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⋊2Q8⋊26C2, D14⋊Q8⋊19C2, (C2×C28).55C23, (C2×Q8).127D14, C22⋊C4.58D14, Dic7.24(C2×D4), C14.78(C22×D4), Dic7⋊3Q8⋊25C2, Dic7⋊Q8⋊15C2, 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×C28).256C22, (C22×C14).204C23, (C4×Dic7).106C22, (C2×Dic7).235C23, (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
Generators and relations for Dic14⋊21D4
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 >
Subgroups: 1212 in 280 conjugacy classes, 115 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, 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, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, C2×Q8, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C14, C4×D4, C4×Q8, C22⋊Q8, C22⋊Q8, C4⋊Q8, C22×Q8, Dic14, Dic14, C4×D7, C2×Dic7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×Q8, C22×D7, C22×C14, D4×Q8, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, D14⋊C4, D14⋊C4, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C2×Dic14, C2×C4×D7, C2×C4×D7, Q8×D7, C22×Dic7, C2×C7⋊D4, C22×C28, Q8×C14, 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⋊21D4
Quotients: C1, C2, C22, D4, Q8, C23, D7, C2×D4, C2×Q8, C24, D14, C22×D4, C22×Q8, 2- 1+4, C22×D7, D4×Q8, D4×D7, Q8×D7, C23×D7, C2×D4×D7, C2×Q8×D7, D4.10D14, Dic14⋊21D4
►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 32 15 46)(2 31 16 45)(3 30 17 44)(4 29 18 43)(5 56 19 42)(6 55 20 41)(7 54 21 40)(8 53 22 39)(9 52 23 38)(10 51 24 37)(11 50 25 36)(12 49 26 35)(13 48 27 34)(14 47 28 33)(57 160 71 146)(58 159 72 145)(59 158 73 144)(60 157 74 143)(61 156 75 142)(62 155 76 141)(63 154 77 168)(64 153 78 167)(65 152 79 166)(66 151 80 165)(67 150 81 164)(68 149 82 163)(69 148 83 162)(70 147 84 161)(85 135 99 121)(86 134 100 120)(87 133 101 119)(88 132 102 118)(89 131 103 117)(90 130 104 116)(91 129 105 115)(92 128 106 114)(93 127 107 113)(94 126 108 140)(95 125 109 139)(96 124 110 138)(97 123 111 137)(98 122 112 136)(169 211 183 197)(170 210 184 224)(171 209 185 223)(172 208 186 222)(173 207 187 221)(174 206 188 220)(175 205 189 219)(176 204 190 218)(177 203 191 217)(178 202 192 216)(179 201 193 215)(180 200 194 214)(181 199 195 213)(182 198 196 212)
(1 167 172 112)(2 152 173 97)(3 165 174 110)(4 150 175 95)(5 163 176 108)(6 148 177 93)(7 161 178 106)(8 146 179 91)(9 159 180 104)(10 144 181 89)(11 157 182 102)(12 142 183 87)(13 155 184 100)(14 168 185 85)(15 153 186 98)(16 166 187 111)(17 151 188 96)(18 164 189 109)(19 149 190 94)(20 162 191 107)(21 147 192 92)(22 160 193 105)(23 145 194 90)(24 158 195 103)(25 143 196 88)(26 156 169 101)(27 141 170 86)(28 154 171 99)(29 81 205 125)(30 66 206 138)(31 79 207 123)(32 64 208 136)(33 77 209 121)(34 62 210 134)(35 75 211 119)(36 60 212 132)(37 73 213 117)(38 58 214 130)(39 71 215 115)(40 84 216 128)(41 69 217 113)(42 82 218 126)(43 67 219 139)(44 80 220 124)(45 65 221 137)(46 78 222 122)(47 63 223 135)(48 76 224 120)(49 61 197 133)(50 74 198 118)(51 59 199 131)(52 72 200 116)(53 57 201 129)(54 70 202 114)(55 83 203 127)(56 68 204 140)
(1 112)(2 85)(3 86)(4 87)(5 88)(6 89)(7 90)(8 91)(9 92)(10 93)(11 94)(12 95)(13 96)(14 97)(15 98)(16 99)(17 100)(18 101)(19 102)(20 103)(21 104)(22 105)(23 106)(24 107)(25 108)(26 109)(27 110)(28 111)(29 133)(30 134)(31 135)(32 136)(33 137)(34 138)(35 139)(36 140)(37 113)(38 114)(39 115)(40 116)(41 117)(42 118)(43 119)(44 120)(45 121)(46 122)(47 123)(48 124)(49 125)(50 126)(51 127)(52 128)(53 129)(54 130)(55 131)(56 132)(57 201)(58 202)(59 203)(60 204)(61 205)(62 206)(63 207)(64 208)(65 209)(66 210)(67 211)(68 212)(69 213)(70 214)(71 215)(72 216)(73 217)(74 218)(75 219)(76 220)(77 221)(78 222)(79 223)(80 224)(81 197)(82 198)(83 199)(84 200)(141 174)(142 175)(143 176)(144 177)(145 178)(146 179)(147 180)(148 181)(149 182)(150 183)(151 184)(152 185)(153 186)(154 187)(155 188)(156 189)(157 190)(158 191)(159 192)(160 193)(161 194)(162 195)(163 196)(164 169)(165 170)(166 171)(167 172)(168 173)
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), (1,32,15,46)(2,31,16,45)(3,30,17,44)(4,29,18,43)(5,56,19,42)(6,55,20,41)(7,54,21,40)(8,53,22,39)(9,52,23,38)(10,51,24,37)(11,50,25,36)(12,49,26,35)(13,48,27,34)(14,47,28,33)(57,160,71,146)(58,159,72,145)(59,158,73,144)(60,157,74,143)(61,156,75,142)(62,155,76,141)(63,154,77,168)(64,153,78,167)(65,152,79,166)(66,151,80,165)(67,150,81,164)(68,149,82,163)(69,148,83,162)(70,147,84,161)(85,135,99,121)(86,134,100,120)(87,133,101,119)(88,132,102,118)(89,131,103,117)(90,130,104,116)(91,129,105,115)(92,128,106,114)(93,127,107,113)(94,126,108,140)(95,125,109,139)(96,124,110,138)(97,123,111,137)(98,122,112,136)(169,211,183,197)(170,210,184,224)(171,209,185,223)(172,208,186,222)(173,207,187,221)(174,206,188,220)(175,205,189,219)(176,204,190,218)(177,203,191,217)(178,202,192,216)(179,201,193,215)(180,200,194,214)(181,199,195,213)(182,198,196,212), (1,167,172,112)(2,152,173,97)(3,165,174,110)(4,150,175,95)(5,163,176,108)(6,148,177,93)(7,161,178,106)(8,146,179,91)(9,159,180,104)(10,144,181,89)(11,157,182,102)(12,142,183,87)(13,155,184,100)(14,168,185,85)(15,153,186,98)(16,166,187,111)(17,151,188,96)(18,164,189,109)(19,149,190,94)(20,162,191,107)(21,147,192,92)(22,160,193,105)(23,145,194,90)(24,158,195,103)(25,143,196,88)(26,156,169,101)(27,141,170,86)(28,154,171,99)(29,81,205,125)(30,66,206,138)(31,79,207,123)(32,64,208,136)(33,77,209,121)(34,62,210,134)(35,75,211,119)(36,60,212,132)(37,73,213,117)(38,58,214,130)(39,71,215,115)(40,84,216,128)(41,69,217,113)(42,82,218,126)(43,67,219,139)(44,80,220,124)(45,65,221,137)(46,78,222,122)(47,63,223,135)(48,76,224,120)(49,61,197,133)(50,74,198,118)(51,59,199,131)(52,72,200,116)(53,57,201,129)(54,70,202,114)(55,83,203,127)(56,68,204,140), (1,112)(2,85)(3,86)(4,87)(5,88)(6,89)(7,90)(8,91)(9,92)(10,93)(11,94)(12,95)(13,96)(14,97)(15,98)(16,99)(17,100)(18,101)(19,102)(20,103)(21,104)(22,105)(23,106)(24,107)(25,108)(26,109)(27,110)(28,111)(29,133)(30,134)(31,135)(32,136)(33,137)(34,138)(35,139)(36,140)(37,113)(38,114)(39,115)(40,116)(41,117)(42,118)(43,119)(44,120)(45,121)(46,122)(47,123)(48,124)(49,125)(50,126)(51,127)(52,128)(53,129)(54,130)(55,131)(56,132)(57,201)(58,202)(59,203)(60,204)(61,205)(62,206)(63,207)(64,208)(65,209)(66,210)(67,211)(68,212)(69,213)(70,214)(71,215)(72,216)(73,217)(74,218)(75,219)(76,220)(77,221)(78,222)(79,223)(80,224)(81,197)(82,198)(83,199)(84,200)(141,174)(142,175)(143,176)(144,177)(145,178)(146,179)(147,180)(148,181)(149,182)(150,183)(151,184)(152,185)(153,186)(154,187)(155,188)(156,189)(157,190)(158,191)(159,192)(160,193)(161,194)(162,195)(163,196)(164,169)(165,170)(166,171)(167,172)(168,173)>;
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), (1,32,15,46)(2,31,16,45)(3,30,17,44)(4,29,18,43)(5,56,19,42)(6,55,20,41)(7,54,21,40)(8,53,22,39)(9,52,23,38)(10,51,24,37)(11,50,25,36)(12,49,26,35)(13,48,27,34)(14,47,28,33)(57,160,71,146)(58,159,72,145)(59,158,73,144)(60,157,74,143)(61,156,75,142)(62,155,76,141)(63,154,77,168)(64,153,78,167)(65,152,79,166)(66,151,80,165)(67,150,81,164)(68,149,82,163)(69,148,83,162)(70,147,84,161)(85,135,99,121)(86,134,100,120)(87,133,101,119)(88,132,102,118)(89,131,103,117)(90,130,104,116)(91,129,105,115)(92,128,106,114)(93,127,107,113)(94,126,108,140)(95,125,109,139)(96,124,110,138)(97,123,111,137)(98,122,112,136)(169,211,183,197)(170,210,184,224)(171,209,185,223)(172,208,186,222)(173,207,187,221)(174,206,188,220)(175,205,189,219)(176,204,190,218)(177,203,191,217)(178,202,192,216)(179,201,193,215)(180,200,194,214)(181,199,195,213)(182,198,196,212), (1,167,172,112)(2,152,173,97)(3,165,174,110)(4,150,175,95)(5,163,176,108)(6,148,177,93)(7,161,178,106)(8,146,179,91)(9,159,180,104)(10,144,181,89)(11,157,182,102)(12,142,183,87)(13,155,184,100)(14,168,185,85)(15,153,186,98)(16,166,187,111)(17,151,188,96)(18,164,189,109)(19,149,190,94)(20,162,191,107)(21,147,192,92)(22,160,193,105)(23,145,194,90)(24,158,195,103)(25,143,196,88)(26,156,169,101)(27,141,170,86)(28,154,171,99)(29,81,205,125)(30,66,206,138)(31,79,207,123)(32,64,208,136)(33,77,209,121)(34,62,210,134)(35,75,211,119)(36,60,212,132)(37,73,213,117)(38,58,214,130)(39,71,215,115)(40,84,216,128)(41,69,217,113)(42,82,218,126)(43,67,219,139)(44,80,220,124)(45,65,221,137)(46,78,222,122)(47,63,223,135)(48,76,224,120)(49,61,197,133)(50,74,198,118)(51,59,199,131)(52,72,200,116)(53,57,201,129)(54,70,202,114)(55,83,203,127)(56,68,204,140), (1,112)(2,85)(3,86)(4,87)(5,88)(6,89)(7,90)(8,91)(9,92)(10,93)(11,94)(12,95)(13,96)(14,97)(15,98)(16,99)(17,100)(18,101)(19,102)(20,103)(21,104)(22,105)(23,106)(24,107)(25,108)(26,109)(27,110)(28,111)(29,133)(30,134)(31,135)(32,136)(33,137)(34,138)(35,139)(36,140)(37,113)(38,114)(39,115)(40,116)(41,117)(42,118)(43,119)(44,120)(45,121)(46,122)(47,123)(48,124)(49,125)(50,126)(51,127)(52,128)(53,129)(54,130)(55,131)(56,132)(57,201)(58,202)(59,203)(60,204)(61,205)(62,206)(63,207)(64,208)(65,209)(66,210)(67,211)(68,212)(69,213)(70,214)(71,215)(72,216)(73,217)(74,218)(75,219)(76,220)(77,221)(78,222)(79,223)(80,224)(81,197)(82,198)(83,199)(84,200)(141,174)(142,175)(143,176)(144,177)(145,178)(146,179)(147,180)(148,181)(149,182)(150,183)(151,184)(152,185)(153,186)(154,187)(155,188)(156,189)(157,190)(158,191)(159,192)(160,193)(161,194)(162,195)(163,196)(164,169)(165,170)(166,171)(167,172)(168,173) );
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)], [(1,32,15,46),(2,31,16,45),(3,30,17,44),(4,29,18,43),(5,56,19,42),(6,55,20,41),(7,54,21,40),(8,53,22,39),(9,52,23,38),(10,51,24,37),(11,50,25,36),(12,49,26,35),(13,48,27,34),(14,47,28,33),(57,160,71,146),(58,159,72,145),(59,158,73,144),(60,157,74,143),(61,156,75,142),(62,155,76,141),(63,154,77,168),(64,153,78,167),(65,152,79,166),(66,151,80,165),(67,150,81,164),(68,149,82,163),(69,148,83,162),(70,147,84,161),(85,135,99,121),(86,134,100,120),(87,133,101,119),(88,132,102,118),(89,131,103,117),(90,130,104,116),(91,129,105,115),(92,128,106,114),(93,127,107,113),(94,126,108,140),(95,125,109,139),(96,124,110,138),(97,123,111,137),(98,122,112,136),(169,211,183,197),(170,210,184,224),(171,209,185,223),(172,208,186,222),(173,207,187,221),(174,206,188,220),(175,205,189,219),(176,204,190,218),(177,203,191,217),(178,202,192,216),(179,201,193,215),(180,200,194,214),(181,199,195,213),(182,198,196,212)], [(1,167,172,112),(2,152,173,97),(3,165,174,110),(4,150,175,95),(5,163,176,108),(6,148,177,93),(7,161,178,106),(8,146,179,91),(9,159,180,104),(10,144,181,89),(11,157,182,102),(12,142,183,87),(13,155,184,100),(14,168,185,85),(15,153,186,98),(16,166,187,111),(17,151,188,96),(18,164,189,109),(19,149,190,94),(20,162,191,107),(21,147,192,92),(22,160,193,105),(23,145,194,90),(24,158,195,103),(25,143,196,88),(26,156,169,101),(27,141,170,86),(28,154,171,99),(29,81,205,125),(30,66,206,138),(31,79,207,123),(32,64,208,136),(33,77,209,121),(34,62,210,134),(35,75,211,119),(36,60,212,132),(37,73,213,117),(38,58,214,130),(39,71,215,115),(40,84,216,128),(41,69,217,113),(42,82,218,126),(43,67,219,139),(44,80,220,124),(45,65,221,137),(46,78,222,122),(47,63,223,135),(48,76,224,120),(49,61,197,133),(50,74,198,118),(51,59,199,131),(52,72,200,116),(53,57,201,129),(54,70,202,114),(55,83,203,127),(56,68,204,140)], [(1,112),(2,85),(3,86),(4,87),(5,88),(6,89),(7,90),(8,91),(9,92),(10,93),(11,94),(12,95),(13,96),(14,97),(15,98),(16,99),(17,100),(18,101),(19,102),(20,103),(21,104),(22,105),(23,106),(24,107),(25,108),(26,109),(27,110),(28,111),(29,133),(30,134),(31,135),(32,136),(33,137),(34,138),(35,139),(36,140),(37,113),(38,114),(39,115),(40,116),(41,117),(42,118),(43,119),(44,120),(45,121),(46,122),(47,123),(48,124),(49,125),(50,126),(51,127),(52,128),(53,129),(54,130),(55,131),(56,132),(57,201),(58,202),(59,203),(60,204),(61,205),(62,206),(63,207),(64,208),(65,209),(66,210),(67,211),(68,212),(69,213),(70,214),(71,215),(72,216),(73,217),(74,218),(75,219),(76,220),(77,221),(78,222),(79,223),(80,224),(81,197),(82,198),(83,199),(84,200),(141,174),(142,175),(143,176),(144,177),(145,178),(146,179),(147,180),(148,181),(149,182),(150,183),(151,184),(152,185),(153,186),(154,187),(155,188),(156,189),(157,190),(158,191),(159,192),(160,193),(161,194),(162,195),(163,196),(164,169),(165,170),(166,171),(167,172),(168,173)]])
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 |
Matrix representation of Dic14⋊21D4 ►in 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] >;
Dic14⋊21D4 in GAP, Magma, Sage, TeX
{\rm 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