metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic14⋊19D4, C14.692- 1+4, C4⋊D4⋊6D7, C7⋊3(Q8⋊5D4), C4.108(D4×D7), C4⋊C4.176D14, (D4×Dic7)⋊15C2, C28.224(C2×D4), C22⋊C4.5D14, D14⋊2Q8⋊19C2, Dic7⋊D4⋊9C2, (C2×D4).151D14, Dic7.20(C2×D4), C14.61(C22×D4), Dic7⋊3Q8⋊19C2, C28.17D4⋊14C2, C22⋊1(D4⋊2D7), C23.9(C22×D7), (C2×C28).500C23, (C2×C14).142C24, D14⋊C4.11C22, (C22×C4).218D14, Dic7.D4⋊17C2, C22⋊Dic14⋊16C2, (C22×Dic14)⋊16C2, (D4×C14).116C22, Dic7⋊C4.13C22, C4⋊Dic7.204C22, (C22×C14).13C23, (C2×Dic7).65C23, (C4×Dic7).89C22, (C22×D7).61C23, C22.163(C23×D7), C23.D7.20C22, (C22×C28).236C22, C2.27(D4.10D14), (C2×Dic14).245C22, (C22×Dic7).103C22, C2.34(C2×D4×D7), (C7×C4⋊D4)⋊7C2, (C4×C7⋊D4)⋊14C2, (C2×C14)⋊4(C4○D4), C14.80(C2×C4○D4), (C2×D4⋊2D7)⋊10C2, (C2×C4×D7).81C22, C2.31(C2×D4⋊2D7), (C7×C4⋊C4).138C22, (C2×C4).173(C22×D7), (C7×C22⋊C4).7C22, (C2×C7⋊D4).118C22, SmallGroup(448,1051)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic14⋊19D4
G = < a,b,c,d | a28=c4=d2=1, b2=a14, bab-1=a-1, cac-1=a15, ad=da, bc=cb, bd=db, dcd=c-1 >
Subgroups: 1260 in 290 conjugacy classes, 107 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, C23, D7, C14, C14, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×D4, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C14, C4×D4, C4×Q8, C4⋊D4, C4⋊D4, C22⋊Q8, C4.4D4, C22×Q8, C2×C4○D4, Dic14, Dic14, C4×D7, C2×Dic7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C22×C14, Q8⋊5D4, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, D14⋊C4, D14⋊C4, C23.D7, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C2×Dic14, C2×C4×D7, D4⋊2D7, C22×Dic7, C2×C7⋊D4, C2×C7⋊D4, C22×C28, D4×C14, D4×C14, C22⋊Dic14, Dic7.D4, Dic7⋊3Q8, D14⋊2Q8, C4×C7⋊D4, D4×Dic7, C28.17D4, Dic7⋊D4, C7×C4⋊D4, C22×Dic14, C2×D4⋊2D7, Dic14⋊19D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C22×D4, C2×C4○D4, 2- 1+4, C22×D7, Q8⋊5D4, D4×D7, D4⋊2D7, C23×D7, C2×D4×D7, C2×D4⋊2D7, D4.10D14, Dic14⋊19D4
►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)
(1 113 15 127)(2 140 16 126)(3 139 17 125)(4 138 18 124)(5 137 19 123)(6 136 20 122)(7 135 21 121)(8 134 22 120)(9 133 23 119)(10 132 24 118)(11 131 25 117)(12 130 26 116)(13 129 27 115)(14 128 28 114)(29 193 43 179)(30 192 44 178)(31 191 45 177)(32 190 46 176)(33 189 47 175)(34 188 48 174)(35 187 49 173)(36 186 50 172)(37 185 51 171)(38 184 52 170)(39 183 53 169)(40 182 54 196)(41 181 55 195)(42 180 56 194)(57 221 71 207)(58 220 72 206)(59 219 73 205)(60 218 74 204)(61 217 75 203)(62 216 76 202)(63 215 77 201)(64 214 78 200)(65 213 79 199)(66 212 80 198)(67 211 81 197)(68 210 82 224)(69 209 83 223)(70 208 84 222)(85 143 99 157)(86 142 100 156)(87 141 101 155)(88 168 102 154)(89 167 103 153)(90 166 104 152)(91 165 105 151)(92 164 106 150)(93 163 107 149)(94 162 108 148)(95 161 109 147)(96 160 110 146)(97 159 111 145)(98 158 112 144)
(1 94 75 30)(2 109 76 45)(3 96 77 32)(4 111 78 47)(5 98 79 34)(6 85 80 49)(7 100 81 36)(8 87 82 51)(9 102 83 38)(10 89 84 53)(11 104 57 40)(12 91 58 55)(13 106 59 42)(14 93 60 29)(15 108 61 44)(16 95 62 31)(17 110 63 46)(18 97 64 33)(19 112 65 48)(20 99 66 35)(21 86 67 50)(22 101 68 37)(23 88 69 52)(24 103 70 39)(25 90 71 54)(26 105 72 41)(27 92 73 56)(28 107 74 43)(113 162 203 192)(114 149 204 179)(115 164 205 194)(116 151 206 181)(117 166 207 196)(118 153 208 183)(119 168 209 170)(120 155 210 185)(121 142 211 172)(122 157 212 187)(123 144 213 174)(124 159 214 189)(125 146 215 176)(126 161 216 191)(127 148 217 178)(128 163 218 193)(129 150 219 180)(130 165 220 195)(131 152 221 182)(132 167 222 169)(133 154 223 184)(134 141 224 171)(135 156 197 186)(136 143 198 173)(137 158 199 188)(138 145 200 175)(139 160 201 190)(140 147 202 177)
(1 15)(2 16)(3 17)(4 18)(5 19)(6 20)(7 21)(8 22)(9 23)(10 24)(11 25)(12 26)(13 27)(14 28)(29 107)(30 108)(31 109)(32 110)(33 111)(34 112)(35 85)(36 86)(37 87)(38 88)(39 89)(40 90)(41 91)(42 92)(43 93)(44 94)(45 95)(46 96)(47 97)(48 98)(49 99)(50 100)(51 101)(52 102)(53 103)(54 104)(55 105)(56 106)(57 71)(58 72)(59 73)(60 74)(61 75)(62 76)(63 77)(64 78)(65 79)(66 80)(67 81)(68 82)(69 83)(70 84)(113 127)(114 128)(115 129)(116 130)(117 131)(118 132)(119 133)(120 134)(121 135)(122 136)(123 137)(124 138)(125 139)(126 140)(141 185)(142 186)(143 187)(144 188)(145 189)(146 190)(147 191)(148 192)(149 193)(150 194)(151 195)(152 196)(153 169)(154 170)(155 171)(156 172)(157 173)(158 174)(159 175)(160 176)(161 177)(162 178)(163 179)(164 180)(165 181)(166 182)(167 183)(168 184)(197 211)(198 212)(199 213)(200 214)(201 215)(202 216)(203 217)(204 218)(205 219)(206 220)(207 221)(208 222)(209 223)(210 224)
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), (1,113,15,127)(2,140,16,126)(3,139,17,125)(4,138,18,124)(5,137,19,123)(6,136,20,122)(7,135,21,121)(8,134,22,120)(9,133,23,119)(10,132,24,118)(11,131,25,117)(12,130,26,116)(13,129,27,115)(14,128,28,114)(29,193,43,179)(30,192,44,178)(31,191,45,177)(32,190,46,176)(33,189,47,175)(34,188,48,174)(35,187,49,173)(36,186,50,172)(37,185,51,171)(38,184,52,170)(39,183,53,169)(40,182,54,196)(41,181,55,195)(42,180,56,194)(57,221,71,207)(58,220,72,206)(59,219,73,205)(60,218,74,204)(61,217,75,203)(62,216,76,202)(63,215,77,201)(64,214,78,200)(65,213,79,199)(66,212,80,198)(67,211,81,197)(68,210,82,224)(69,209,83,223)(70,208,84,222)(85,143,99,157)(86,142,100,156)(87,141,101,155)(88,168,102,154)(89,167,103,153)(90,166,104,152)(91,165,105,151)(92,164,106,150)(93,163,107,149)(94,162,108,148)(95,161,109,147)(96,160,110,146)(97,159,111,145)(98,158,112,144), (1,94,75,30)(2,109,76,45)(3,96,77,32)(4,111,78,47)(5,98,79,34)(6,85,80,49)(7,100,81,36)(8,87,82,51)(9,102,83,38)(10,89,84,53)(11,104,57,40)(12,91,58,55)(13,106,59,42)(14,93,60,29)(15,108,61,44)(16,95,62,31)(17,110,63,46)(18,97,64,33)(19,112,65,48)(20,99,66,35)(21,86,67,50)(22,101,68,37)(23,88,69,52)(24,103,70,39)(25,90,71,54)(26,105,72,41)(27,92,73,56)(28,107,74,43)(113,162,203,192)(114,149,204,179)(115,164,205,194)(116,151,206,181)(117,166,207,196)(118,153,208,183)(119,168,209,170)(120,155,210,185)(121,142,211,172)(122,157,212,187)(123,144,213,174)(124,159,214,189)(125,146,215,176)(126,161,216,191)(127,148,217,178)(128,163,218,193)(129,150,219,180)(130,165,220,195)(131,152,221,182)(132,167,222,169)(133,154,223,184)(134,141,224,171)(135,156,197,186)(136,143,198,173)(137,158,199,188)(138,145,200,175)(139,160,201,190)(140,147,202,177), (1,15)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(29,107)(30,108)(31,109)(32,110)(33,111)(34,112)(35,85)(36,86)(37,87)(38,88)(39,89)(40,90)(41,91)(42,92)(43,93)(44,94)(45,95)(46,96)(47,97)(48,98)(49,99)(50,100)(51,101)(52,102)(53,103)(54,104)(55,105)(56,106)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81)(68,82)(69,83)(70,84)(113,127)(114,128)(115,129)(116,130)(117,131)(118,132)(119,133)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140)(141,185)(142,186)(143,187)(144,188)(145,189)(146,190)(147,191)(148,192)(149,193)(150,194)(151,195)(152,196)(153,169)(154,170)(155,171)(156,172)(157,173)(158,174)(159,175)(160,176)(161,177)(162,178)(163,179)(164,180)(165,181)(166,182)(167,183)(168,184)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224)>;
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), (1,113,15,127)(2,140,16,126)(3,139,17,125)(4,138,18,124)(5,137,19,123)(6,136,20,122)(7,135,21,121)(8,134,22,120)(9,133,23,119)(10,132,24,118)(11,131,25,117)(12,130,26,116)(13,129,27,115)(14,128,28,114)(29,193,43,179)(30,192,44,178)(31,191,45,177)(32,190,46,176)(33,189,47,175)(34,188,48,174)(35,187,49,173)(36,186,50,172)(37,185,51,171)(38,184,52,170)(39,183,53,169)(40,182,54,196)(41,181,55,195)(42,180,56,194)(57,221,71,207)(58,220,72,206)(59,219,73,205)(60,218,74,204)(61,217,75,203)(62,216,76,202)(63,215,77,201)(64,214,78,200)(65,213,79,199)(66,212,80,198)(67,211,81,197)(68,210,82,224)(69,209,83,223)(70,208,84,222)(85,143,99,157)(86,142,100,156)(87,141,101,155)(88,168,102,154)(89,167,103,153)(90,166,104,152)(91,165,105,151)(92,164,106,150)(93,163,107,149)(94,162,108,148)(95,161,109,147)(96,160,110,146)(97,159,111,145)(98,158,112,144), (1,94,75,30)(2,109,76,45)(3,96,77,32)(4,111,78,47)(5,98,79,34)(6,85,80,49)(7,100,81,36)(8,87,82,51)(9,102,83,38)(10,89,84,53)(11,104,57,40)(12,91,58,55)(13,106,59,42)(14,93,60,29)(15,108,61,44)(16,95,62,31)(17,110,63,46)(18,97,64,33)(19,112,65,48)(20,99,66,35)(21,86,67,50)(22,101,68,37)(23,88,69,52)(24,103,70,39)(25,90,71,54)(26,105,72,41)(27,92,73,56)(28,107,74,43)(113,162,203,192)(114,149,204,179)(115,164,205,194)(116,151,206,181)(117,166,207,196)(118,153,208,183)(119,168,209,170)(120,155,210,185)(121,142,211,172)(122,157,212,187)(123,144,213,174)(124,159,214,189)(125,146,215,176)(126,161,216,191)(127,148,217,178)(128,163,218,193)(129,150,219,180)(130,165,220,195)(131,152,221,182)(132,167,222,169)(133,154,223,184)(134,141,224,171)(135,156,197,186)(136,143,198,173)(137,158,199,188)(138,145,200,175)(139,160,201,190)(140,147,202,177), (1,15)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(29,107)(30,108)(31,109)(32,110)(33,111)(34,112)(35,85)(36,86)(37,87)(38,88)(39,89)(40,90)(41,91)(42,92)(43,93)(44,94)(45,95)(46,96)(47,97)(48,98)(49,99)(50,100)(51,101)(52,102)(53,103)(54,104)(55,105)(56,106)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81)(68,82)(69,83)(70,84)(113,127)(114,128)(115,129)(116,130)(117,131)(118,132)(119,133)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140)(141,185)(142,186)(143,187)(144,188)(145,189)(146,190)(147,191)(148,192)(149,193)(150,194)(151,195)(152,196)(153,169)(154,170)(155,171)(156,172)(157,173)(158,174)(159,175)(160,176)(161,177)(162,178)(163,179)(164,180)(165,181)(166,182)(167,183)(168,184)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224) );
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)], [(1,113,15,127),(2,140,16,126),(3,139,17,125),(4,138,18,124),(5,137,19,123),(6,136,20,122),(7,135,21,121),(8,134,22,120),(9,133,23,119),(10,132,24,118),(11,131,25,117),(12,130,26,116),(13,129,27,115),(14,128,28,114),(29,193,43,179),(30,192,44,178),(31,191,45,177),(32,190,46,176),(33,189,47,175),(34,188,48,174),(35,187,49,173),(36,186,50,172),(37,185,51,171),(38,184,52,170),(39,183,53,169),(40,182,54,196),(41,181,55,195),(42,180,56,194),(57,221,71,207),(58,220,72,206),(59,219,73,205),(60,218,74,204),(61,217,75,203),(62,216,76,202),(63,215,77,201),(64,214,78,200),(65,213,79,199),(66,212,80,198),(67,211,81,197),(68,210,82,224),(69,209,83,223),(70,208,84,222),(85,143,99,157),(86,142,100,156),(87,141,101,155),(88,168,102,154),(89,167,103,153),(90,166,104,152),(91,165,105,151),(92,164,106,150),(93,163,107,149),(94,162,108,148),(95,161,109,147),(96,160,110,146),(97,159,111,145),(98,158,112,144)], [(1,94,75,30),(2,109,76,45),(3,96,77,32),(4,111,78,47),(5,98,79,34),(6,85,80,49),(7,100,81,36),(8,87,82,51),(9,102,83,38),(10,89,84,53),(11,104,57,40),(12,91,58,55),(13,106,59,42),(14,93,60,29),(15,108,61,44),(16,95,62,31),(17,110,63,46),(18,97,64,33),(19,112,65,48),(20,99,66,35),(21,86,67,50),(22,101,68,37),(23,88,69,52),(24,103,70,39),(25,90,71,54),(26,105,72,41),(27,92,73,56),(28,107,74,43),(113,162,203,192),(114,149,204,179),(115,164,205,194),(116,151,206,181),(117,166,207,196),(118,153,208,183),(119,168,209,170),(120,155,210,185),(121,142,211,172),(122,157,212,187),(123,144,213,174),(124,159,214,189),(125,146,215,176),(126,161,216,191),(127,148,217,178),(128,163,218,193),(129,150,219,180),(130,165,220,195),(131,152,221,182),(132,167,222,169),(133,154,223,184),(134,141,224,171),(135,156,197,186),(136,143,198,173),(137,158,199,188),(138,145,200,175),(139,160,201,190),(140,147,202,177)], [(1,15),(2,16),(3,17),(4,18),(5,19),(6,20),(7,21),(8,22),(9,23),(10,24),(11,25),(12,26),(13,27),(14,28),(29,107),(30,108),(31,109),(32,110),(33,111),(34,112),(35,85),(36,86),(37,87),(38,88),(39,89),(40,90),(41,91),(42,92),(43,93),(44,94),(45,95),(46,96),(47,97),(48,98),(49,99),(50,100),(51,101),(52,102),(53,103),(54,104),(55,105),(56,106),(57,71),(58,72),(59,73),(60,74),(61,75),(62,76),(63,77),(64,78),(65,79),(66,80),(67,81),(68,82),(69,83),(70,84),(113,127),(114,128),(115,129),(116,130),(117,131),(118,132),(119,133),(120,134),(121,135),(122,136),(123,137),(124,138),(125,139),(126,140),(141,185),(142,186),(143,187),(144,188),(145,189),(146,190),(147,191),(148,192),(149,193),(150,194),(151,195),(152,196),(153,169),(154,170),(155,171),(156,172),(157,173),(158,174),(159,175),(160,176),(161,177),(162,178),(163,179),(164,180),(165,181),(166,182),(167,183),(168,184),(197,211),(198,212),(199,213),(200,214),(201,215),(202,216),(203,217),(204,218),(205,219),(206,220),(207,221),(208,222),(209,223),(210,224)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | 4B | 4C | 4D | 4E | 4F | ··· | 4M | 4N | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 14P | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28R |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 28 | 2 | 2 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | D14 | 2- 1+4 | D4×D7 | D4⋊2D7 | D4.10D14 |
| kernel | Dic14⋊19D4 | C22⋊Dic14 | Dic7.D4 | Dic7⋊3Q8 | D14⋊2Q8 | C4×C7⋊D4 | D4×Dic7 | C28.17D4 | Dic7⋊D4 | C7×C4⋊D4 | C22×Dic14 | C2×D4⋊2D7 | Dic14 | C4⋊D4 | C2×C14 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C14 | C4 | C22 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 2 | 1 | 2 | 1 | 1 | 1 | 4 | 3 | 4 | 6 | 3 | 3 | 9 | 1 | 6 | 6 | 6 |
Matrix representation of Dic14⋊19D4 ►in GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 1 | 0 | 0 |
| 0 | 0 | 27 | 22 | 0 | 0 |
| 0 | 0 | 0 | 0 | 18 | 21 |
| 0 | 0 | 0 | 0 | 8 | 11 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 25 | 0 | 0 |
| 0 | 0 | 6 | 24 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 1 | 2 | 0 | 0 | 0 | 0 |
| 28 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 28 | 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 | 28 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,25,27,0,0,0,0,1,22,0,0,0,0,0,0,18,8,0,0,0,0,21,11],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,5,6,0,0,0,0,25,24,0,0,0,0,0,0,0,17,0,0,0,0,17,0],[1,28,0,0,0,0,2,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,0,28,0,0,0,0,28,0],[1,28,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28] >;
Dic14⋊19D4 in GAP, Magma, Sage, TeX
{\rm Dic}_{14}\rtimes_{19}D_4 % in TeX
G:=Group("Dic14:19D4"); // GroupNames label
G:=SmallGroup(448,1051);
// by ID
G=gap.SmallGroup(448,1051);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,477,232,570,185,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=c^4=d^2=1,b^2=a^14,b*a*b^-1=a^-1,c*a*c^-1=a^15,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d=c^-1>;
// generators/relations