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, C22⋊Dic14⋊16C2, Dic7.D4⋊17C2, (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
Subgroups: 1260 in 290 conjugacy classes, 107 normal (43 characteristic)
C1, C2 [×3], C2 [×5], C4 [×2], C4 [×12], C22, C22 [×2], C22 [×11], C7, C2×C4 [×2], C2×C4 [×2], C2×C4 [×19], D4 [×12], Q8 [×10], C23, C23 [×2], C23, D7, C14 [×3], C14 [×4], C42 [×3], C22⋊C4 [×2], C22⋊C4 [×8], C4⋊C4, C4⋊C4 [×5], C22×C4, C22×C4 [×5], C2×D4, C2×D4 [×2], C2×D4 [×3], C2×Q8 [×8], C4○D4 [×4], Dic7 [×4], Dic7 [×5], C28 [×2], C28 [×3], D14 [×3], C2×C14, C2×C14 [×2], C2×C14 [×8], C4×D4 [×3], C4×Q8, C4⋊D4, C4⋊D4 [×2], C22⋊Q8 [×3], C4.4D4 [×3], C22×Q8, C2×C4○D4, Dic14 [×4], Dic14 [×6], C4×D7 [×2], C2×Dic7 [×3], C2×Dic7 [×4], C2×Dic7 [×8], C7⋊D4 [×6], C2×C28 [×2], C2×C28 [×2], C2×C28 [×2], C7×D4 [×6], C22×D7, C22×C14, C22×C14 [×2], Q8⋊5D4, C4×Dic7, C4×Dic7 [×2], Dic7⋊C4, Dic7⋊C4 [×2], C4⋊Dic7 [×2], D14⋊C4, D14⋊C4 [×2], C23.D7, C23.D7 [×4], C7×C22⋊C4 [×2], C7×C4⋊C4, C2×Dic14 [×2], C2×Dic14 [×2], C2×Dic14 [×4], C2×C4×D7, D4⋊2D7 [×4], C22×Dic7 [×4], C2×C7⋊D4, C2×C7⋊D4 [×2], C22×C28, D4×C14, D4×C14 [×2], C22⋊Dic14 [×2], Dic7.D4 [×2], Dic7⋊3Q8, D14⋊2Q8, C4×C7⋊D4, D4×Dic7 [×2], C28.17D4, Dic7⋊D4 [×2], C7×C4⋊D4, C22×Dic14, C2×D4⋊2D7, Dic14⋊19D4
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], Q8⋊5D4, D4×D7 [×2], D4⋊2D7 [×2], C23×D7, C2×D4×D7, C2×D4⋊2D7, D4.10D14, Dic14⋊19D4
Generators and relations
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 >
►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)
(1 102 15 88)(2 101 16 87)(3 100 17 86)(4 99 18 85)(5 98 19 112)(6 97 20 111)(7 96 21 110)(8 95 22 109)(9 94 23 108)(10 93 24 107)(11 92 25 106)(12 91 26 105)(13 90 27 104)(14 89 28 103)(29 180 43 194)(30 179 44 193)(31 178 45 192)(32 177 46 191)(33 176 47 190)(34 175 48 189)(35 174 49 188)(36 173 50 187)(37 172 51 186)(38 171 52 185)(39 170 53 184)(40 169 54 183)(41 196 55 182)(42 195 56 181)(57 134 71 120)(58 133 72 119)(59 132 73 118)(60 131 74 117)(61 130 75 116)(62 129 76 115)(63 128 77 114)(64 127 78 113)(65 126 79 140)(66 125 80 139)(67 124 81 138)(68 123 82 137)(69 122 83 136)(70 121 84 135)(141 208 155 222)(142 207 156 221)(143 206 157 220)(144 205 158 219)(145 204 159 218)(146 203 160 217)(147 202 161 216)(148 201 162 215)(149 200 163 214)(150 199 164 213)(151 198 165 212)(152 197 166 211)(153 224 167 210)(154 223 168 209)
(1 162 57 29)(2 149 58 44)(3 164 59 31)(4 151 60 46)(5 166 61 33)(6 153 62 48)(7 168 63 35)(8 155 64 50)(9 142 65 37)(10 157 66 52)(11 144 67 39)(12 159 68 54)(13 146 69 41)(14 161 70 56)(15 148 71 43)(16 163 72 30)(17 150 73 45)(18 165 74 32)(19 152 75 47)(20 167 76 34)(21 154 77 49)(22 141 78 36)(23 156 79 51)(24 143 80 38)(25 158 81 53)(26 145 82 40)(27 160 83 55)(28 147 84 42)(85 212 117 177)(86 199 118 192)(87 214 119 179)(88 201 120 194)(89 216 121 181)(90 203 122 196)(91 218 123 183)(92 205 124 170)(93 220 125 185)(94 207 126 172)(95 222 127 187)(96 209 128 174)(97 224 129 189)(98 211 130 176)(99 198 131 191)(100 213 132 178)(101 200 133 193)(102 215 134 180)(103 202 135 195)(104 217 136 182)(105 204 137 169)(106 219 138 184)(107 206 139 171)(108 221 140 186)(109 208 113 173)(110 223 114 188)(111 210 115 175)(112 197 116 190)
(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)(29 148)(30 149)(31 150)(32 151)(33 152)(34 153)(35 154)(36 155)(37 156)(38 157)(39 158)(40 159)(41 160)(42 161)(43 162)(44 163)(45 164)(46 165)(47 166)(48 167)(49 168)(50 141)(51 142)(52 143)(53 144)(54 145)(55 146)(56 147)(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)(85 99)(86 100)(87 101)(88 102)(89 103)(90 104)(91 105)(92 106)(93 107)(94 108)(95 109)(96 110)(97 111)(98 112)(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)(169 218)(170 219)(171 220)(172 221)(173 222)(174 223)(175 224)(176 197)(177 198)(178 199)(179 200)(180 201)(181 202)(182 203)(183 204)(184 205)(185 206)(186 207)(187 208)(188 209)(189 210)(190 211)(191 212)(192 213)(193 214)(194 215)(195 216)(196 217)
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), (1,102,15,88)(2,101,16,87)(3,100,17,86)(4,99,18,85)(5,98,19,112)(6,97,20,111)(7,96,21,110)(8,95,22,109)(9,94,23,108)(10,93,24,107)(11,92,25,106)(12,91,26,105)(13,90,27,104)(14,89,28,103)(29,180,43,194)(30,179,44,193)(31,178,45,192)(32,177,46,191)(33,176,47,190)(34,175,48,189)(35,174,49,188)(36,173,50,187)(37,172,51,186)(38,171,52,185)(39,170,53,184)(40,169,54,183)(41,196,55,182)(42,195,56,181)(57,134,71,120)(58,133,72,119)(59,132,73,118)(60,131,74,117)(61,130,75,116)(62,129,76,115)(63,128,77,114)(64,127,78,113)(65,126,79,140)(66,125,80,139)(67,124,81,138)(68,123,82,137)(69,122,83,136)(70,121,84,135)(141,208,155,222)(142,207,156,221)(143,206,157,220)(144,205,158,219)(145,204,159,218)(146,203,160,217)(147,202,161,216)(148,201,162,215)(149,200,163,214)(150,199,164,213)(151,198,165,212)(152,197,166,211)(153,224,167,210)(154,223,168,209), (1,162,57,29)(2,149,58,44)(3,164,59,31)(4,151,60,46)(5,166,61,33)(6,153,62,48)(7,168,63,35)(8,155,64,50)(9,142,65,37)(10,157,66,52)(11,144,67,39)(12,159,68,54)(13,146,69,41)(14,161,70,56)(15,148,71,43)(16,163,72,30)(17,150,73,45)(18,165,74,32)(19,152,75,47)(20,167,76,34)(21,154,77,49)(22,141,78,36)(23,156,79,51)(24,143,80,38)(25,158,81,53)(26,145,82,40)(27,160,83,55)(28,147,84,42)(85,212,117,177)(86,199,118,192)(87,214,119,179)(88,201,120,194)(89,216,121,181)(90,203,122,196)(91,218,123,183)(92,205,124,170)(93,220,125,185)(94,207,126,172)(95,222,127,187)(96,209,128,174)(97,224,129,189)(98,211,130,176)(99,198,131,191)(100,213,132,178)(101,200,133,193)(102,215,134,180)(103,202,135,195)(104,217,136,182)(105,204,137,169)(106,219,138,184)(107,206,139,171)(108,221,140,186)(109,208,113,173)(110,223,114,188)(111,210,115,175)(112,197,116,190), (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)(29,148)(30,149)(31,150)(32,151)(33,152)(34,153)(35,154)(36,155)(37,156)(38,157)(39,158)(40,159)(41,160)(42,161)(43,162)(44,163)(45,164)(46,165)(47,166)(48,167)(49,168)(50,141)(51,142)(52,143)(53,144)(54,145)(55,146)(56,147)(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)(85,99)(86,100)(87,101)(88,102)(89,103)(90,104)(91,105)(92,106)(93,107)(94,108)(95,109)(96,110)(97,111)(98,112)(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)(169,218)(170,219)(171,220)(172,221)(173,222)(174,223)(175,224)(176,197)(177,198)(178,199)(179,200)(180,201)(181,202)(182,203)(183,204)(184,205)(185,206)(186,207)(187,208)(188,209)(189,210)(190,211)(191,212)(192,213)(193,214)(194,215)(195,216)(196,217)>;
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), (1,102,15,88)(2,101,16,87)(3,100,17,86)(4,99,18,85)(5,98,19,112)(6,97,20,111)(7,96,21,110)(8,95,22,109)(9,94,23,108)(10,93,24,107)(11,92,25,106)(12,91,26,105)(13,90,27,104)(14,89,28,103)(29,180,43,194)(30,179,44,193)(31,178,45,192)(32,177,46,191)(33,176,47,190)(34,175,48,189)(35,174,49,188)(36,173,50,187)(37,172,51,186)(38,171,52,185)(39,170,53,184)(40,169,54,183)(41,196,55,182)(42,195,56,181)(57,134,71,120)(58,133,72,119)(59,132,73,118)(60,131,74,117)(61,130,75,116)(62,129,76,115)(63,128,77,114)(64,127,78,113)(65,126,79,140)(66,125,80,139)(67,124,81,138)(68,123,82,137)(69,122,83,136)(70,121,84,135)(141,208,155,222)(142,207,156,221)(143,206,157,220)(144,205,158,219)(145,204,159,218)(146,203,160,217)(147,202,161,216)(148,201,162,215)(149,200,163,214)(150,199,164,213)(151,198,165,212)(152,197,166,211)(153,224,167,210)(154,223,168,209), (1,162,57,29)(2,149,58,44)(3,164,59,31)(4,151,60,46)(5,166,61,33)(6,153,62,48)(7,168,63,35)(8,155,64,50)(9,142,65,37)(10,157,66,52)(11,144,67,39)(12,159,68,54)(13,146,69,41)(14,161,70,56)(15,148,71,43)(16,163,72,30)(17,150,73,45)(18,165,74,32)(19,152,75,47)(20,167,76,34)(21,154,77,49)(22,141,78,36)(23,156,79,51)(24,143,80,38)(25,158,81,53)(26,145,82,40)(27,160,83,55)(28,147,84,42)(85,212,117,177)(86,199,118,192)(87,214,119,179)(88,201,120,194)(89,216,121,181)(90,203,122,196)(91,218,123,183)(92,205,124,170)(93,220,125,185)(94,207,126,172)(95,222,127,187)(96,209,128,174)(97,224,129,189)(98,211,130,176)(99,198,131,191)(100,213,132,178)(101,200,133,193)(102,215,134,180)(103,202,135,195)(104,217,136,182)(105,204,137,169)(106,219,138,184)(107,206,139,171)(108,221,140,186)(109,208,113,173)(110,223,114,188)(111,210,115,175)(112,197,116,190), (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)(29,148)(30,149)(31,150)(32,151)(33,152)(34,153)(35,154)(36,155)(37,156)(38,157)(39,158)(40,159)(41,160)(42,161)(43,162)(44,163)(45,164)(46,165)(47,166)(48,167)(49,168)(50,141)(51,142)(52,143)(53,144)(54,145)(55,146)(56,147)(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)(85,99)(86,100)(87,101)(88,102)(89,103)(90,104)(91,105)(92,106)(93,107)(94,108)(95,109)(96,110)(97,111)(98,112)(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)(169,218)(170,219)(171,220)(172,221)(173,222)(174,223)(175,224)(176,197)(177,198)(178,199)(179,200)(180,201)(181,202)(182,203)(183,204)(184,205)(185,206)(186,207)(187,208)(188,209)(189,210)(190,211)(191,212)(192,213)(193,214)(194,215)(195,216)(196,217) );
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)], [(1,102,15,88),(2,101,16,87),(3,100,17,86),(4,99,18,85),(5,98,19,112),(6,97,20,111),(7,96,21,110),(8,95,22,109),(9,94,23,108),(10,93,24,107),(11,92,25,106),(12,91,26,105),(13,90,27,104),(14,89,28,103),(29,180,43,194),(30,179,44,193),(31,178,45,192),(32,177,46,191),(33,176,47,190),(34,175,48,189),(35,174,49,188),(36,173,50,187),(37,172,51,186),(38,171,52,185),(39,170,53,184),(40,169,54,183),(41,196,55,182),(42,195,56,181),(57,134,71,120),(58,133,72,119),(59,132,73,118),(60,131,74,117),(61,130,75,116),(62,129,76,115),(63,128,77,114),(64,127,78,113),(65,126,79,140),(66,125,80,139),(67,124,81,138),(68,123,82,137),(69,122,83,136),(70,121,84,135),(141,208,155,222),(142,207,156,221),(143,206,157,220),(144,205,158,219),(145,204,159,218),(146,203,160,217),(147,202,161,216),(148,201,162,215),(149,200,163,214),(150,199,164,213),(151,198,165,212),(152,197,166,211),(153,224,167,210),(154,223,168,209)], [(1,162,57,29),(2,149,58,44),(3,164,59,31),(4,151,60,46),(5,166,61,33),(6,153,62,48),(7,168,63,35),(8,155,64,50),(9,142,65,37),(10,157,66,52),(11,144,67,39),(12,159,68,54),(13,146,69,41),(14,161,70,56),(15,148,71,43),(16,163,72,30),(17,150,73,45),(18,165,74,32),(19,152,75,47),(20,167,76,34),(21,154,77,49),(22,141,78,36),(23,156,79,51),(24,143,80,38),(25,158,81,53),(26,145,82,40),(27,160,83,55),(28,147,84,42),(85,212,117,177),(86,199,118,192),(87,214,119,179),(88,201,120,194),(89,216,121,181),(90,203,122,196),(91,218,123,183),(92,205,124,170),(93,220,125,185),(94,207,126,172),(95,222,127,187),(96,209,128,174),(97,224,129,189),(98,211,130,176),(99,198,131,191),(100,213,132,178),(101,200,133,193),(102,215,134,180),(103,202,135,195),(104,217,136,182),(105,204,137,169),(106,219,138,184),(107,206,139,171),(108,221,140,186),(109,208,113,173),(110,223,114,188),(111,210,115,175),(112,197,116,190)], [(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),(29,148),(30,149),(31,150),(32,151),(33,152),(34,153),(35,154),(36,155),(37,156),(38,157),(39,158),(40,159),(41,160),(42,161),(43,162),(44,163),(45,164),(46,165),(47,166),(48,167),(49,168),(50,141),(51,142),(52,143),(53,144),(54,145),(55,146),(56,147),(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),(85,99),(86,100),(87,101),(88,102),(89,103),(90,104),(91,105),(92,106),(93,107),(94,108),(95,109),(96,110),(97,111),(98,112),(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),(169,218),(170,219),(171,220),(172,221),(173,222),(174,223),(175,224),(176,197),(177,198),(178,199),(179,200),(180,201),(181,202),(182,203),(183,204),(184,205),(185,206),(186,207),(187,208),(188,209),(189,210),(190,211),(191,212),(192,213),(193,214),(194,215),(195,216),(196,217)])
Matrix representation ►G ⊆ 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] >;
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 |
In GAP, Magma, Sage, TeX
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
×
⋊
ℤ
𝔽
○
≀