,81,198),(14,142,82,199),(15,143,83,200),(16,144,84,201),(17,145,57,202),(18,146,58,203),(19,147,59,204),(20,148,60,205),(21,149,61,206),(22,150,62,207),(23,151,63,208),(24,152,64,209),(25,153,65,210),(26,154,66,211),(27,155,67,212),(28,156,68,213),(29,101,132,183),(30,102,133,184),(31,103,134,185),(32,104,135,186),(33,105,136,187),(34,106,137,188),(35,107,138,189),(36,108,139,190),(37,109,140,191),(38,110,113,192),(39,111,114,193),(40,112,115,194),(41,85,116,195),(42,86,117,196),(43,87,118,169),(44,88,119,170),(45,89,120,171),(46,90,121,172),(47,91,122,173),(48,92,123,174),(49,93,124,175),(50,94,125,176),(51,95,126,177),(52,96,127,178),(53,97,128,179),(54,98,129,180),(55,99,130,181),(56,100,131,182)], [(1,126,69,51),(2,127,70,52),(3,128,71,53),(4,129,72,54),(5,130,73,55),(6,131,74,56),(7,132,75,29),(8,133,76,30),(9,134,77,31),(10,135,78,32),(11,136,79,33),(12,137,80,34),(13,138,81,35),(14,139,82,36),(15,140,83,37),(16,113,84,38),(17,114,57,39),(18,115,58,40),(19,116,59,41),(20,117,60,42),(21,118,61,43),(22,119,62,44),(23,120,63,45),(24,121,64,46),(25,122,65,47),(26,123,66,48),(27,124,67,49),(28,125,68,50),(85,204,195,147),(86,205,196,148),(87,206,169,149),(88,207,170,150),(89,208,171,151),(90,209,172,152),(91,210,173,153),(92,211,174,154),(93,212,175,155),(94,213,176,156),(95,214,177,157),(96,215,178,158),(97,216,179,159),(98,217,180,160),(99,218,181,161),(100,219,182,162),(101,220,183,163),(102,221,184,164),(103,222,185,165),(104,223,186,166),(105,224,187,167),(106,197,188,168),(107,198,189,141),(108,199,190,142),(109,200,191,143),(110,201,192,144),(111,202,193,145),(112,203,194,146)], [(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)], [(1,206),(2,205),(3,204),(4,203),(5,202),(6,201),(7,200),(8,199),(9,198),(10,197),(11,224),(12,223),(13,222),(14,221),(15,220),(16,219),(17,218),(18,217),(19,216),(20,215),(21,214),(22,213),(23,212),(24,211),(25,210),(26,209),(27,208),(28,207),(29,109),(30,108),(31,107),(32,106),(33,105),(34,104),(35,103),(36,102),(37,101),(38,100),(39,99),(40,98),(41,97),(42,96),(43,95),(44,94),(45,93),(46,92),(47,91),(48,90),(49,89),(50,88),(51,87),(52,86),(53,85),(54,112),(55,111),(56,110),(57,161),(58,160),(59,159),(60,158),(61,157),(62,156),(63,155),(64,154),(65,153),(66,152),(67,151),(68,150),(69,149),(70,148),(71,147),(72,146),(73,145),(74,144),(75,143),(76,142),(77,141),(78,168),(79,167),(80,166),(81,165),(82,164),(83,163),(84,162),(113,182),(114,181),(115,180),(116,179),(117,178),(118,177),(119,176),(120,175),(121,174),(122,173),(123,172),(124,171),(125,170),(126,169),(127,196),(128,195),(129,194),(130,193),(131,192),(132,191),(133,190),(134,189),(135,188),(136,187),(137,186),(138,185),(139,184),(140,183)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | ··· | 2I | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28AV |
| order | 1 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | ··· | 28 | 2 | ··· | 2 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | D28 | 2+ 1+4 | Q8⋊2D7 | D4⋊8D14 |
| kernel | Q8⋊6D28 | C4×D28 | C28⋊4D4 | C4⋊D28 | Q8×C28 | C2×Q8⋊2D7 | C7×Q8 | C4×Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | Q8 | C14 | C4 | C2 |
| # reps | 1 | 3 | 3 | 6 | 1 | 2 | 4 | 3 | 4 | 9 | 9 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of Q8⋊6D28 ►in GL4(𝔽29) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 4 | 5 |
| 0 | 0 | 14 | 25 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 19 | 2 |
| 0 | 0 | 22 | 10 |
| 3 | 25 | 0 | 0 |
| 8 | 9 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 23 | 19 | 0 | 0 |
| 18 | 6 | 0 | 0 |
| 0 | 0 | 4 | 5 |
| 0 | 0 | 26 | 25 |
G:=sub<GL(4,GF(29))| [1,0,0,0,0,1,0,0,0,0,4,14,0,0,5,25],[1,0,0,0,0,1,0,0,0,0,19,22,0,0,2,10],[3,8,0,0,25,9,0,0,0,0,1,0,0,0,0,1],[23,18,0,0,19,6,0,0,0,0,4,26,0,0,5,25] >;
Q8⋊6D28 in GAP, Magma, Sage, TeX
Q_8\rtimes_6D_{28} % in TeX
G:=Group("Q8:6D28"); // GroupNames label
G:=SmallGroup(448,1030);
// by ID
G=gap.SmallGroup(448,1030);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,387,184,675,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=c^28=d^2=1,b^2=a^2,b*a*b^-1=d*a*d=a^-1,a*c=c*a,b*c=c*b,b*d=d*b,d*c*d=c^-1>;
// generators/relations