metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic14⋊10D4, C42.142D14, C14.912- 1+4, C4.71(D4×D7), (C4×D28)⋊44C2, C7⋊5(Q8⋊5D4), C28.64(C2×D4), C28⋊2D4⋊34C2, C4.4D4⋊11D7, D14⋊15(C4○D4), D14⋊D4⋊41C2, D14⋊3Q8⋊29C2, (C4×Dic14)⋊45C2, (C2×D4).174D14, (C2×C28).81C23, (C2×Q8).137D14, C22⋊C4.73D14, Dic7.28(C2×D4), C14.91(C22×D4), Dic7⋊4D4⋊30C2, (C4×C28).186C22, (C2×C14).221C24, C23.43(C22×D7), D14⋊C4.135C22, C22⋊Dic14⋊41C2, Dic7.D4⋊40C2, (D4×C14).156C22, (C2×D28).223C22, C4⋊Dic7.377C22, (C22×C14).51C23, (Q8×C14).127C22, C22.242(C23×D7), C23.D7.55C22, Dic7⋊C4.121C22, (C4×Dic7).214C22, (C2×Dic7).253C23, (C22×D7).216C23, C2.52(D4.10D14), (C2×Dic14).297C22, (C22×Dic7).143C22, (C2×Q8×D7)⋊11C2, C2.64(C2×D4×D7), C2.77(D7×C4○D4), (C2×D4⋊2D7)⋊19C2, C14.188(C2×C4○D4), (C7×C4.4D4)⋊13C2, (C2×C4×D7).121C22, (C2×C4).196(C22×D7), (C2×C7⋊D4).60C22, (C7×C22⋊C4).65C22, SmallGroup(448,1130)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic14⋊10D4
G = < a,b,c,d | a28=c4=d2=1, b2=a14, bab-1=a-1, ac=ca, dad=a13, cbc-1=dbd=a14b, dcd=c-1 >
Subgroups: 1356 in 290 conjugacy classes, 105 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C4.4D4, C4.4D4, C22×Q8, C2×C4○D4, Dic14, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C7×Q8, C22×D7, C22×C14, Q8⋊5D4, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C2×Dic14, C2×Dic14, C2×C4×D7, C2×C4×D7, C2×D28, D4⋊2D7, Q8×D7, C22×Dic7, C2×C7⋊D4, D4×C14, Q8×C14, C4×Dic14, C4×D28, C22⋊Dic14, Dic7⋊4D4, D14⋊D4, Dic7.D4, C28⋊2D4, D14⋊3Q8, C7×C4.4D4, C2×D4⋊2D7, C2×Q8×D7, Dic14⋊10D4
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, C23×D7, C2×D4×D7, D7×C4○D4, D4.10D14, Dic14⋊10D4
►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)
(1 215 15 201)(2 214 16 200)(3 213 17 199)(4 212 18 198)(5 211 19 197)(6 210 20 224)(7 209 21 223)(8 208 22 222)(9 207 23 221)(10 206 24 220)(11 205 25 219)(12 204 26 218)(13 203 27 217)(14 202 28 216)(29 102 43 88)(30 101 44 87)(31 100 45 86)(32 99 46 85)(33 98 47 112)(34 97 48 111)(35 96 49 110)(36 95 50 109)(37 94 51 108)(38 93 52 107)(39 92 53 106)(40 91 54 105)(41 90 55 104)(42 89 56 103)(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)(113 186 127 172)(114 185 128 171)(115 184 129 170)(116 183 130 169)(117 182 131 196)(118 181 132 195)(119 180 133 194)(120 179 134 193)(121 178 135 192)(122 177 136 191)(123 176 137 190)(124 175 138 189)(125 174 139 188)(126 173 140 187)
(1 84 97 123)(2 57 98 124)(3 58 99 125)(4 59 100 126)(5 60 101 127)(6 61 102 128)(7 62 103 129)(8 63 104 130)(9 64 105 131)(10 65 106 132)(11 66 107 133)(12 67 108 134)(13 68 109 135)(14 69 110 136)(15 70 111 137)(16 71 112 138)(17 72 85 139)(18 73 86 140)(19 74 87 113)(20 75 88 114)(21 76 89 115)(22 77 90 116)(23 78 91 117)(24 79 92 118)(25 80 93 119)(26 81 94 120)(27 82 95 121)(28 83 96 122)(29 171 224 156)(30 172 197 157)(31 173 198 158)(32 174 199 159)(33 175 200 160)(34 176 201 161)(35 177 202 162)(36 178 203 163)(37 179 204 164)(38 180 205 165)(39 181 206 166)(40 182 207 167)(41 183 208 168)(42 184 209 141)(43 185 210 142)(44 186 211 143)(45 187 212 144)(46 188 213 145)(47 189 214 146)(48 190 215 147)(49 191 216 148)(50 192 217 149)(51 193 218 150)(52 194 219 151)(53 195 220 152)(54 196 221 153)(55 169 222 154)(56 170 223 155)
(1 70)(2 83)(3 68)(4 81)(5 66)(6 79)(7 64)(8 77)(9 62)(10 75)(11 60)(12 73)(13 58)(14 71)(15 84)(16 69)(17 82)(18 67)(19 80)(20 65)(21 78)(22 63)(23 76)(24 61)(25 74)(26 59)(27 72)(28 57)(29 181)(30 194)(31 179)(32 192)(33 177)(34 190)(35 175)(36 188)(37 173)(38 186)(39 171)(40 184)(41 169)(42 182)(43 195)(44 180)(45 193)(46 178)(47 191)(48 176)(49 189)(50 174)(51 187)(52 172)(53 185)(54 170)(55 183)(56 196)(85 121)(86 134)(87 119)(88 132)(89 117)(90 130)(91 115)(92 128)(93 113)(94 126)(95 139)(96 124)(97 137)(98 122)(99 135)(100 120)(101 133)(102 118)(103 131)(104 116)(105 129)(106 114)(107 127)(108 140)(109 125)(110 138)(111 123)(112 136)(141 207)(142 220)(143 205)(144 218)(145 203)(146 216)(147 201)(148 214)(149 199)(150 212)(151 197)(152 210)(153 223)(154 208)(155 221)(156 206)(157 219)(158 204)(159 217)(160 202)(161 215)(162 200)(163 213)(164 198)(165 211)(166 224)(167 209)(168 222)
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), (1,215,15,201)(2,214,16,200)(3,213,17,199)(4,212,18,198)(5,211,19,197)(6,210,20,224)(7,209,21,223)(8,208,22,222)(9,207,23,221)(10,206,24,220)(11,205,25,219)(12,204,26,218)(13,203,27,217)(14,202,28,216)(29,102,43,88)(30,101,44,87)(31,100,45,86)(32,99,46,85)(33,98,47,112)(34,97,48,111)(35,96,49,110)(36,95,50,109)(37,94,51,108)(38,93,52,107)(39,92,53,106)(40,91,54,105)(41,90,55,104)(42,89,56,103)(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)(113,186,127,172)(114,185,128,171)(115,184,129,170)(116,183,130,169)(117,182,131,196)(118,181,132,195)(119,180,133,194)(120,179,134,193)(121,178,135,192)(122,177,136,191)(123,176,137,190)(124,175,138,189)(125,174,139,188)(126,173,140,187), (1,84,97,123)(2,57,98,124)(3,58,99,125)(4,59,100,126)(5,60,101,127)(6,61,102,128)(7,62,103,129)(8,63,104,130)(9,64,105,131)(10,65,106,132)(11,66,107,133)(12,67,108,134)(13,68,109,135)(14,69,110,136)(15,70,111,137)(16,71,112,138)(17,72,85,139)(18,73,86,140)(19,74,87,113)(20,75,88,114)(21,76,89,115)(22,77,90,116)(23,78,91,117)(24,79,92,118)(25,80,93,119)(26,81,94,120)(27,82,95,121)(28,83,96,122)(29,171,224,156)(30,172,197,157)(31,173,198,158)(32,174,199,159)(33,175,200,160)(34,176,201,161)(35,177,202,162)(36,178,203,163)(37,179,204,164)(38,180,205,165)(39,181,206,166)(40,182,207,167)(41,183,208,168)(42,184,209,141)(43,185,210,142)(44,186,211,143)(45,187,212,144)(46,188,213,145)(47,189,214,146)(48,190,215,147)(49,191,216,148)(50,192,217,149)(51,193,218,150)(52,194,219,151)(53,195,220,152)(54,196,221,153)(55,169,222,154)(56,170,223,155), (1,70)(2,83)(3,68)(4,81)(5,66)(6,79)(7,64)(8,77)(9,62)(10,75)(11,60)(12,73)(13,58)(14,71)(15,84)(16,69)(17,82)(18,67)(19,80)(20,65)(21,78)(22,63)(23,76)(24,61)(25,74)(26,59)(27,72)(28,57)(29,181)(30,194)(31,179)(32,192)(33,177)(34,190)(35,175)(36,188)(37,173)(38,186)(39,171)(40,184)(41,169)(42,182)(43,195)(44,180)(45,193)(46,178)(47,191)(48,176)(49,189)(50,174)(51,187)(52,172)(53,185)(54,170)(55,183)(56,196)(85,121)(86,134)(87,119)(88,132)(89,117)(90,130)(91,115)(92,128)(93,113)(94,126)(95,139)(96,124)(97,137)(98,122)(99,135)(100,120)(101,133)(102,118)(103,131)(104,116)(105,129)(106,114)(107,127)(108,140)(109,125)(110,138)(111,123)(112,136)(141,207)(142,220)(143,205)(144,218)(145,203)(146,216)(147,201)(148,214)(149,199)(150,212)(151,197)(152,210)(153,223)(154,208)(155,221)(156,206)(157,219)(158,204)(159,217)(160,202)(161,215)(162,200)(163,213)(164,198)(165,211)(166,224)(167,209)(168,222)>;
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), (1,215,15,201)(2,214,16,200)(3,213,17,199)(4,212,18,198)(5,211,19,197)(6,210,20,224)(7,209,21,223)(8,208,22,222)(9,207,23,221)(10,206,24,220)(11,205,25,219)(12,204,26,218)(13,203,27,217)(14,202,28,216)(29,102,43,88)(30,101,44,87)(31,100,45,86)(32,99,46,85)(33,98,47,112)(34,97,48,111)(35,96,49,110)(36,95,50,109)(37,94,51,108)(38,93,52,107)(39,92,53,106)(40,91,54,105)(41,90,55,104)(42,89,56,103)(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)(113,186,127,172)(114,185,128,171)(115,184,129,170)(116,183,130,169)(117,182,131,196)(118,181,132,195)(119,180,133,194)(120,179,134,193)(121,178,135,192)(122,177,136,191)(123,176,137,190)(124,175,138,189)(125,174,139,188)(126,173,140,187), (1,84,97,123)(2,57,98,124)(3,58,99,125)(4,59,100,126)(5,60,101,127)(6,61,102,128)(7,62,103,129)(8,63,104,130)(9,64,105,131)(10,65,106,132)(11,66,107,133)(12,67,108,134)(13,68,109,135)(14,69,110,136)(15,70,111,137)(16,71,112,138)(17,72,85,139)(18,73,86,140)(19,74,87,113)(20,75,88,114)(21,76,89,115)(22,77,90,116)(23,78,91,117)(24,79,92,118)(25,80,93,119)(26,81,94,120)(27,82,95,121)(28,83,96,122)(29,171,224,156)(30,172,197,157)(31,173,198,158)(32,174,199,159)(33,175,200,160)(34,176,201,161)(35,177,202,162)(36,178,203,163)(37,179,204,164)(38,180,205,165)(39,181,206,166)(40,182,207,167)(41,183,208,168)(42,184,209,141)(43,185,210,142)(44,186,211,143)(45,187,212,144)(46,188,213,145)(47,189,214,146)(48,190,215,147)(49,191,216,148)(50,192,217,149)(51,193,218,150)(52,194,219,151)(53,195,220,152)(54,196,221,153)(55,169,222,154)(56,170,223,155), (1,70)(2,83)(3,68)(4,81)(5,66)(6,79)(7,64)(8,77)(9,62)(10,75)(11,60)(12,73)(13,58)(14,71)(15,84)(16,69)(17,82)(18,67)(19,80)(20,65)(21,78)(22,63)(23,76)(24,61)(25,74)(26,59)(27,72)(28,57)(29,181)(30,194)(31,179)(32,192)(33,177)(34,190)(35,175)(36,188)(37,173)(38,186)(39,171)(40,184)(41,169)(42,182)(43,195)(44,180)(45,193)(46,178)(47,191)(48,176)(49,189)(50,174)(51,187)(52,172)(53,185)(54,170)(55,183)(56,196)(85,121)(86,134)(87,119)(88,132)(89,117)(90,130)(91,115)(92,128)(93,113)(94,126)(95,139)(96,124)(97,137)(98,122)(99,135)(100,120)(101,133)(102,118)(103,131)(104,116)(105,129)(106,114)(107,127)(108,140)(109,125)(110,138)(111,123)(112,136)(141,207)(142,220)(143,205)(144,218)(145,203)(146,216)(147,201)(148,214)(149,199)(150,212)(151,197)(152,210)(153,223)(154,208)(155,221)(156,206)(157,219)(158,204)(159,217)(160,202)(161,215)(162,200)(163,213)(164,198)(165,211)(166,224)(167,209)(168,222) );
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)], [(1,215,15,201),(2,214,16,200),(3,213,17,199),(4,212,18,198),(5,211,19,197),(6,210,20,224),(7,209,21,223),(8,208,22,222),(9,207,23,221),(10,206,24,220),(11,205,25,219),(12,204,26,218),(13,203,27,217),(14,202,28,216),(29,102,43,88),(30,101,44,87),(31,100,45,86),(32,99,46,85),(33,98,47,112),(34,97,48,111),(35,96,49,110),(36,95,50,109),(37,94,51,108),(38,93,52,107),(39,92,53,106),(40,91,54,105),(41,90,55,104),(42,89,56,103),(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),(113,186,127,172),(114,185,128,171),(115,184,129,170),(116,183,130,169),(117,182,131,196),(118,181,132,195),(119,180,133,194),(120,179,134,193),(121,178,135,192),(122,177,136,191),(123,176,137,190),(124,175,138,189),(125,174,139,188),(126,173,140,187)], [(1,84,97,123),(2,57,98,124),(3,58,99,125),(4,59,100,126),(5,60,101,127),(6,61,102,128),(7,62,103,129),(8,63,104,130),(9,64,105,131),(10,65,106,132),(11,66,107,133),(12,67,108,134),(13,68,109,135),(14,69,110,136),(15,70,111,137),(16,71,112,138),(17,72,85,139),(18,73,86,140),(19,74,87,113),(20,75,88,114),(21,76,89,115),(22,77,90,116),(23,78,91,117),(24,79,92,118),(25,80,93,119),(26,81,94,120),(27,82,95,121),(28,83,96,122),(29,171,224,156),(30,172,197,157),(31,173,198,158),(32,174,199,159),(33,175,200,160),(34,176,201,161),(35,177,202,162),(36,178,203,163),(37,179,204,164),(38,180,205,165),(39,181,206,166),(40,182,207,167),(41,183,208,168),(42,184,209,141),(43,185,210,142),(44,186,211,143),(45,187,212,144),(46,188,213,145),(47,189,214,146),(48,190,215,147),(49,191,216,148),(50,192,217,149),(51,193,218,150),(52,194,219,151),(53,195,220,152),(54,196,221,153),(55,169,222,154),(56,170,223,155)], [(1,70),(2,83),(3,68),(4,81),(5,66),(6,79),(7,64),(8,77),(9,62),(10,75),(11,60),(12,73),(13,58),(14,71),(15,84),(16,69),(17,82),(18,67),(19,80),(20,65),(21,78),(22,63),(23,76),(24,61),(25,74),(26,59),(27,72),(28,57),(29,181),(30,194),(31,179),(32,192),(33,177),(34,190),(35,175),(36,188),(37,173),(38,186),(39,171),(40,184),(41,169),(42,182),(43,195),(44,180),(45,193),(46,178),(47,191),(48,176),(49,189),(50,174),(51,187),(52,172),(53,185),(54,170),(55,183),(56,196),(85,121),(86,134),(87,119),(88,132),(89,117),(90,130),(91,115),(92,128),(93,113),(94,126),(95,139),(96,124),(97,137),(98,122),(99,135),(100,120),(101,133),(102,118),(103,131),(104,116),(105,129),(106,114),(107,127),(108,140),(109,125),(110,138),(111,123),(112,136),(141,207),(142,220),(143,205),(144,218),(145,203),(146,216),(147,201),(148,214),(149,199),(150,212),(151,197),(152,210),(153,223),(154,208),(155,221),(156,206),(157,219),(158,204),(159,217),(160,202),(161,215),(162,200),(163,213),(164,198),(165,211),(166,224),(167,209),(168,222)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | ··· | 4M | 4N | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| order | 1 | 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 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 14 | 14 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 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 | D7×C4○D4 | D4.10D14 |
| kernel | Dic14⋊10D4 | C4×Dic14 | C4×D28 | C22⋊Dic14 | Dic7⋊4D4 | D14⋊D4 | Dic7.D4 | C28⋊2D4 | D14⋊3Q8 | C7×C4.4D4 | C2×D4⋊2D7 | C2×Q8×D7 | Dic14 | C4.4D4 | D14 | C42 | C22⋊C4 | C2×D4 | C2×Q8 | C14 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 4 | 3 | 4 | 3 | 12 | 3 | 3 | 1 | 6 | 6 | 6 |
Matrix representation of Dic14⋊10D4 ►in GL6(𝔽29)
| 17 | 0 | 0 | 0 | 0 | 0 |
| 2 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 1 | 0 | 0 |
| 0 | 0 | 27 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 26 | 22 | 0 | 0 | 0 | 0 |
| 18 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 3 | 0 | 0 |
| 0 | 0 | 24 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 5 | 1 | 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 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 24 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 3 | 0 | 0 |
| 0 | 0 | 24 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
G:=sub<GL(6,GF(29))| [17,2,0,0,0,0,0,12,0,0,0,0,0,0,11,27,0,0,0,0,1,21,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[26,18,0,0,0,0,22,3,0,0,0,0,0,0,25,24,0,0,0,0,3,4,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,5,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,0,1,0,0,0,0,28,0],[1,24,0,0,0,0,0,28,0,0,0,0,0,0,25,24,0,0,0,0,3,4,0,0,0,0,0,0,0,1,0,0,0,0,1,0] >;
Dic14⋊10D4 in GAP, Magma, Sage, TeX
{\rm Dic}_{14}\rtimes_{10}D_4 % in TeX
G:=Group("Dic14:10D4"); // GroupNames label
G:=SmallGroup(448,1130);
// by ID
G=gap.SmallGroup(448,1130);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,100,1571,297,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=c^4=d^2=1,b^2=a^14,b*a*b^-1=a^-1,a*c=c*a,d*a*d=a^13,c*b*c^-1=d*b*d=a^14*b,d*c*d=c^-1>;
// generators/relations