metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic14⋊21D4, C14.762- (1+4), C7⋊3(D4×Q8), C7⋊D4⋊1Q8, C28⋊Q8⋊25C2, D14⋊6(C2×Q8), C22⋊Q8⋊9D7, C22⋊1(Q8×D7), Dic7⋊4(C2×Q8), C4.113(D4×D7), C4⋊C4.190D14, C28.236(C2×D4), D14⋊Q8⋊19C2, D14⋊2Q8⋊26C2, (C2×C28).55C23, (C2×Q8).127D14, C22⋊C4.58D14, Dic7.24(C2×D4), C14.78(C22×D4), Dic7⋊Q8⋊15C2, Dic7⋊3Q8⋊25C2, C14.35(C22×Q8), (C2×C14).176C24, Dic7⋊4D4.1C2, (C22×C4).238D14, D14⋊C4.107C22, C22⋊Dic14⋊23C2, (C22×Dic14)⋊17C2, Dic7⋊C4.28C22, C4⋊Dic7.216C22, (Q8×C14).108C22, C22.197(C23×D7), C23.190(C22×D7), (C22×C14).204C23, (C22×C28).256C22, (C2×Dic7).235C23, (C4×Dic7).106C22, (C22×D7).198C23, C23.D7.117C22, C2.36(D4.10D14), (C2×Dic14).248C22, (C22×Dic7).118C22, (C2×Q8×D7)⋊7C2, C2.51(C2×D4×D7), C2.18(C2×Q8×D7), (C2×C14)⋊3(C2×Q8), (C4×C7⋊D4).7C2, (C7×C22⋊Q8)⋊12C2, (C2×C4×D7).96C22, (C2×C4).49(C22×D7), (C7×C4⋊C4).159C22, (C2×C7⋊D4).124C22, (C7×C22⋊C4).31C22, SmallGroup(448,1085)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1212 in 280 conjugacy classes, 115 normal (43 characteristic)
C1, C2 [×3], C2 [×4], C4 [×2], C4 [×15], C22, C22 [×2], C22 [×6], C7, C2×C4 [×2], C2×C4 [×4], C2×C4 [×19], D4 [×4], Q8 [×16], C23, C23, D7 [×2], C14 [×3], C14 [×2], C42 [×3], C22⋊C4 [×2], C22⋊C4 [×4], C4⋊C4, C4⋊C4 [×2], C4⋊C4 [×9], C22×C4, C22×C4 [×5], C2×D4, C2×Q8, C2×Q8 [×14], Dic7 [×6], Dic7 [×4], C28 [×2], C28 [×5], D14 [×2], D14 [×2], C2×C14, C2×C14 [×2], C2×C14 [×2], C4×D4 [×3], C4×Q8, C22⋊Q8, C22⋊Q8 [×5], C4⋊Q8 [×3], C22×Q8 [×2], Dic14 [×4], Dic14 [×10], C4×D7 [×6], C2×Dic7 [×3], C2×Dic7 [×4], C2×Dic7 [×4], C7⋊D4 [×4], C2×C28 [×2], C2×C28 [×4], C2×C28 [×2], C7×Q8 [×2], C22×D7, C22×C14, D4×Q8, C4×Dic7, C4×Dic7 [×2], Dic7⋊C4, Dic7⋊C4 [×6], C4⋊Dic7 [×2], D14⋊C4, D14⋊C4 [×2], C23.D7, C7×C22⋊C4 [×2], C7×C4⋊C4, C7×C4⋊C4 [×2], C2×Dic14 [×2], C2×Dic14 [×4], C2×Dic14 [×4], C2×C4×D7, C2×C4×D7 [×2], Q8×D7 [×4], C22×Dic7 [×2], C2×C7⋊D4, C22×C28, Q8×C14, C22⋊Dic14 [×2], Dic7⋊4D4 [×2], Dic7⋊3Q8, C28⋊Q8 [×2], D14⋊Q8 [×2], D14⋊2Q8, C4×C7⋊D4, Dic7⋊Q8, C7×C22⋊Q8, C22×Dic14, C2×Q8×D7, Dic14⋊21D4
Quotients:
C1, C2 [×15], C22 [×35], D4 [×4], Q8 [×4], C23 [×15], D7, C2×D4 [×6], C2×Q8 [×6], C24, D14 [×7], C22×D4, C22×Q8, 2- (1+4), C22×D7 [×7], D4×Q8, D4×D7 [×2], Q8×D7 [×2], C23×D7, C2×D4×D7, C2×Q8×D7, D4.10D14, Dic14⋊21D4
Generators and relations
G = < a,b,c,d | a28=c4=d2=1, b2=a14, bab-1=a-1, cac-1=a13, 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 56 15 42)(2 55 16 41)(3 54 17 40)(4 53 18 39)(5 52 19 38)(6 51 20 37)(7 50 21 36)(8 49 22 35)(9 48 23 34)(10 47 24 33)(11 46 25 32)(12 45 26 31)(13 44 27 30)(14 43 28 29)(57 118 71 132)(58 117 72 131)(59 116 73 130)(60 115 74 129)(61 114 75 128)(62 113 76 127)(63 140 77 126)(64 139 78 125)(65 138 79 124)(66 137 80 123)(67 136 81 122)(68 135 82 121)(69 134 83 120)(70 133 84 119)(85 202 99 216)(86 201 100 215)(87 200 101 214)(88 199 102 213)(89 198 103 212)(90 197 104 211)(91 224 105 210)(92 223 106 209)(93 222 107 208)(94 221 108 207)(95 220 109 206)(96 219 110 205)(97 218 111 204)(98 217 112 203)(141 178 155 192)(142 177 156 191)(143 176 157 190)(144 175 158 189)(145 174 159 188)(146 173 160 187)(147 172 161 186)(148 171 162 185)(149 170 163 184)(150 169 164 183)(151 196 165 182)(152 195 166 181)(153 194 167 180)(154 193 168 179)
(1 61 193 218)(2 74 194 203)(3 59 195 216)(4 72 196 201)(5 57 169 214)(6 70 170 199)(7 83 171 212)(8 68 172 197)(9 81 173 210)(10 66 174 223)(11 79 175 208)(12 64 176 221)(13 77 177 206)(14 62 178 219)(15 75 179 204)(16 60 180 217)(17 73 181 202)(18 58 182 215)(19 71 183 200)(20 84 184 213)(21 69 185 198)(22 82 186 211)(23 67 187 224)(24 80 188 209)(25 65 189 222)(26 78 190 207)(27 63 191 220)(28 76 192 205)(29 127 141 96)(30 140 142 109)(31 125 143 94)(32 138 144 107)(33 123 145 92)(34 136 146 105)(35 121 147 90)(36 134 148 103)(37 119 149 88)(38 132 150 101)(39 117 151 86)(40 130 152 99)(41 115 153 112)(42 128 154 97)(43 113 155 110)(44 126 156 95)(45 139 157 108)(46 124 158 93)(47 137 159 106)(48 122 160 91)(49 135 161 104)(50 120 162 89)(51 133 163 102)(52 118 164 87)(53 131 165 100)(54 116 166 85)(55 129 167 98)(56 114 168 111)
(1 218)(2 219)(3 220)(4 221)(5 222)(6 223)(7 224)(8 197)(9 198)(10 199)(11 200)(12 201)(13 202)(14 203)(15 204)(16 205)(17 206)(18 207)(19 208)(20 209)(21 210)(22 211)(23 212)(24 213)(25 214)(26 215)(27 216)(28 217)(29 112)(30 85)(31 86)(32 87)(33 88)(34 89)(35 90)(36 91)(37 92)(38 93)(39 94)(40 95)(41 96)(42 97)(43 98)(44 99)(45 100)(46 101)(47 102)(48 103)(49 104)(50 105)(51 106)(52 107)(53 108)(54 109)(55 110)(56 111)(57 189)(58 190)(59 191)(60 192)(61 193)(62 194)(63 195)(64 196)(65 169)(66 170)(67 171)(68 172)(69 173)(70 174)(71 175)(72 176)(73 177)(74 178)(75 179)(76 180)(77 181)(78 182)(79 183)(80 184)(81 185)(82 186)(83 187)(84 188)(113 167)(114 168)(115 141)(116 142)(117 143)(118 144)(119 145)(120 146)(121 147)(122 148)(123 149)(124 150)(125 151)(126 152)(127 153)(128 154)(129 155)(130 156)(131 157)(132 158)(133 159)(134 160)(135 161)(136 162)(137 163)(138 164)(139 165)(140 166)
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), (1,56,15,42)(2,55,16,41)(3,54,17,40)(4,53,18,39)(5,52,19,38)(6,51,20,37)(7,50,21,36)(8,49,22,35)(9,48,23,34)(10,47,24,33)(11,46,25,32)(12,45,26,31)(13,44,27,30)(14,43,28,29)(57,118,71,132)(58,117,72,131)(59,116,73,130)(60,115,74,129)(61,114,75,128)(62,113,76,127)(63,140,77,126)(64,139,78,125)(65,138,79,124)(66,137,80,123)(67,136,81,122)(68,135,82,121)(69,134,83,120)(70,133,84,119)(85,202,99,216)(86,201,100,215)(87,200,101,214)(88,199,102,213)(89,198,103,212)(90,197,104,211)(91,224,105,210)(92,223,106,209)(93,222,107,208)(94,221,108,207)(95,220,109,206)(96,219,110,205)(97,218,111,204)(98,217,112,203)(141,178,155,192)(142,177,156,191)(143,176,157,190)(144,175,158,189)(145,174,159,188)(146,173,160,187)(147,172,161,186)(148,171,162,185)(149,170,163,184)(150,169,164,183)(151,196,165,182)(152,195,166,181)(153,194,167,180)(154,193,168,179), (1,61,193,218)(2,74,194,203)(3,59,195,216)(4,72,196,201)(5,57,169,214)(6,70,170,199)(7,83,171,212)(8,68,172,197)(9,81,173,210)(10,66,174,223)(11,79,175,208)(12,64,176,221)(13,77,177,206)(14,62,178,219)(15,75,179,204)(16,60,180,217)(17,73,181,202)(18,58,182,215)(19,71,183,200)(20,84,184,213)(21,69,185,198)(22,82,186,211)(23,67,187,224)(24,80,188,209)(25,65,189,222)(26,78,190,207)(27,63,191,220)(28,76,192,205)(29,127,141,96)(30,140,142,109)(31,125,143,94)(32,138,144,107)(33,123,145,92)(34,136,146,105)(35,121,147,90)(36,134,148,103)(37,119,149,88)(38,132,150,101)(39,117,151,86)(40,130,152,99)(41,115,153,112)(42,128,154,97)(43,113,155,110)(44,126,156,95)(45,139,157,108)(46,124,158,93)(47,137,159,106)(48,122,160,91)(49,135,161,104)(50,120,162,89)(51,133,163,102)(52,118,164,87)(53,131,165,100)(54,116,166,85)(55,129,167,98)(56,114,168,111), (1,218)(2,219)(3,220)(4,221)(5,222)(6,223)(7,224)(8,197)(9,198)(10,199)(11,200)(12,201)(13,202)(14,203)(15,204)(16,205)(17,206)(18,207)(19,208)(20,209)(21,210)(22,211)(23,212)(24,213)(25,214)(26,215)(27,216)(28,217)(29,112)(30,85)(31,86)(32,87)(33,88)(34,89)(35,90)(36,91)(37,92)(38,93)(39,94)(40,95)(41,96)(42,97)(43,98)(44,99)(45,100)(46,101)(47,102)(48,103)(49,104)(50,105)(51,106)(52,107)(53,108)(54,109)(55,110)(56,111)(57,189)(58,190)(59,191)(60,192)(61,193)(62,194)(63,195)(64,196)(65,169)(66,170)(67,171)(68,172)(69,173)(70,174)(71,175)(72,176)(73,177)(74,178)(75,179)(76,180)(77,181)(78,182)(79,183)(80,184)(81,185)(82,186)(83,187)(84,188)(113,167)(114,168)(115,141)(116,142)(117,143)(118,144)(119,145)(120,146)(121,147)(122,148)(123,149)(124,150)(125,151)(126,152)(127,153)(128,154)(129,155)(130,156)(131,157)(132,158)(133,159)(134,160)(135,161)(136,162)(137,163)(138,164)(139,165)(140,166)>;
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), (1,56,15,42)(2,55,16,41)(3,54,17,40)(4,53,18,39)(5,52,19,38)(6,51,20,37)(7,50,21,36)(8,49,22,35)(9,48,23,34)(10,47,24,33)(11,46,25,32)(12,45,26,31)(13,44,27,30)(14,43,28,29)(57,118,71,132)(58,117,72,131)(59,116,73,130)(60,115,74,129)(61,114,75,128)(62,113,76,127)(63,140,77,126)(64,139,78,125)(65,138,79,124)(66,137,80,123)(67,136,81,122)(68,135,82,121)(69,134,83,120)(70,133,84,119)(85,202,99,216)(86,201,100,215)(87,200,101,214)(88,199,102,213)(89,198,103,212)(90,197,104,211)(91,224,105,210)(92,223,106,209)(93,222,107,208)(94,221,108,207)(95,220,109,206)(96,219,110,205)(97,218,111,204)(98,217,112,203)(141,178,155,192)(142,177,156,191)(143,176,157,190)(144,175,158,189)(145,174,159,188)(146,173,160,187)(147,172,161,186)(148,171,162,185)(149,170,163,184)(150,169,164,183)(151,196,165,182)(152,195,166,181)(153,194,167,180)(154,193,168,179), (1,61,193,218)(2,74,194,203)(3,59,195,216)(4,72,196,201)(5,57,169,214)(6,70,170,199)(7,83,171,212)(8,68,172,197)(9,81,173,210)(10,66,174,223)(11,79,175,208)(12,64,176,221)(13,77,177,206)(14,62,178,219)(15,75,179,204)(16,60,180,217)(17,73,181,202)(18,58,182,215)(19,71,183,200)(20,84,184,213)(21,69,185,198)(22,82,186,211)(23,67,187,224)(24,80,188,209)(25,65,189,222)(26,78,190,207)(27,63,191,220)(28,76,192,205)(29,127,141,96)(30,140,142,109)(31,125,143,94)(32,138,144,107)(33,123,145,92)(34,136,146,105)(35,121,147,90)(36,134,148,103)(37,119,149,88)(38,132,150,101)(39,117,151,86)(40,130,152,99)(41,115,153,112)(42,128,154,97)(43,113,155,110)(44,126,156,95)(45,139,157,108)(46,124,158,93)(47,137,159,106)(48,122,160,91)(49,135,161,104)(50,120,162,89)(51,133,163,102)(52,118,164,87)(53,131,165,100)(54,116,166,85)(55,129,167,98)(56,114,168,111), (1,218)(2,219)(3,220)(4,221)(5,222)(6,223)(7,224)(8,197)(9,198)(10,199)(11,200)(12,201)(13,202)(14,203)(15,204)(16,205)(17,206)(18,207)(19,208)(20,209)(21,210)(22,211)(23,212)(24,213)(25,214)(26,215)(27,216)(28,217)(29,112)(30,85)(31,86)(32,87)(33,88)(34,89)(35,90)(36,91)(37,92)(38,93)(39,94)(40,95)(41,96)(42,97)(43,98)(44,99)(45,100)(46,101)(47,102)(48,103)(49,104)(50,105)(51,106)(52,107)(53,108)(54,109)(55,110)(56,111)(57,189)(58,190)(59,191)(60,192)(61,193)(62,194)(63,195)(64,196)(65,169)(66,170)(67,171)(68,172)(69,173)(70,174)(71,175)(72,176)(73,177)(74,178)(75,179)(76,180)(77,181)(78,182)(79,183)(80,184)(81,185)(82,186)(83,187)(84,188)(113,167)(114,168)(115,141)(116,142)(117,143)(118,144)(119,145)(120,146)(121,147)(122,148)(123,149)(124,150)(125,151)(126,152)(127,153)(128,154)(129,155)(130,156)(131,157)(132,158)(133,159)(134,160)(135,161)(136,162)(137,163)(138,164)(139,165)(140,166) );
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)], [(1,56,15,42),(2,55,16,41),(3,54,17,40),(4,53,18,39),(5,52,19,38),(6,51,20,37),(7,50,21,36),(8,49,22,35),(9,48,23,34),(10,47,24,33),(11,46,25,32),(12,45,26,31),(13,44,27,30),(14,43,28,29),(57,118,71,132),(58,117,72,131),(59,116,73,130),(60,115,74,129),(61,114,75,128),(62,113,76,127),(63,140,77,126),(64,139,78,125),(65,138,79,124),(66,137,80,123),(67,136,81,122),(68,135,82,121),(69,134,83,120),(70,133,84,119),(85,202,99,216),(86,201,100,215),(87,200,101,214),(88,199,102,213),(89,198,103,212),(90,197,104,211),(91,224,105,210),(92,223,106,209),(93,222,107,208),(94,221,108,207),(95,220,109,206),(96,219,110,205),(97,218,111,204),(98,217,112,203),(141,178,155,192),(142,177,156,191),(143,176,157,190),(144,175,158,189),(145,174,159,188),(146,173,160,187),(147,172,161,186),(148,171,162,185),(149,170,163,184),(150,169,164,183),(151,196,165,182),(152,195,166,181),(153,194,167,180),(154,193,168,179)], [(1,61,193,218),(2,74,194,203),(3,59,195,216),(4,72,196,201),(5,57,169,214),(6,70,170,199),(7,83,171,212),(8,68,172,197),(9,81,173,210),(10,66,174,223),(11,79,175,208),(12,64,176,221),(13,77,177,206),(14,62,178,219),(15,75,179,204),(16,60,180,217),(17,73,181,202),(18,58,182,215),(19,71,183,200),(20,84,184,213),(21,69,185,198),(22,82,186,211),(23,67,187,224),(24,80,188,209),(25,65,189,222),(26,78,190,207),(27,63,191,220),(28,76,192,205),(29,127,141,96),(30,140,142,109),(31,125,143,94),(32,138,144,107),(33,123,145,92),(34,136,146,105),(35,121,147,90),(36,134,148,103),(37,119,149,88),(38,132,150,101),(39,117,151,86),(40,130,152,99),(41,115,153,112),(42,128,154,97),(43,113,155,110),(44,126,156,95),(45,139,157,108),(46,124,158,93),(47,137,159,106),(48,122,160,91),(49,135,161,104),(50,120,162,89),(51,133,163,102),(52,118,164,87),(53,131,165,100),(54,116,166,85),(55,129,167,98),(56,114,168,111)], [(1,218),(2,219),(3,220),(4,221),(5,222),(6,223),(7,224),(8,197),(9,198),(10,199),(11,200),(12,201),(13,202),(14,203),(15,204),(16,205),(17,206),(18,207),(19,208),(20,209),(21,210),(22,211),(23,212),(24,213),(25,214),(26,215),(27,216),(28,217),(29,112),(30,85),(31,86),(32,87),(33,88),(34,89),(35,90),(36,91),(37,92),(38,93),(39,94),(40,95),(41,96),(42,97),(43,98),(44,99),(45,100),(46,101),(47,102),(48,103),(49,104),(50,105),(51,106),(52,107),(53,108),(54,109),(55,110),(56,111),(57,189),(58,190),(59,191),(60,192),(61,193),(62,194),(63,195),(64,196),(65,169),(66,170),(67,171),(68,172),(69,173),(70,174),(71,175),(72,176),(73,177),(74,178),(75,179),(76,180),(77,181),(78,182),(79,183),(80,184),(81,185),(82,186),(83,187),(84,188),(113,167),(114,168),(115,141),(116,142),(117,143),(118,144),(119,145),(120,146),(121,147),(122,148),(123,149),(124,150),(125,151),(126,152),(127,153),(128,154),(129,155),(130,156),(131,157),(132,158),(133,159),(134,160),(135,161),(136,162),(137,163),(138,164),(139,165),(140,166)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 2 | 11 | 0 | 0 | 0 | 0 |
| 18 | 27 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 28 | 0 | 0 |
| 0 | 0 | 6 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 28 | 27 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 4 | 0 | 0 |
| 0 | 0 | 0 | 28 | 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 | 25 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 27 |
| 0 | 0 | 0 | 0 | 1 | 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 | 27 |
| 0 | 0 | 0 | 0 | 0 | 28 |
G:=sub<GL(6,GF(29))| [2,18,0,0,0,0,11,27,0,0,0,0,0,0,8,6,0,0,0,0,28,3,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,1,0,0,0,0,27,1,0,0,0,0,0,0,1,0,0,0,0,0,4,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,25,1,0,0,0,0,0,0,1,1,0,0,0,0,27,28],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,27,28] >;
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | ··· | 4G | 4H | ··· | 4M | 4N | 4O | 4P | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 14 | 14 | 2 | 2 | 4 | ··· | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 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 | Q8 | D7 | D14 | D14 | D14 | D14 | 2- (1+4) | D4×D7 | Q8×D7 | D4.10D14 |
| kernel | Dic14⋊21D4 | C22⋊Dic14 | Dic7⋊4D4 | Dic7⋊3Q8 | C28⋊Q8 | D14⋊Q8 | D14⋊2Q8 | C4×C7⋊D4 | Dic7⋊Q8 | C7×C22⋊Q8 | C22×Dic14 | C2×Q8×D7 | Dic14 | C7⋊D4 | C22⋊Q8 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×Q8 | C14 | C4 | C22 | C2 |
| # reps | 1 | 2 | 2 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 4 | 4 | 3 | 6 | 9 | 3 | 3 | 1 | 6 | 6 | 6 |
In GAP, Magma, Sage, TeX
Dic_{14}\rtimes_{21}D_4 % in TeX
G:=Group("Dic14:21D4"); // GroupNames label
G:=SmallGroup(448,1085);
// by ID
G=gap.SmallGroup(448,1085);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,100,570,185,80,18822]);
// 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^13,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d=c^-1>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀