Copied to
clipboard

G = D2824D4order 448 = 26·7

2nd semidirect product of D28 and D4 acting through Inn(D28)

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D2824D4, C42.109D14, C14.592- 1+4, (C4×D4)⋊13D7, (C4×D28)⋊29C2, (D4×C28)⋊15C2, C282(C4○D4), C43(C4○D28), C282D48C2, C72(D46D4), C4.140(D4×D7), C4⋊C4.316D14, C282Q824C2, D14.15(C2×D4), C28.346(C2×D4), (C2×D4).214D14, D14.D46C2, (C2×C14).95C24, C14.50(C22×D4), C28.48D420C2, (C2×C28).783C23, (C4×C28).152C22, D14⋊C4.98C22, C22⋊C4.110D14, (C22×C4).208D14, C23.95(C22×D7), (D4×C14).257C22, (C2×D28).287C22, Dic7⋊C4.65C22, C4⋊Dic7.199C22, (C2×Dic7).41C23, C22.120(C23×D7), C23.D7.12C22, (C22×C14).165C23, (C22×C28).107C22, (C22×D7).173C23, C2.16(D4.10D14), (C2×Dic14).239C22, C2.23(C2×D4×D7), (D7×C4⋊C4)⋊15C2, (C2×C4○D28)⋊8C2, C2.46(C2×C4○D28), C14.42(C2×C4○D4), (C2×C4×D7).64C22, (C7×C4⋊C4).326C22, (C2×C4).579(C22×D7), (C2×C7⋊D4).113C22, (C7×C22⋊C4).122C22, SmallGroup(448,1004)

Series: Derived Chief Lower central Upper central

C1C2×C14 — D2824D4
C1C7C14C2×C14C22×D7C2×C4×D7D7×C4⋊C4 — D2824D4
C7C2×C14 — D2824D4
C1C22C4×D4

Generators and relations for D2824D4
 G = < a,b,c,d | a28=b2=c4=d2=1, bab=a-1, ac=ca, ad=da, bc=cb, dbd=a14b, dcd=c-1 >

Subgroups: 1332 in 292 conjugacy classes, 107 normal (29 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C4○D4, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C4⋊C4, C4×D4, C4×D4, C4⋊D4, C22⋊Q8, C22.D4, C4⋊Q8, C2×C4○D4, Dic14, C4×D7, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, D46D4, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C4○D28, C2×C7⋊D4, C22×C28, D4×C14, C282Q8, C4×D28, D14.D4, D7×C4⋊C4, C28.48D4, C282D4, D4×C28, C2×C4○D28, D2824D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C22×D4, C2×C4○D4, 2- 1+4, C22×D7, D46D4, C4○D28, D4×D7, C23×D7, C2×C4○D28, C2×D4×D7, D4.10D14, D2824D4

Smallest permutation representation of D2824D4
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 46)(2 45)(3 44)(4 43)(5 42)(6 41)(7 40)(8 39)(9 38)(10 37)(11 36)(12 35)(13 34)(14 33)(15 32)(16 31)(17 30)(18 29)(19 56)(20 55)(21 54)(22 53)(23 52)(24 51)(25 50)(26 49)(27 48)(28 47)(57 116)(58 115)(59 114)(60 113)(61 140)(62 139)(63 138)(64 137)(65 136)(66 135)(67 134)(68 133)(69 132)(70 131)(71 130)(72 129)(73 128)(74 127)(75 126)(76 125)(77 124)(78 123)(79 122)(80 121)(81 120)(82 119)(83 118)(84 117)(85 145)(86 144)(87 143)(88 142)(89 141)(90 168)(91 167)(92 166)(93 165)(94 164)(95 163)(96 162)(97 161)(98 160)(99 159)(100 158)(101 157)(102 156)(103 155)(104 154)(105 153)(106 152)(107 151)(108 150)(109 149)(110 148)(111 147)(112 146)(169 205)(170 204)(171 203)(172 202)(173 201)(174 200)(175 199)(176 198)(177 197)(178 224)(179 223)(180 222)(181 221)(182 220)(183 219)(184 218)(185 217)(186 216)(187 215)(188 214)(189 213)(190 212)(191 211)(192 210)(193 209)(194 208)(195 207)(196 206)
(1 162 40 90)(2 163 41 91)(3 164 42 92)(4 165 43 93)(5 166 44 94)(6 167 45 95)(7 168 46 96)(8 141 47 97)(9 142 48 98)(10 143 49 99)(11 144 50 100)(12 145 51 101)(13 146 52 102)(14 147 53 103)(15 148 54 104)(16 149 55 105)(17 150 56 106)(18 151 29 107)(19 152 30 108)(20 153 31 109)(21 154 32 110)(22 155 33 111)(23 156 34 112)(24 157 35 85)(25 158 36 86)(26 159 37 87)(27 160 38 88)(28 161 39 89)(57 207 134 185)(58 208 135 186)(59 209 136 187)(60 210 137 188)(61 211 138 189)(62 212 139 190)(63 213 140 191)(64 214 113 192)(65 215 114 193)(66 216 115 194)(67 217 116 195)(68 218 117 196)(69 219 118 169)(70 220 119 170)(71 221 120 171)(72 222 121 172)(73 223 122 173)(74 224 123 174)(75 197 124 175)(76 198 125 176)(77 199 126 177)(78 200 127 178)(79 201 128 179)(80 202 129 180)(81 203 130 181)(82 204 131 182)(83 205 132 183)(84 206 133 184)
(1 216)(2 217)(3 218)(4 219)(5 220)(6 221)(7 222)(8 223)(9 224)(10 197)(11 198)(12 199)(13 200)(14 201)(15 202)(16 203)(17 204)(18 205)(19 206)(20 207)(21 208)(22 209)(23 210)(24 211)(25 212)(26 213)(27 214)(28 215)(29 183)(30 184)(31 185)(32 186)(33 187)(34 188)(35 189)(36 190)(37 191)(38 192)(39 193)(40 194)(41 195)(42 196)(43 169)(44 170)(45 171)(46 172)(47 173)(48 174)(49 175)(50 176)(51 177)(52 178)(53 179)(54 180)(55 181)(56 182)(57 153)(58 154)(59 155)(60 156)(61 157)(62 158)(63 159)(64 160)(65 161)(66 162)(67 163)(68 164)(69 165)(70 166)(71 167)(72 168)(73 141)(74 142)(75 143)(76 144)(77 145)(78 146)(79 147)(80 148)(81 149)(82 150)(83 151)(84 152)(85 138)(86 139)(87 140)(88 113)(89 114)(90 115)(91 116)(92 117)(93 118)(94 119)(95 120)(96 121)(97 122)(98 123)(99 124)(100 125)(101 126)(102 127)(103 128)(104 129)(105 130)(106 131)(107 132)(108 133)(109 134)(110 135)(111 136)(112 137)

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), (1,46)(2,45)(3,44)(4,43)(5,42)(6,41)(7,40)(8,39)(9,38)(10,37)(11,36)(12,35)(13,34)(14,33)(15,32)(16,31)(17,30)(18,29)(19,56)(20,55)(21,54)(22,53)(23,52)(24,51)(25,50)(26,49)(27,48)(28,47)(57,116)(58,115)(59,114)(60,113)(61,140)(62,139)(63,138)(64,137)(65,136)(66,135)(67,134)(68,133)(69,132)(70,131)(71,130)(72,129)(73,128)(74,127)(75,126)(76,125)(77,124)(78,123)(79,122)(80,121)(81,120)(82,119)(83,118)(84,117)(85,145)(86,144)(87,143)(88,142)(89,141)(90,168)(91,167)(92,166)(93,165)(94,164)(95,163)(96,162)(97,161)(98,160)(99,159)(100,158)(101,157)(102,156)(103,155)(104,154)(105,153)(106,152)(107,151)(108,150)(109,149)(110,148)(111,147)(112,146)(169,205)(170,204)(171,203)(172,202)(173,201)(174,200)(175,199)(176,198)(177,197)(178,224)(179,223)(180,222)(181,221)(182,220)(183,219)(184,218)(185,217)(186,216)(187,215)(188,214)(189,213)(190,212)(191,211)(192,210)(193,209)(194,208)(195,207)(196,206), (1,162,40,90)(2,163,41,91)(3,164,42,92)(4,165,43,93)(5,166,44,94)(6,167,45,95)(7,168,46,96)(8,141,47,97)(9,142,48,98)(10,143,49,99)(11,144,50,100)(12,145,51,101)(13,146,52,102)(14,147,53,103)(15,148,54,104)(16,149,55,105)(17,150,56,106)(18,151,29,107)(19,152,30,108)(20,153,31,109)(21,154,32,110)(22,155,33,111)(23,156,34,112)(24,157,35,85)(25,158,36,86)(26,159,37,87)(27,160,38,88)(28,161,39,89)(57,207,134,185)(58,208,135,186)(59,209,136,187)(60,210,137,188)(61,211,138,189)(62,212,139,190)(63,213,140,191)(64,214,113,192)(65,215,114,193)(66,216,115,194)(67,217,116,195)(68,218,117,196)(69,219,118,169)(70,220,119,170)(71,221,120,171)(72,222,121,172)(73,223,122,173)(74,224,123,174)(75,197,124,175)(76,198,125,176)(77,199,126,177)(78,200,127,178)(79,201,128,179)(80,202,129,180)(81,203,130,181)(82,204,131,182)(83,205,132,183)(84,206,133,184), (1,216)(2,217)(3,218)(4,219)(5,220)(6,221)(7,222)(8,223)(9,224)(10,197)(11,198)(12,199)(13,200)(14,201)(15,202)(16,203)(17,204)(18,205)(19,206)(20,207)(21,208)(22,209)(23,210)(24,211)(25,212)(26,213)(27,214)(28,215)(29,183)(30,184)(31,185)(32,186)(33,187)(34,188)(35,189)(36,190)(37,191)(38,192)(39,193)(40,194)(41,195)(42,196)(43,169)(44,170)(45,171)(46,172)(47,173)(48,174)(49,175)(50,176)(51,177)(52,178)(53,179)(54,180)(55,181)(56,182)(57,153)(58,154)(59,155)(60,156)(61,157)(62,158)(63,159)(64,160)(65,161)(66,162)(67,163)(68,164)(69,165)(70,166)(71,167)(72,168)(73,141)(74,142)(75,143)(76,144)(77,145)(78,146)(79,147)(80,148)(81,149)(82,150)(83,151)(84,152)(85,138)(86,139)(87,140)(88,113)(89,114)(90,115)(91,116)(92,117)(93,118)(94,119)(95,120)(96,121)(97,122)(98,123)(99,124)(100,125)(101,126)(102,127)(103,128)(104,129)(105,130)(106,131)(107,132)(108,133)(109,134)(110,135)(111,136)(112,137)>;

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), (1,46)(2,45)(3,44)(4,43)(5,42)(6,41)(7,40)(8,39)(9,38)(10,37)(11,36)(12,35)(13,34)(14,33)(15,32)(16,31)(17,30)(18,29)(19,56)(20,55)(21,54)(22,53)(23,52)(24,51)(25,50)(26,49)(27,48)(28,47)(57,116)(58,115)(59,114)(60,113)(61,140)(62,139)(63,138)(64,137)(65,136)(66,135)(67,134)(68,133)(69,132)(70,131)(71,130)(72,129)(73,128)(74,127)(75,126)(76,125)(77,124)(78,123)(79,122)(80,121)(81,120)(82,119)(83,118)(84,117)(85,145)(86,144)(87,143)(88,142)(89,141)(90,168)(91,167)(92,166)(93,165)(94,164)(95,163)(96,162)(97,161)(98,160)(99,159)(100,158)(101,157)(102,156)(103,155)(104,154)(105,153)(106,152)(107,151)(108,150)(109,149)(110,148)(111,147)(112,146)(169,205)(170,204)(171,203)(172,202)(173,201)(174,200)(175,199)(176,198)(177,197)(178,224)(179,223)(180,222)(181,221)(182,220)(183,219)(184,218)(185,217)(186,216)(187,215)(188,214)(189,213)(190,212)(191,211)(192,210)(193,209)(194,208)(195,207)(196,206), (1,162,40,90)(2,163,41,91)(3,164,42,92)(4,165,43,93)(5,166,44,94)(6,167,45,95)(7,168,46,96)(8,141,47,97)(9,142,48,98)(10,143,49,99)(11,144,50,100)(12,145,51,101)(13,146,52,102)(14,147,53,103)(15,148,54,104)(16,149,55,105)(17,150,56,106)(18,151,29,107)(19,152,30,108)(20,153,31,109)(21,154,32,110)(22,155,33,111)(23,156,34,112)(24,157,35,85)(25,158,36,86)(26,159,37,87)(27,160,38,88)(28,161,39,89)(57,207,134,185)(58,208,135,186)(59,209,136,187)(60,210,137,188)(61,211,138,189)(62,212,139,190)(63,213,140,191)(64,214,113,192)(65,215,114,193)(66,216,115,194)(67,217,116,195)(68,218,117,196)(69,219,118,169)(70,220,119,170)(71,221,120,171)(72,222,121,172)(73,223,122,173)(74,224,123,174)(75,197,124,175)(76,198,125,176)(77,199,126,177)(78,200,127,178)(79,201,128,179)(80,202,129,180)(81,203,130,181)(82,204,131,182)(83,205,132,183)(84,206,133,184), (1,216)(2,217)(3,218)(4,219)(5,220)(6,221)(7,222)(8,223)(9,224)(10,197)(11,198)(12,199)(13,200)(14,201)(15,202)(16,203)(17,204)(18,205)(19,206)(20,207)(21,208)(22,209)(23,210)(24,211)(25,212)(26,213)(27,214)(28,215)(29,183)(30,184)(31,185)(32,186)(33,187)(34,188)(35,189)(36,190)(37,191)(38,192)(39,193)(40,194)(41,195)(42,196)(43,169)(44,170)(45,171)(46,172)(47,173)(48,174)(49,175)(50,176)(51,177)(52,178)(53,179)(54,180)(55,181)(56,182)(57,153)(58,154)(59,155)(60,156)(61,157)(62,158)(63,159)(64,160)(65,161)(66,162)(67,163)(68,164)(69,165)(70,166)(71,167)(72,168)(73,141)(74,142)(75,143)(76,144)(77,145)(78,146)(79,147)(80,148)(81,149)(82,150)(83,151)(84,152)(85,138)(86,139)(87,140)(88,113)(89,114)(90,115)(91,116)(92,117)(93,118)(94,119)(95,120)(96,121)(97,122)(98,123)(99,124)(100,125)(101,126)(102,127)(103,128)(104,129)(105,130)(106,131)(107,132)(108,133)(109,134)(110,135)(111,136)(112,137) );

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)], [(1,46),(2,45),(3,44),(4,43),(5,42),(6,41),(7,40),(8,39),(9,38),(10,37),(11,36),(12,35),(13,34),(14,33),(15,32),(16,31),(17,30),(18,29),(19,56),(20,55),(21,54),(22,53),(23,52),(24,51),(25,50),(26,49),(27,48),(28,47),(57,116),(58,115),(59,114),(60,113),(61,140),(62,139),(63,138),(64,137),(65,136),(66,135),(67,134),(68,133),(69,132),(70,131),(71,130),(72,129),(73,128),(74,127),(75,126),(76,125),(77,124),(78,123),(79,122),(80,121),(81,120),(82,119),(83,118),(84,117),(85,145),(86,144),(87,143),(88,142),(89,141),(90,168),(91,167),(92,166),(93,165),(94,164),(95,163),(96,162),(97,161),(98,160),(99,159),(100,158),(101,157),(102,156),(103,155),(104,154),(105,153),(106,152),(107,151),(108,150),(109,149),(110,148),(111,147),(112,146),(169,205),(170,204),(171,203),(172,202),(173,201),(174,200),(175,199),(176,198),(177,197),(178,224),(179,223),(180,222),(181,221),(182,220),(183,219),(184,218),(185,217),(186,216),(187,215),(188,214),(189,213),(190,212),(191,211),(192,210),(193,209),(194,208),(195,207),(196,206)], [(1,162,40,90),(2,163,41,91),(3,164,42,92),(4,165,43,93),(5,166,44,94),(6,167,45,95),(7,168,46,96),(8,141,47,97),(9,142,48,98),(10,143,49,99),(11,144,50,100),(12,145,51,101),(13,146,52,102),(14,147,53,103),(15,148,54,104),(16,149,55,105),(17,150,56,106),(18,151,29,107),(19,152,30,108),(20,153,31,109),(21,154,32,110),(22,155,33,111),(23,156,34,112),(24,157,35,85),(25,158,36,86),(26,159,37,87),(27,160,38,88),(28,161,39,89),(57,207,134,185),(58,208,135,186),(59,209,136,187),(60,210,137,188),(61,211,138,189),(62,212,139,190),(63,213,140,191),(64,214,113,192),(65,215,114,193),(66,216,115,194),(67,217,116,195),(68,218,117,196),(69,219,118,169),(70,220,119,170),(71,221,120,171),(72,222,121,172),(73,223,122,173),(74,224,123,174),(75,197,124,175),(76,198,125,176),(77,199,126,177),(78,200,127,178),(79,201,128,179),(80,202,129,180),(81,203,130,181),(82,204,131,182),(83,205,132,183),(84,206,133,184)], [(1,216),(2,217),(3,218),(4,219),(5,220),(6,221),(7,222),(8,223),(9,224),(10,197),(11,198),(12,199),(13,200),(14,201),(15,202),(16,203),(17,204),(18,205),(19,206),(20,207),(21,208),(22,209),(23,210),(24,211),(25,212),(26,213),(27,214),(28,215),(29,183),(30,184),(31,185),(32,186),(33,187),(34,188),(35,189),(36,190),(37,191),(38,192),(39,193),(40,194),(41,195),(42,196),(43,169),(44,170),(45,171),(46,172),(47,173),(48,174),(49,175),(50,176),(51,177),(52,178),(53,179),(54,180),(55,181),(56,182),(57,153),(58,154),(59,155),(60,156),(61,157),(62,158),(63,159),(64,160),(65,161),(66,162),(67,163),(68,164),(69,165),(70,166),(71,167),(72,168),(73,141),(74,142),(75,143),(76,144),(77,145),(78,146),(79,147),(80,148),(81,149),(82,150),(83,151),(84,152),(85,138),(86,139),(87,140),(88,113),(89,114),(90,115),(91,116),(92,117),(93,118),(94,119),(95,120),(96,121),(97,122),(98,123),(99,124),(100,125),(101,126),(102,127),(103,128),(104,129),(105,130),(106,131),(107,132),(108,133),(109,134),(110,135),(111,136),(112,137)]])

85 conjugacy classes

class 1 2A2B2C2D2E2F2G2H2I4A···4H4I4J···4O7A7B7C14A···14I14J···14U28A···28L28M···28AJ
order12222222224···444···477714···1414···1428···2828···28
size111144141414142···2428···282222···24···42···24···4

85 irreducible representations

dim111111111222222222444
type++++++++++++++++-+-
imageC1C2C2C2C2C2C2C2C2D4D7C4○D4D14D14D14D14D14C4○D282- 1+4D4×D7D4.10D14
kernelD2824D4C282Q8C4×D28D14.D4D7×C4⋊C4C28.48D4C282D4D4×C28C2×C4○D28D28C4×D4C28C42C22⋊C4C4⋊C4C22×C4C2×D4C4C14C4C2
# reps1114222124343636324166

Matrix representation of D2824D4 in GL6(𝔽29)

1420000
3150000
0011800
00112500
0000280
0000028
,
2800000
1410000
0028000
0018100
0000280
0000028
,
100000
010000
0028000
0002800
0000117
0000528
,
23240000
760000
001000
000100
00002327
000036

G:=sub<GL(6,GF(29))| [14,3,0,0,0,0,2,15,0,0,0,0,0,0,1,11,0,0,0,0,18,25,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,14,0,0,0,0,0,1,0,0,0,0,0,0,28,18,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,5,0,0,0,0,17,28],[23,7,0,0,0,0,24,6,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,23,3,0,0,0,0,27,6] >;

D2824D4 in GAP, Magma, Sage, TeX

D_{28}\rtimes_{24}D_4
% in TeX

G:=Group("D28:24D4");
// GroupNames label

G:=SmallGroup(448,1004);
// by ID

G=gap.SmallGroup(448,1004);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,387,100,675,570,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^28=b^2=c^4=d^2=1,b*a*b=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d=a^14*b,d*c*d=c^-1>;
// generators/relations

׿
×
𝔽