metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×C28).289D4, (C22×D7).4Q8, C22.50(Q8×D7), C2.7(C28⋊D4), (C2×Dic7).61D4, C22.248(D4×D7), (C22×C4).44D14, C14.16(C4⋊1D4), C7⋊3(C23.4Q8), C2.8(D14⋊3Q8), C14.50(C22⋊Q8), C14.C42⋊43C2, C2.22(D14⋊Q8), (C22×C28).31C22, (C23×D7).21C22, C23.381(C22×D7), C2.21(D14.5D4), C22.109(C4○D28), (C22×C14).356C23, C22.52(Q8⋊2D7), C14.54(C22.D4), (C22×Dic7).61C22, C2.14(C23.23D14), (C2×C4⋊C4)⋊10D7, (C14×C4⋊C4)⋊26C2, (C2×C14).85(C2×Q8), (C2×Dic7⋊C4)⋊14C2, (C2×D14⋊C4).14C2, (C2×C14).453(C2×D4), (C2×C4).42(C7⋊D4), C22.141(C2×C7⋊D4), (C2×C14).191(C4○D4), SmallGroup(448,526)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×C28).289D4
G = < a,b,c,d | a2=b28=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=ab-1, dbd=ab13, dcd=ab14c-1 >
Subgroups: 996 in 186 conjugacy classes, 61 normal (25 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, C23, C23, D7, C14, C14, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C24, Dic7, C28, D14, C2×C14, C2×C14, C2.C42, C2×C22⋊C4, C2×C4⋊C4, C2×C4⋊C4, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C23.4Q8, Dic7⋊C4, D14⋊C4, C7×C4⋊C4, C22×Dic7, C22×Dic7, C22×C28, C22×C28, C23×D7, C14.C42, C2×Dic7⋊C4, C2×D14⋊C4, C2×D14⋊C4, C14×C4⋊C4, (C2×C28).289D4
Quotients: C1, C2, C22, D4, Q8, C23, D7, C2×D4, C2×Q8, C4○D4, D14, C22⋊Q8, C22.D4, C4⋊1D4, C7⋊D4, C22×D7, C23.4Q8, C4○D28, D4×D7, Q8×D7, Q8⋊2D7, C2×C7⋊D4, D14.5D4, D14⋊Q8, C23.23D14, C28⋊D4, D14⋊3Q8, (C2×C28).289D4
►On 224 points
Generators in S224
(1 35)(2 36)(3 37)(4 38)(5 39)(6 40)(7 41)(8 42)(9 43)(10 44)(11 45)(12 46)(13 47)(14 48)(15 49)(16 50)(17 51)(18 52)(19 53)(20 54)(21 55)(22 56)(23 29)(24 30)(25 31)(26 32)(27 33)(28 34)(57 109)(58 110)(59 111)(60 112)(61 85)(62 86)(63 87)(64 88)(65 89)(66 90)(67 91)(68 92)(69 93)(70 94)(71 95)(72 96)(73 97)(74 98)(75 99)(76 100)(77 101)(78 102)(79 103)(80 104)(81 105)(82 106)(83 107)(84 108)(113 142)(114 143)(115 144)(116 145)(117 146)(118 147)(119 148)(120 149)(121 150)(122 151)(123 152)(124 153)(125 154)(126 155)(127 156)(128 157)(129 158)(130 159)(131 160)(132 161)(133 162)(134 163)(135 164)(136 165)(137 166)(138 167)(139 168)(140 141)(169 209)(170 210)(171 211)(172 212)(173 213)(174 214)(175 215)(176 216)(177 217)(178 218)(179 219)(180 220)(181 221)(182 222)(183 223)(184 224)(185 197)(186 198)(187 199)(188 200)(189 201)(190 202)(191 203)(192 204)(193 205)(194 206)(195 207)(196 208)
(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)
(1 200 119 109)(2 187 120 84)(3 198 121 107)(4 185 122 82)(5 224 123 105)(6 183 124 80)(7 222 125 103)(8 181 126 78)(9 220 127 101)(10 179 128 76)(11 218 129 99)(12 177 130 74)(13 216 131 97)(14 175 132 72)(15 214 133 95)(16 173 134 70)(17 212 135 93)(18 171 136 68)(19 210 137 91)(20 169 138 66)(21 208 139 89)(22 195 140 64)(23 206 113 87)(24 193 114 62)(25 204 115 85)(26 191 116 60)(27 202 117 111)(28 189 118 58)(29 194 142 63)(30 205 143 86)(31 192 144 61)(32 203 145 112)(33 190 146 59)(34 201 147 110)(35 188 148 57)(36 199 149 108)(37 186 150 83)(38 197 151 106)(39 184 152 81)(40 223 153 104)(41 182 154 79)(42 221 155 102)(43 180 156 77)(44 219 157 100)(45 178 158 75)(46 217 159 98)(47 176 160 73)(48 215 161 96)(49 174 162 71)(50 213 163 94)(51 172 164 69)(52 211 165 92)(53 170 166 67)(54 209 167 90)(55 196 168 65)(56 207 141 88)
(1 15)(2 34)(3 13)(4 32)(5 11)(6 30)(7 9)(8 56)(10 54)(12 52)(14 50)(16 48)(17 27)(18 46)(19 25)(20 44)(21 23)(22 42)(24 40)(26 38)(28 36)(29 55)(31 53)(33 51)(35 49)(37 47)(39 45)(41 43)(57 200)(58 173)(59 198)(60 171)(61 224)(62 169)(63 222)(64 195)(65 220)(66 193)(67 218)(68 191)(69 216)(70 189)(71 214)(72 187)(73 212)(74 185)(75 210)(76 183)(77 208)(78 181)(79 206)(80 179)(81 204)(82 177)(83 202)(84 175)(85 184)(86 209)(87 182)(88 207)(89 180)(90 205)(91 178)(92 203)(93 176)(94 201)(95 174)(96 199)(97 172)(98 197)(99 170)(100 223)(101 196)(102 221)(103 194)(104 219)(105 192)(106 217)(107 190)(108 215)(109 188)(110 213)(111 186)(112 211)(113 139)(114 153)(115 137)(116 151)(117 135)(118 149)(119 133)(120 147)(121 131)(122 145)(123 129)(124 143)(125 127)(126 141)(128 167)(130 165)(132 163)(134 161)(136 159)(138 157)(140 155)(142 168)(144 166)(146 164)(148 162)(150 160)(152 158)(154 156)
G:=sub<Sym(224)| (1,35)(2,36)(3,37)(4,38)(5,39)(6,40)(7,41)(8,42)(9,43)(10,44)(11,45)(12,46)(13,47)(14,48)(15,49)(16,50)(17,51)(18,52)(19,53)(20,54)(21,55)(22,56)(23,29)(24,30)(25,31)(26,32)(27,33)(28,34)(57,109)(58,110)(59,111)(60,112)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)(69,93)(70,94)(71,95)(72,96)(73,97)(74,98)(75,99)(76,100)(77,101)(78,102)(79,103)(80,104)(81,105)(82,106)(83,107)(84,108)(113,142)(114,143)(115,144)(116,145)(117,146)(118,147)(119,148)(120,149)(121,150)(122,151)(123,152)(124,153)(125,154)(126,155)(127,156)(128,157)(129,158)(130,159)(131,160)(132,161)(133,162)(134,163)(135,164)(136,165)(137,166)(138,167)(139,168)(140,141)(169,209)(170,210)(171,211)(172,212)(173,213)(174,214)(175,215)(176,216)(177,217)(178,218)(179,219)(180,220)(181,221)(182,222)(183,223)(184,224)(185,197)(186,198)(187,199)(188,200)(189,201)(190,202)(191,203)(192,204)(193,205)(194,206)(195,207)(196,208), (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), (1,200,119,109)(2,187,120,84)(3,198,121,107)(4,185,122,82)(5,224,123,105)(6,183,124,80)(7,222,125,103)(8,181,126,78)(9,220,127,101)(10,179,128,76)(11,218,129,99)(12,177,130,74)(13,216,131,97)(14,175,132,72)(15,214,133,95)(16,173,134,70)(17,212,135,93)(18,171,136,68)(19,210,137,91)(20,169,138,66)(21,208,139,89)(22,195,140,64)(23,206,113,87)(24,193,114,62)(25,204,115,85)(26,191,116,60)(27,202,117,111)(28,189,118,58)(29,194,142,63)(30,205,143,86)(31,192,144,61)(32,203,145,112)(33,190,146,59)(34,201,147,110)(35,188,148,57)(36,199,149,108)(37,186,150,83)(38,197,151,106)(39,184,152,81)(40,223,153,104)(41,182,154,79)(42,221,155,102)(43,180,156,77)(44,219,157,100)(45,178,158,75)(46,217,159,98)(47,176,160,73)(48,215,161,96)(49,174,162,71)(50,213,163,94)(51,172,164,69)(52,211,165,92)(53,170,166,67)(54,209,167,90)(55,196,168,65)(56,207,141,88), (1,15)(2,34)(3,13)(4,32)(5,11)(6,30)(7,9)(8,56)(10,54)(12,52)(14,50)(16,48)(17,27)(18,46)(19,25)(20,44)(21,23)(22,42)(24,40)(26,38)(28,36)(29,55)(31,53)(33,51)(35,49)(37,47)(39,45)(41,43)(57,200)(58,173)(59,198)(60,171)(61,224)(62,169)(63,222)(64,195)(65,220)(66,193)(67,218)(68,191)(69,216)(70,189)(71,214)(72,187)(73,212)(74,185)(75,210)(76,183)(77,208)(78,181)(79,206)(80,179)(81,204)(82,177)(83,202)(84,175)(85,184)(86,209)(87,182)(88,207)(89,180)(90,205)(91,178)(92,203)(93,176)(94,201)(95,174)(96,199)(97,172)(98,197)(99,170)(100,223)(101,196)(102,221)(103,194)(104,219)(105,192)(106,217)(107,190)(108,215)(109,188)(110,213)(111,186)(112,211)(113,139)(114,153)(115,137)(116,151)(117,135)(118,149)(119,133)(120,147)(121,131)(122,145)(123,129)(124,143)(125,127)(126,141)(128,167)(130,165)(132,163)(134,161)(136,159)(138,157)(140,155)(142,168)(144,166)(146,164)(148,162)(150,160)(152,158)(154,156)>;
G:=Group( (1,35)(2,36)(3,37)(4,38)(5,39)(6,40)(7,41)(8,42)(9,43)(10,44)(11,45)(12,46)(13,47)(14,48)(15,49)(16,50)(17,51)(18,52)(19,53)(20,54)(21,55)(22,56)(23,29)(24,30)(25,31)(26,32)(27,33)(28,34)(57,109)(58,110)(59,111)(60,112)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)(69,93)(70,94)(71,95)(72,96)(73,97)(74,98)(75,99)(76,100)(77,101)(78,102)(79,103)(80,104)(81,105)(82,106)(83,107)(84,108)(113,142)(114,143)(115,144)(116,145)(117,146)(118,147)(119,148)(120,149)(121,150)(122,151)(123,152)(124,153)(125,154)(126,155)(127,156)(128,157)(129,158)(130,159)(131,160)(132,161)(133,162)(134,163)(135,164)(136,165)(137,166)(138,167)(139,168)(140,141)(169,209)(170,210)(171,211)(172,212)(173,213)(174,214)(175,215)(176,216)(177,217)(178,218)(179,219)(180,220)(181,221)(182,222)(183,223)(184,224)(185,197)(186,198)(187,199)(188,200)(189,201)(190,202)(191,203)(192,204)(193,205)(194,206)(195,207)(196,208), (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), (1,200,119,109)(2,187,120,84)(3,198,121,107)(4,185,122,82)(5,224,123,105)(6,183,124,80)(7,222,125,103)(8,181,126,78)(9,220,127,101)(10,179,128,76)(11,218,129,99)(12,177,130,74)(13,216,131,97)(14,175,132,72)(15,214,133,95)(16,173,134,70)(17,212,135,93)(18,171,136,68)(19,210,137,91)(20,169,138,66)(21,208,139,89)(22,195,140,64)(23,206,113,87)(24,193,114,62)(25,204,115,85)(26,191,116,60)(27,202,117,111)(28,189,118,58)(29,194,142,63)(30,205,143,86)(31,192,144,61)(32,203,145,112)(33,190,146,59)(34,201,147,110)(35,188,148,57)(36,199,149,108)(37,186,150,83)(38,197,151,106)(39,184,152,81)(40,223,153,104)(41,182,154,79)(42,221,155,102)(43,180,156,77)(44,219,157,100)(45,178,158,75)(46,217,159,98)(47,176,160,73)(48,215,161,96)(49,174,162,71)(50,213,163,94)(51,172,164,69)(52,211,165,92)(53,170,166,67)(54,209,167,90)(55,196,168,65)(56,207,141,88), (1,15)(2,34)(3,13)(4,32)(5,11)(6,30)(7,9)(8,56)(10,54)(12,52)(14,50)(16,48)(17,27)(18,46)(19,25)(20,44)(21,23)(22,42)(24,40)(26,38)(28,36)(29,55)(31,53)(33,51)(35,49)(37,47)(39,45)(41,43)(57,200)(58,173)(59,198)(60,171)(61,224)(62,169)(63,222)(64,195)(65,220)(66,193)(67,218)(68,191)(69,216)(70,189)(71,214)(72,187)(73,212)(74,185)(75,210)(76,183)(77,208)(78,181)(79,206)(80,179)(81,204)(82,177)(83,202)(84,175)(85,184)(86,209)(87,182)(88,207)(89,180)(90,205)(91,178)(92,203)(93,176)(94,201)(95,174)(96,199)(97,172)(98,197)(99,170)(100,223)(101,196)(102,221)(103,194)(104,219)(105,192)(106,217)(107,190)(108,215)(109,188)(110,213)(111,186)(112,211)(113,139)(114,153)(115,137)(116,151)(117,135)(118,149)(119,133)(120,147)(121,131)(122,145)(123,129)(124,143)(125,127)(126,141)(128,167)(130,165)(132,163)(134,161)(136,159)(138,157)(140,155)(142,168)(144,166)(146,164)(148,162)(150,160)(152,158)(154,156) );
G=PermutationGroup([[(1,35),(2,36),(3,37),(4,38),(5,39),(6,40),(7,41),(8,42),(9,43),(10,44),(11,45),(12,46),(13,47),(14,48),(15,49),(16,50),(17,51),(18,52),(19,53),(20,54),(21,55),(22,56),(23,29),(24,30),(25,31),(26,32),(27,33),(28,34),(57,109),(58,110),(59,111),(60,112),(61,85),(62,86),(63,87),(64,88),(65,89),(66,90),(67,91),(68,92),(69,93),(70,94),(71,95),(72,96),(73,97),(74,98),(75,99),(76,100),(77,101),(78,102),(79,103),(80,104),(81,105),(82,106),(83,107),(84,108),(113,142),(114,143),(115,144),(116,145),(117,146),(118,147),(119,148),(120,149),(121,150),(122,151),(123,152),(124,153),(125,154),(126,155),(127,156),(128,157),(129,158),(130,159),(131,160),(132,161),(133,162),(134,163),(135,164),(136,165),(137,166),(138,167),(139,168),(140,141),(169,209),(170,210),(171,211),(172,212),(173,213),(174,214),(175,215),(176,216),(177,217),(178,218),(179,219),(180,220),(181,221),(182,222),(183,223),(184,224),(185,197),(186,198),(187,199),(188,200),(189,201),(190,202),(191,203),(192,204),(193,205),(194,206),(195,207),(196,208)], [(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)], [(1,200,119,109),(2,187,120,84),(3,198,121,107),(4,185,122,82),(5,224,123,105),(6,183,124,80),(7,222,125,103),(8,181,126,78),(9,220,127,101),(10,179,128,76),(11,218,129,99),(12,177,130,74),(13,216,131,97),(14,175,132,72),(15,214,133,95),(16,173,134,70),(17,212,135,93),(18,171,136,68),(19,210,137,91),(20,169,138,66),(21,208,139,89),(22,195,140,64),(23,206,113,87),(24,193,114,62),(25,204,115,85),(26,191,116,60),(27,202,117,111),(28,189,118,58),(29,194,142,63),(30,205,143,86),(31,192,144,61),(32,203,145,112),(33,190,146,59),(34,201,147,110),(35,188,148,57),(36,199,149,108),(37,186,150,83),(38,197,151,106),(39,184,152,81),(40,223,153,104),(41,182,154,79),(42,221,155,102),(43,180,156,77),(44,219,157,100),(45,178,158,75),(46,217,159,98),(47,176,160,73),(48,215,161,96),(49,174,162,71),(50,213,163,94),(51,172,164,69),(52,211,165,92),(53,170,166,67),(54,209,167,90),(55,196,168,65),(56,207,141,88)], [(1,15),(2,34),(3,13),(4,32),(5,11),(6,30),(7,9),(8,56),(10,54),(12,52),(14,50),(16,48),(17,27),(18,46),(19,25),(20,44),(21,23),(22,42),(24,40),(26,38),(28,36),(29,55),(31,53),(33,51),(35,49),(37,47),(39,45),(41,43),(57,200),(58,173),(59,198),(60,171),(61,224),(62,169),(63,222),(64,195),(65,220),(66,193),(67,218),(68,191),(69,216),(70,189),(71,214),(72,187),(73,212),(74,185),(75,210),(76,183),(77,208),(78,181),(79,206),(80,179),(81,204),(82,177),(83,202),(84,175),(85,184),(86,209),(87,182),(88,207),(89,180),(90,205),(91,178),(92,203),(93,176),(94,201),(95,174),(96,199),(97,172),(98,197),(99,170),(100,223),(101,196),(102,221),(103,194),(104,219),(105,192),(106,217),(107,190),(108,215),(109,188),(110,213),(111,186),(112,211),(113,139),(114,153),(115,137),(116,151),(117,135),(118,149),(119,133),(120,147),(121,131),(122,145),(123,129),(124,143),(125,127),(126,141),(128,167),(130,165),(132,163),(134,161),(136,159),(138,157),(140,155),(142,168),(144,166),(146,164),(148,162),(150,160),(152,158),(154,156)]])
82 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 4A | ··· | 4F | 4G | ··· | 4L | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 28 | 28 | 4 | ··· | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | + | + | + | - | + | |||
| image | C1 | C2 | C2 | C2 | C2 | D4 | D4 | Q8 | D7 | C4○D4 | D14 | C7⋊D4 | C4○D28 | D4×D7 | Q8×D7 | Q8⋊2D7 |
| kernel | (C2×C28).289D4 | C14.C42 | C2×Dic7⋊C4 | C2×D14⋊C4 | C14×C4⋊C4 | C2×Dic7 | C2×C28 | C22×D7 | C2×C4⋊C4 | C2×C14 | C22×C4 | C2×C4 | C22 | C22 | C22 | C22 |
| # reps | 1 | 1 | 2 | 3 | 1 | 4 | 2 | 2 | 3 | 6 | 9 | 12 | 24 | 6 | 3 | 3 |
Matrix representation of (C2×C28).289D4 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 2 | 0 | 0 |
| 0 | 0 | 1 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 10 | 18 |
| 0 | 0 | 0 | 0 | 17 | 22 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 28 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 18 |
| 0 | 0 | 0 | 0 | 27 | 21 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 12 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 10 | 1 |
| 0 | 0 | 0 | 0 | 17 | 19 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,1,0,0,0,0,28,0,0,0,0,0,0,0,17,1,0,0,0,0,2,12,0,0,0,0,0,0,10,17,0,0,0,0,18,22],[0,28,0,0,0,0,1,0,0,0,0,0,0,0,12,28,0,0,0,0,0,17,0,0,0,0,0,0,8,27,0,0,0,0,18,21],[28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,12,0,0,0,0,0,28,0,0,0,0,0,0,10,17,0,0,0,0,1,19] >;
(C2×C28).289D4 in GAP, Magma, Sage, TeX
(C_2\times C_{28})._{289}D_4 % in TeX
G:=Group("(C2xC28).289D4"); // GroupNames label
G:=SmallGroup(448,526);
// by ID
G=gap.SmallGroup(448,526);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,232,254,387,268,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^28=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=a*b^-1,d*b*d=a*b^13,d*c*d=a*b^14*c^-1>;
// generators/relations