metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28⋊12D4, C42.172D14, C14.352- (1+4), C4⋊Q8⋊10D7, C4.73(D4×D7), (C4×D28)⋊51C2, C28⋊7(C4○D4), C7⋊7(D4⋊6D4), C28.71(C2×D4), C28⋊1D4⋊40C2, C4⋊C4.123D14, C4⋊2(Q8⋊2D7), D14.25(C2×D4), D14⋊3Q8⋊35C2, (C2×Q8).145D14, D14.5D4⋊46C2, (C4×C28).211C22, (C2×C28).103C23, (C2×C14).270C24, C14.100(C22×D4), D14⋊C4.151C22, (C2×D28).271C22, Dic7⋊C4.60C22, C4⋊Dic7.384C22, (Q8×C14).137C22, C22.291(C23×D7), (C2×Dic7).141C23, (C22×D7).231C23, C2.36(Q8.10D14), C2.73(C2×D4×D7), (D7×C4⋊C4)⋊44C2, (C7×C4⋊Q8)⋊12C2, (C2×Q8⋊2D7)⋊13C2, C14.121(C2×C4○D4), C2.28(C2×Q8⋊2D7), (C2×C4×D7).144C22, (C2×C4).93(C22×D7), (C7×C4⋊C4).213C22, SmallGroup(448,1179)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1452 in 292 conjugacy classes, 107 normal (27 characteristic)
C1, C2 [×3], C2 [×6], C4 [×4], C4 [×9], C22, C22 [×14], C7, C2×C4 [×3], C2×C4 [×4], C2×C4 [×20], D4 [×14], Q8 [×4], C23 [×4], D7 [×6], C14 [×3], C42, C22⋊C4 [×8], C4⋊C4 [×4], C4⋊C4 [×6], C22×C4 [×8], C2×D4 [×6], C2×Q8 [×2], C4○D4 [×8], Dic7 [×4], C28 [×4], C28 [×5], D14 [×4], D14 [×10], C2×C14, C2×C4⋊C4 [×2], C4×D4 [×2], C4⋊D4 [×2], C22⋊Q8 [×2], C22.D4 [×4], C4⋊Q8, C2×C4○D4 [×2], C4×D7 [×16], D28 [×4], D28 [×10], C2×Dic7 [×4], C2×C28 [×3], C2×C28 [×4], C7×Q8 [×4], C22×D7 [×4], D4⋊6D4, Dic7⋊C4 [×4], C4⋊Dic7 [×2], D14⋊C4 [×8], C4×C28, C7×C4⋊C4 [×4], C2×C4×D7 [×8], C2×D28 [×2], C2×D28 [×4], Q8⋊2D7 [×8], Q8×C14 [×2], C4×D28 [×2], D7×C4⋊C4 [×2], D14.5D4 [×4], C28⋊1D4 [×2], D14⋊3Q8 [×2], C7×C4⋊Q8, C2×Q8⋊2D7 [×2], D28⋊12D4
Quotients:
C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D7, C2×D4 [×6], C4○D4 [×2], C24, D14 [×7], C22×D4, C2×C4○D4, 2- (1+4), C22×D7 [×7], D4⋊6D4, D4×D7 [×2], Q8⋊2D7 [×2], C23×D7, C2×D4×D7, C2×Q8⋊2D7, Q8.10D14, D28⋊12D4
Generators and relations
G = < a,b,c,d | a28=b2=c4=d2=1, bab=a-1, ac=ca, dad=a13, bc=cb, dbd=a26b, dcd=c-1 >
►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 7)(2 6)(3 5)(8 28)(9 27)(10 26)(11 25)(12 24)(13 23)(14 22)(15 21)(16 20)(17 19)(29 33)(30 32)(34 56)(35 55)(36 54)(37 53)(38 52)(39 51)(40 50)(41 49)(42 48)(43 47)(44 46)(57 69)(58 68)(59 67)(60 66)(61 65)(62 64)(70 84)(71 83)(72 82)(73 81)(74 80)(75 79)(76 78)(85 99)(86 98)(87 97)(88 96)(89 95)(90 94)(91 93)(100 112)(101 111)(102 110)(103 109)(104 108)(105 107)(113 125)(114 124)(115 123)(116 122)(117 121)(118 120)(126 140)(127 139)(128 138)(129 137)(130 136)(131 135)(132 134)(141 163)(142 162)(143 161)(144 160)(145 159)(146 158)(147 157)(148 156)(149 155)(150 154)(151 153)(164 168)(165 167)(169 195)(170 194)(171 193)(172 192)(173 191)(174 190)(175 189)(176 188)(177 187)(178 186)(179 185)(180 184)(181 183)(197 219)(198 218)(199 217)(200 216)(201 215)(202 214)(203 213)(204 212)(205 211)(206 210)(207 209)(220 224)(221 223)
(1 116 149 74)(2 117 150 75)(3 118 151 76)(4 119 152 77)(5 120 153 78)(6 121 154 79)(7 122 155 80)(8 123 156 81)(9 124 157 82)(10 125 158 83)(11 126 159 84)(12 127 160 57)(13 128 161 58)(14 129 162 59)(15 130 163 60)(16 131 164 61)(17 132 165 62)(18 133 166 63)(19 134 167 64)(20 135 168 65)(21 136 141 66)(22 137 142 67)(23 138 143 68)(24 139 144 69)(25 140 145 70)(26 113 146 71)(27 114 147 72)(28 115 148 73)(29 206 90 180)(30 207 91 181)(31 208 92 182)(32 209 93 183)(33 210 94 184)(34 211 95 185)(35 212 96 186)(36 213 97 187)(37 214 98 188)(38 215 99 189)(39 216 100 190)(40 217 101 191)(41 218 102 192)(42 219 103 193)(43 220 104 194)(44 221 105 195)(45 222 106 196)(46 223 107 169)(47 224 108 170)(48 197 109 171)(49 198 110 172)(50 199 111 173)(51 200 112 174)(52 201 85 175)(53 202 86 176)(54 203 87 177)(55 204 88 178)(56 205 89 179)
(1 49)(2 34)(3 47)(4 32)(5 45)(6 30)(7 43)(8 56)(9 41)(10 54)(11 39)(12 52)(13 37)(14 50)(15 35)(16 48)(17 33)(18 46)(19 31)(20 44)(21 29)(22 42)(23 55)(24 40)(25 53)(26 38)(27 51)(28 36)(57 201)(58 214)(59 199)(60 212)(61 197)(62 210)(63 223)(64 208)(65 221)(66 206)(67 219)(68 204)(69 217)(70 202)(71 215)(72 200)(73 213)(74 198)(75 211)(76 224)(77 209)(78 222)(79 207)(80 220)(81 205)(82 218)(83 203)(84 216)(85 160)(86 145)(87 158)(88 143)(89 156)(90 141)(91 154)(92 167)(93 152)(94 165)(95 150)(96 163)(97 148)(98 161)(99 146)(100 159)(101 144)(102 157)(103 142)(104 155)(105 168)(106 153)(107 166)(108 151)(109 164)(110 149)(111 162)(112 147)(113 189)(114 174)(115 187)(116 172)(117 185)(118 170)(119 183)(120 196)(121 181)(122 194)(123 179)(124 192)(125 177)(126 190)(127 175)(128 188)(129 173)(130 186)(131 171)(132 184)(133 169)(134 182)(135 195)(136 180)(137 193)(138 178)(139 191)(140 176)
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), (1,7)(2,6)(3,5)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)(29,33)(30,32)(34,56)(35,55)(36,54)(37,53)(38,52)(39,51)(40,50)(41,49)(42,48)(43,47)(44,46)(57,69)(58,68)(59,67)(60,66)(61,65)(62,64)(70,84)(71,83)(72,82)(73,81)(74,80)(75,79)(76,78)(85,99)(86,98)(87,97)(88,96)(89,95)(90,94)(91,93)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(113,125)(114,124)(115,123)(116,122)(117,121)(118,120)(126,140)(127,139)(128,138)(129,137)(130,136)(131,135)(132,134)(141,163)(142,162)(143,161)(144,160)(145,159)(146,158)(147,157)(148,156)(149,155)(150,154)(151,153)(164,168)(165,167)(169,195)(170,194)(171,193)(172,192)(173,191)(174,190)(175,189)(176,188)(177,187)(178,186)(179,185)(180,184)(181,183)(197,219)(198,218)(199,217)(200,216)(201,215)(202,214)(203,213)(204,212)(205,211)(206,210)(207,209)(220,224)(221,223), (1,116,149,74)(2,117,150,75)(3,118,151,76)(4,119,152,77)(5,120,153,78)(6,121,154,79)(7,122,155,80)(8,123,156,81)(9,124,157,82)(10,125,158,83)(11,126,159,84)(12,127,160,57)(13,128,161,58)(14,129,162,59)(15,130,163,60)(16,131,164,61)(17,132,165,62)(18,133,166,63)(19,134,167,64)(20,135,168,65)(21,136,141,66)(22,137,142,67)(23,138,143,68)(24,139,144,69)(25,140,145,70)(26,113,146,71)(27,114,147,72)(28,115,148,73)(29,206,90,180)(30,207,91,181)(31,208,92,182)(32,209,93,183)(33,210,94,184)(34,211,95,185)(35,212,96,186)(36,213,97,187)(37,214,98,188)(38,215,99,189)(39,216,100,190)(40,217,101,191)(41,218,102,192)(42,219,103,193)(43,220,104,194)(44,221,105,195)(45,222,106,196)(46,223,107,169)(47,224,108,170)(48,197,109,171)(49,198,110,172)(50,199,111,173)(51,200,112,174)(52,201,85,175)(53,202,86,176)(54,203,87,177)(55,204,88,178)(56,205,89,179), (1,49)(2,34)(3,47)(4,32)(5,45)(6,30)(7,43)(8,56)(9,41)(10,54)(11,39)(12,52)(13,37)(14,50)(15,35)(16,48)(17,33)(18,46)(19,31)(20,44)(21,29)(22,42)(23,55)(24,40)(25,53)(26,38)(27,51)(28,36)(57,201)(58,214)(59,199)(60,212)(61,197)(62,210)(63,223)(64,208)(65,221)(66,206)(67,219)(68,204)(69,217)(70,202)(71,215)(72,200)(73,213)(74,198)(75,211)(76,224)(77,209)(78,222)(79,207)(80,220)(81,205)(82,218)(83,203)(84,216)(85,160)(86,145)(87,158)(88,143)(89,156)(90,141)(91,154)(92,167)(93,152)(94,165)(95,150)(96,163)(97,148)(98,161)(99,146)(100,159)(101,144)(102,157)(103,142)(104,155)(105,168)(106,153)(107,166)(108,151)(109,164)(110,149)(111,162)(112,147)(113,189)(114,174)(115,187)(116,172)(117,185)(118,170)(119,183)(120,196)(121,181)(122,194)(123,179)(124,192)(125,177)(126,190)(127,175)(128,188)(129,173)(130,186)(131,171)(132,184)(133,169)(134,182)(135,195)(136,180)(137,193)(138,178)(139,191)(140,176)>;
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), (1,7)(2,6)(3,5)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)(29,33)(30,32)(34,56)(35,55)(36,54)(37,53)(38,52)(39,51)(40,50)(41,49)(42,48)(43,47)(44,46)(57,69)(58,68)(59,67)(60,66)(61,65)(62,64)(70,84)(71,83)(72,82)(73,81)(74,80)(75,79)(76,78)(85,99)(86,98)(87,97)(88,96)(89,95)(90,94)(91,93)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(113,125)(114,124)(115,123)(116,122)(117,121)(118,120)(126,140)(127,139)(128,138)(129,137)(130,136)(131,135)(132,134)(141,163)(142,162)(143,161)(144,160)(145,159)(146,158)(147,157)(148,156)(149,155)(150,154)(151,153)(164,168)(165,167)(169,195)(170,194)(171,193)(172,192)(173,191)(174,190)(175,189)(176,188)(177,187)(178,186)(179,185)(180,184)(181,183)(197,219)(198,218)(199,217)(200,216)(201,215)(202,214)(203,213)(204,212)(205,211)(206,210)(207,209)(220,224)(221,223), (1,116,149,74)(2,117,150,75)(3,118,151,76)(4,119,152,77)(5,120,153,78)(6,121,154,79)(7,122,155,80)(8,123,156,81)(9,124,157,82)(10,125,158,83)(11,126,159,84)(12,127,160,57)(13,128,161,58)(14,129,162,59)(15,130,163,60)(16,131,164,61)(17,132,165,62)(18,133,166,63)(19,134,167,64)(20,135,168,65)(21,136,141,66)(22,137,142,67)(23,138,143,68)(24,139,144,69)(25,140,145,70)(26,113,146,71)(27,114,147,72)(28,115,148,73)(29,206,90,180)(30,207,91,181)(31,208,92,182)(32,209,93,183)(33,210,94,184)(34,211,95,185)(35,212,96,186)(36,213,97,187)(37,214,98,188)(38,215,99,189)(39,216,100,190)(40,217,101,191)(41,218,102,192)(42,219,103,193)(43,220,104,194)(44,221,105,195)(45,222,106,196)(46,223,107,169)(47,224,108,170)(48,197,109,171)(49,198,110,172)(50,199,111,173)(51,200,112,174)(52,201,85,175)(53,202,86,176)(54,203,87,177)(55,204,88,178)(56,205,89,179), (1,49)(2,34)(3,47)(4,32)(5,45)(6,30)(7,43)(8,56)(9,41)(10,54)(11,39)(12,52)(13,37)(14,50)(15,35)(16,48)(17,33)(18,46)(19,31)(20,44)(21,29)(22,42)(23,55)(24,40)(25,53)(26,38)(27,51)(28,36)(57,201)(58,214)(59,199)(60,212)(61,197)(62,210)(63,223)(64,208)(65,221)(66,206)(67,219)(68,204)(69,217)(70,202)(71,215)(72,200)(73,213)(74,198)(75,211)(76,224)(77,209)(78,222)(79,207)(80,220)(81,205)(82,218)(83,203)(84,216)(85,160)(86,145)(87,158)(88,143)(89,156)(90,141)(91,154)(92,167)(93,152)(94,165)(95,150)(96,163)(97,148)(98,161)(99,146)(100,159)(101,144)(102,157)(103,142)(104,155)(105,168)(106,153)(107,166)(108,151)(109,164)(110,149)(111,162)(112,147)(113,189)(114,174)(115,187)(116,172)(117,185)(118,170)(119,183)(120,196)(121,181)(122,194)(123,179)(124,192)(125,177)(126,190)(127,175)(128,188)(129,173)(130,186)(131,171)(132,184)(133,169)(134,182)(135,195)(136,180)(137,193)(138,178)(139,191)(140,176) );
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)], [(1,7),(2,6),(3,5),(8,28),(9,27),(10,26),(11,25),(12,24),(13,23),(14,22),(15,21),(16,20),(17,19),(29,33),(30,32),(34,56),(35,55),(36,54),(37,53),(38,52),(39,51),(40,50),(41,49),(42,48),(43,47),(44,46),(57,69),(58,68),(59,67),(60,66),(61,65),(62,64),(70,84),(71,83),(72,82),(73,81),(74,80),(75,79),(76,78),(85,99),(86,98),(87,97),(88,96),(89,95),(90,94),(91,93),(100,112),(101,111),(102,110),(103,109),(104,108),(105,107),(113,125),(114,124),(115,123),(116,122),(117,121),(118,120),(126,140),(127,139),(128,138),(129,137),(130,136),(131,135),(132,134),(141,163),(142,162),(143,161),(144,160),(145,159),(146,158),(147,157),(148,156),(149,155),(150,154),(151,153),(164,168),(165,167),(169,195),(170,194),(171,193),(172,192),(173,191),(174,190),(175,189),(176,188),(177,187),(178,186),(179,185),(180,184),(181,183),(197,219),(198,218),(199,217),(200,216),(201,215),(202,214),(203,213),(204,212),(205,211),(206,210),(207,209),(220,224),(221,223)], [(1,116,149,74),(2,117,150,75),(3,118,151,76),(4,119,152,77),(5,120,153,78),(6,121,154,79),(7,122,155,80),(8,123,156,81),(9,124,157,82),(10,125,158,83),(11,126,159,84),(12,127,160,57),(13,128,161,58),(14,129,162,59),(15,130,163,60),(16,131,164,61),(17,132,165,62),(18,133,166,63),(19,134,167,64),(20,135,168,65),(21,136,141,66),(22,137,142,67),(23,138,143,68),(24,139,144,69),(25,140,145,70),(26,113,146,71),(27,114,147,72),(28,115,148,73),(29,206,90,180),(30,207,91,181),(31,208,92,182),(32,209,93,183),(33,210,94,184),(34,211,95,185),(35,212,96,186),(36,213,97,187),(37,214,98,188),(38,215,99,189),(39,216,100,190),(40,217,101,191),(41,218,102,192),(42,219,103,193),(43,220,104,194),(44,221,105,195),(45,222,106,196),(46,223,107,169),(47,224,108,170),(48,197,109,171),(49,198,110,172),(50,199,111,173),(51,200,112,174),(52,201,85,175),(53,202,86,176),(54,203,87,177),(55,204,88,178),(56,205,89,179)], [(1,49),(2,34),(3,47),(4,32),(5,45),(6,30),(7,43),(8,56),(9,41),(10,54),(11,39),(12,52),(13,37),(14,50),(15,35),(16,48),(17,33),(18,46),(19,31),(20,44),(21,29),(22,42),(23,55),(24,40),(25,53),(26,38),(27,51),(28,36),(57,201),(58,214),(59,199),(60,212),(61,197),(62,210),(63,223),(64,208),(65,221),(66,206),(67,219),(68,204),(69,217),(70,202),(71,215),(72,200),(73,213),(74,198),(75,211),(76,224),(77,209),(78,222),(79,207),(80,220),(81,205),(82,218),(83,203),(84,216),(85,160),(86,145),(87,158),(88,143),(89,156),(90,141),(91,154),(92,167),(93,152),(94,165),(95,150),(96,163),(97,148),(98,161),(99,146),(100,159),(101,144),(102,157),(103,142),(104,155),(105,168),(106,153),(107,166),(108,151),(109,164),(110,149),(111,162),(112,147),(113,189),(114,174),(115,187),(116,172),(117,185),(118,170),(119,183),(120,196),(121,181),(122,194),(123,179),(124,192),(125,177),(126,190),(127,175),(128,188),(129,173),(130,186),(131,171),(132,184),(133,169),(134,182),(135,195),(136,180),(137,193),(138,178),(139,191),(140,176)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 28 | 5 | 0 | 0 | 0 | 0 |
| 17 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 3 | 0 | 0 |
| 0 | 0 | 26 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 17 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 3 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 6 | 5 |
| 0 | 0 | 0 | 0 | 10 | 23 |
| 17 | 2 | 0 | 0 | 0 | 0 |
| 1 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 26 | 0 | 0 |
| 0 | 0 | 21 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 10 | 4 |
| 0 | 0 | 0 | 0 | 26 | 19 |
G:=sub<GL(6,GF(29))| [28,17,0,0,0,0,5,1,0,0,0,0,0,0,1,26,0,0,0,0,3,21,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,17,0,0,0,0,0,1,0,0,0,0,0,0,28,3,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,6,10,0,0,0,0,5,23],[17,1,0,0,0,0,2,12,0,0,0,0,0,0,21,21,0,0,0,0,26,8,0,0,0,0,0,0,10,26,0,0,0,0,4,19] >;
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | ··· | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | 2- (1+4) | D4×D7 | Q8⋊2D7 | Q8.10D14 |
| kernel | D28⋊12D4 | C4×D28 | D7×C4⋊C4 | D14.5D4 | C28⋊1D4 | D14⋊3Q8 | C7×C4⋊Q8 | C2×Q8⋊2D7 | D28 | C4⋊Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | C14 | C4 | C4 | C2 |
| # reps | 1 | 2 | 2 | 4 | 2 | 2 | 1 | 2 | 4 | 3 | 4 | 3 | 12 | 6 | 1 | 6 | 6 | 6 |
In GAP, Magma, Sage, TeX
D_{28}\rtimes_{12}D_4 % in TeX
G:=Group("D28:12D4"); // GroupNames label
G:=SmallGroup(448,1179);
// by ID
G=gap.SmallGroup(448,1179);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,268,1571,297,136,18822]);
// 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,d*a*d=a^13,b*c=c*b,d*b*d=a^26*b,d*c*d=c^-1>;
// generators/relations
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ℤ
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