metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14⋊C4⋊6C4, D14⋊4(C4⋊C4), C14.68(C4×D4), (C2×C28).251D4, C14.41C22≀C2, C22.27(Q8×D7), (C22×D7).89D4, (C22×C4).42D14, C22.112(D4×D7), (C22×D7).10Q8, C2.4(C23⋊D14), C7⋊4(C23.8Q8), C2.4(D14⋊3Q8), C2.7(D14⋊Q8), (C2×Dic7).177D4, C14.49(C22⋊Q8), C2.19(D28⋊C4), C14.C42⋊40C2, C2.6(D14.5D4), C22.58(C4○D28), (C23×D7).90C22, C23.297(C22×D7), (C22×C28).347C22, (C22×C14).353C23, C22.29(Q8⋊2D7), C14.51(C22.D4), (C22×Dic7).59C22, (C2×C4⋊C4)⋊7D7, (C2×C4)⋊4(C4×D7), (C14×C4⋊C4)⋊24C2, C2.22(D7×C4⋊C4), (C2×C28)⋊21(C2×C4), C14.21(C2×C4⋊C4), C2.13(C4×C7⋊D4), (C2×Dic7)⋊7(C2×C4), (C2×C14).84(C2×Q8), (D7×C22×C4).19C2, C22.138(C2×C4×D7), (C2×Dic7⋊C4)⋊13C2, (C2×D14⋊C4).12C2, (C2×C14).334(C2×D4), C22.68(C2×C7⋊D4), (C2×C4).169(C7⋊D4), (C22×D7).42(C2×C4), (C2×C14).190(C4○D4), (C2×C14).121(C22×C4), SmallGroup(448,523)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14⋊C4⋊6C4
G = < a,b,c,d | a14=b2=c4=d4=1, bab=a-1, ac=ca, ad=da, cbc-1=a7b, bd=db, dcd-1=c-1 >
Subgroups: 1156 in 234 conjugacy classes, 77 normal (51 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, C23, C23, D7, C14, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C24, Dic7, C28, D14, D14, C2×C14, C2.C42, C2×C22⋊C4, C2×C4⋊C4, C2×C4⋊C4, C23×C4, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C23.8Q8, Dic7⋊C4, D14⋊C4, D14⋊C4, C7×C4⋊C4, C2×C4×D7, C22×Dic7, C22×C28, C23×D7, C14.C42, C2×Dic7⋊C4, C2×D14⋊C4, C14×C4⋊C4, D7×C22×C4, D14⋊C4⋊6C4
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D7, C4⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, D14, C2×C4⋊C4, C4×D4, C22≀C2, C22⋊Q8, C22.D4, C4×D7, C7⋊D4, C22×D7, C23.8Q8, C2×C4×D7, C4○D28, D4×D7, Q8×D7, Q8⋊2D7, C2×C7⋊D4, D7×C4⋊C4, D28⋊C4, D14.5D4, D14⋊Q8, C4×C7⋊D4, C23⋊D14, D14⋊3Q8, D14⋊C4⋊6C4
►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 14)(2 13)(3 12)(4 11)(5 10)(6 9)(7 8)(15 17)(18 28)(19 27)(20 26)(21 25)(22 24)(29 34)(30 33)(31 32)(35 42)(36 41)(37 40)(38 39)(43 51)(44 50)(45 49)(46 48)(52 56)(53 55)(57 58)(59 70)(60 69)(61 68)(62 67)(63 66)(64 65)(71 77)(72 76)(73 75)(78 84)(79 83)(80 82)(85 91)(86 90)(87 89)(92 98)(93 97)(94 96)(99 100)(101 112)(102 111)(103 110)(104 109)(105 108)(106 107)(113 122)(114 121)(115 120)(116 119)(117 118)(123 126)(124 125)(127 139)(128 138)(129 137)(130 136)(131 135)(132 134)(141 147)(142 146)(143 145)(148 154)(149 153)(150 152)(155 168)(156 167)(157 166)(158 165)(159 164)(160 163)(161 162)(169 174)(170 173)(171 172)(175 182)(176 181)(177 180)(178 179)(183 187)(184 186)(188 196)(189 195)(190 194)(191 193)(197 208)(198 207)(199 206)(200 205)(201 204)(202 203)(209 210)(211 213)(214 224)(215 223)(216 222)(217 221)(218 220)
(1 130 32 189)(2 131 33 190)(3 132 34 191)(4 133 35 192)(5 134 36 193)(6 135 37 194)(7 136 38 195)(8 137 39 196)(9 138 40 183)(10 139 41 184)(11 140 42 185)(12 127 29 186)(13 128 30 187)(14 129 31 188)(15 198 87 174)(16 199 88 175)(17 200 89 176)(18 201 90 177)(19 202 91 178)(20 203 92 179)(21 204 93 180)(22 205 94 181)(23 206 95 182)(24 207 96 169)(25 208 97 170)(26 209 98 171)(27 210 85 172)(28 197 86 173)(43 57 222 117)(44 58 223 118)(45 59 224 119)(46 60 211 120)(47 61 212 121)(48 62 213 122)(49 63 214 123)(50 64 215 124)(51 65 216 125)(52 66 217 126)(53 67 218 113)(54 68 219 114)(55 69 220 115)(56 70 221 116)(71 107 148 155)(72 108 149 156)(73 109 150 157)(74 110 151 158)(75 111 152 159)(76 112 153 160)(77 99 154 161)(78 100 141 162)(79 101 142 163)(80 102 143 164)(81 103 144 165)(82 104 145 166)(83 105 146 167)(84 106 147 168)
(1 125 203 155)(2 126 204 156)(3 113 205 157)(4 114 206 158)(5 115 207 159)(6 116 208 160)(7 117 209 161)(8 118 210 162)(9 119 197 163)(10 120 198 164)(11 121 199 165)(12 122 200 166)(13 123 201 167)(14 124 202 168)(15 80 184 46)(16 81 185 47)(17 82 186 48)(18 83 187 49)(19 84 188 50)(20 71 189 51)(21 72 190 52)(22 73 191 53)(23 74 192 54)(24 75 193 55)(25 76 194 56)(26 77 195 43)(27 78 196 44)(28 79 183 45)(29 62 176 104)(30 63 177 105)(31 64 178 106)(32 65 179 107)(33 66 180 108)(34 67 181 109)(35 68 182 110)(36 69 169 111)(37 70 170 112)(38 57 171 99)(39 58 172 100)(40 59 173 101)(41 60 174 102)(42 61 175 103)(85 141 137 223)(86 142 138 224)(87 143 139 211)(88 144 140 212)(89 145 127 213)(90 146 128 214)(91 147 129 215)(92 148 130 216)(93 149 131 217)(94 150 132 218)(95 151 133 219)(96 152 134 220)(97 153 135 221)(98 154 136 222)
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), (1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,17)(18,28)(19,27)(20,26)(21,25)(22,24)(29,34)(30,33)(31,32)(35,42)(36,41)(37,40)(38,39)(43,51)(44,50)(45,49)(46,48)(52,56)(53,55)(57,58)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)(71,77)(72,76)(73,75)(78,84)(79,83)(80,82)(85,91)(86,90)(87,89)(92,98)(93,97)(94,96)(99,100)(101,112)(102,111)(103,110)(104,109)(105,108)(106,107)(113,122)(114,121)(115,120)(116,119)(117,118)(123,126)(124,125)(127,139)(128,138)(129,137)(130,136)(131,135)(132,134)(141,147)(142,146)(143,145)(148,154)(149,153)(150,152)(155,168)(156,167)(157,166)(158,165)(159,164)(160,163)(161,162)(169,174)(170,173)(171,172)(175,182)(176,181)(177,180)(178,179)(183,187)(184,186)(188,196)(189,195)(190,194)(191,193)(197,208)(198,207)(199,206)(200,205)(201,204)(202,203)(209,210)(211,213)(214,224)(215,223)(216,222)(217,221)(218,220), (1,130,32,189)(2,131,33,190)(3,132,34,191)(4,133,35,192)(5,134,36,193)(6,135,37,194)(7,136,38,195)(8,137,39,196)(9,138,40,183)(10,139,41,184)(11,140,42,185)(12,127,29,186)(13,128,30,187)(14,129,31,188)(15,198,87,174)(16,199,88,175)(17,200,89,176)(18,201,90,177)(19,202,91,178)(20,203,92,179)(21,204,93,180)(22,205,94,181)(23,206,95,182)(24,207,96,169)(25,208,97,170)(26,209,98,171)(27,210,85,172)(28,197,86,173)(43,57,222,117)(44,58,223,118)(45,59,224,119)(46,60,211,120)(47,61,212,121)(48,62,213,122)(49,63,214,123)(50,64,215,124)(51,65,216,125)(52,66,217,126)(53,67,218,113)(54,68,219,114)(55,69,220,115)(56,70,221,116)(71,107,148,155)(72,108,149,156)(73,109,150,157)(74,110,151,158)(75,111,152,159)(76,112,153,160)(77,99,154,161)(78,100,141,162)(79,101,142,163)(80,102,143,164)(81,103,144,165)(82,104,145,166)(83,105,146,167)(84,106,147,168), (1,125,203,155)(2,126,204,156)(3,113,205,157)(4,114,206,158)(5,115,207,159)(6,116,208,160)(7,117,209,161)(8,118,210,162)(9,119,197,163)(10,120,198,164)(11,121,199,165)(12,122,200,166)(13,123,201,167)(14,124,202,168)(15,80,184,46)(16,81,185,47)(17,82,186,48)(18,83,187,49)(19,84,188,50)(20,71,189,51)(21,72,190,52)(22,73,191,53)(23,74,192,54)(24,75,193,55)(25,76,194,56)(26,77,195,43)(27,78,196,44)(28,79,183,45)(29,62,176,104)(30,63,177,105)(31,64,178,106)(32,65,179,107)(33,66,180,108)(34,67,181,109)(35,68,182,110)(36,69,169,111)(37,70,170,112)(38,57,171,99)(39,58,172,100)(40,59,173,101)(41,60,174,102)(42,61,175,103)(85,141,137,223)(86,142,138,224)(87,143,139,211)(88,144,140,212)(89,145,127,213)(90,146,128,214)(91,147,129,215)(92,148,130,216)(93,149,131,217)(94,150,132,218)(95,151,133,219)(96,152,134,220)(97,153,135,221)(98,154,136,222)>;
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), (1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,17)(18,28)(19,27)(20,26)(21,25)(22,24)(29,34)(30,33)(31,32)(35,42)(36,41)(37,40)(38,39)(43,51)(44,50)(45,49)(46,48)(52,56)(53,55)(57,58)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)(71,77)(72,76)(73,75)(78,84)(79,83)(80,82)(85,91)(86,90)(87,89)(92,98)(93,97)(94,96)(99,100)(101,112)(102,111)(103,110)(104,109)(105,108)(106,107)(113,122)(114,121)(115,120)(116,119)(117,118)(123,126)(124,125)(127,139)(128,138)(129,137)(130,136)(131,135)(132,134)(141,147)(142,146)(143,145)(148,154)(149,153)(150,152)(155,168)(156,167)(157,166)(158,165)(159,164)(160,163)(161,162)(169,174)(170,173)(171,172)(175,182)(176,181)(177,180)(178,179)(183,187)(184,186)(188,196)(189,195)(190,194)(191,193)(197,208)(198,207)(199,206)(200,205)(201,204)(202,203)(209,210)(211,213)(214,224)(215,223)(216,222)(217,221)(218,220), (1,130,32,189)(2,131,33,190)(3,132,34,191)(4,133,35,192)(5,134,36,193)(6,135,37,194)(7,136,38,195)(8,137,39,196)(9,138,40,183)(10,139,41,184)(11,140,42,185)(12,127,29,186)(13,128,30,187)(14,129,31,188)(15,198,87,174)(16,199,88,175)(17,200,89,176)(18,201,90,177)(19,202,91,178)(20,203,92,179)(21,204,93,180)(22,205,94,181)(23,206,95,182)(24,207,96,169)(25,208,97,170)(26,209,98,171)(27,210,85,172)(28,197,86,173)(43,57,222,117)(44,58,223,118)(45,59,224,119)(46,60,211,120)(47,61,212,121)(48,62,213,122)(49,63,214,123)(50,64,215,124)(51,65,216,125)(52,66,217,126)(53,67,218,113)(54,68,219,114)(55,69,220,115)(56,70,221,116)(71,107,148,155)(72,108,149,156)(73,109,150,157)(74,110,151,158)(75,111,152,159)(76,112,153,160)(77,99,154,161)(78,100,141,162)(79,101,142,163)(80,102,143,164)(81,103,144,165)(82,104,145,166)(83,105,146,167)(84,106,147,168), (1,125,203,155)(2,126,204,156)(3,113,205,157)(4,114,206,158)(5,115,207,159)(6,116,208,160)(7,117,209,161)(8,118,210,162)(9,119,197,163)(10,120,198,164)(11,121,199,165)(12,122,200,166)(13,123,201,167)(14,124,202,168)(15,80,184,46)(16,81,185,47)(17,82,186,48)(18,83,187,49)(19,84,188,50)(20,71,189,51)(21,72,190,52)(22,73,191,53)(23,74,192,54)(24,75,193,55)(25,76,194,56)(26,77,195,43)(27,78,196,44)(28,79,183,45)(29,62,176,104)(30,63,177,105)(31,64,178,106)(32,65,179,107)(33,66,180,108)(34,67,181,109)(35,68,182,110)(36,69,169,111)(37,70,170,112)(38,57,171,99)(39,58,172,100)(40,59,173,101)(41,60,174,102)(42,61,175,103)(85,141,137,223)(86,142,138,224)(87,143,139,211)(88,144,140,212)(89,145,127,213)(90,146,128,214)(91,147,129,215)(92,148,130,216)(93,149,131,217)(94,150,132,218)(95,151,133,219)(96,152,134,220)(97,153,135,221)(98,154,136,222) );
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)], [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,17),(18,28),(19,27),(20,26),(21,25),(22,24),(29,34),(30,33),(31,32),(35,42),(36,41),(37,40),(38,39),(43,51),(44,50),(45,49),(46,48),(52,56),(53,55),(57,58),(59,70),(60,69),(61,68),(62,67),(63,66),(64,65),(71,77),(72,76),(73,75),(78,84),(79,83),(80,82),(85,91),(86,90),(87,89),(92,98),(93,97),(94,96),(99,100),(101,112),(102,111),(103,110),(104,109),(105,108),(106,107),(113,122),(114,121),(115,120),(116,119),(117,118),(123,126),(124,125),(127,139),(128,138),(129,137),(130,136),(131,135),(132,134),(141,147),(142,146),(143,145),(148,154),(149,153),(150,152),(155,168),(156,167),(157,166),(158,165),(159,164),(160,163),(161,162),(169,174),(170,173),(171,172),(175,182),(176,181),(177,180),(178,179),(183,187),(184,186),(188,196),(189,195),(190,194),(191,193),(197,208),(198,207),(199,206),(200,205),(201,204),(202,203),(209,210),(211,213),(214,224),(215,223),(216,222),(217,221),(218,220)], [(1,130,32,189),(2,131,33,190),(3,132,34,191),(4,133,35,192),(5,134,36,193),(6,135,37,194),(7,136,38,195),(8,137,39,196),(9,138,40,183),(10,139,41,184),(11,140,42,185),(12,127,29,186),(13,128,30,187),(14,129,31,188),(15,198,87,174),(16,199,88,175),(17,200,89,176),(18,201,90,177),(19,202,91,178),(20,203,92,179),(21,204,93,180),(22,205,94,181),(23,206,95,182),(24,207,96,169),(25,208,97,170),(26,209,98,171),(27,210,85,172),(28,197,86,173),(43,57,222,117),(44,58,223,118),(45,59,224,119),(46,60,211,120),(47,61,212,121),(48,62,213,122),(49,63,214,123),(50,64,215,124),(51,65,216,125),(52,66,217,126),(53,67,218,113),(54,68,219,114),(55,69,220,115),(56,70,221,116),(71,107,148,155),(72,108,149,156),(73,109,150,157),(74,110,151,158),(75,111,152,159),(76,112,153,160),(77,99,154,161),(78,100,141,162),(79,101,142,163),(80,102,143,164),(81,103,144,165),(82,104,145,166),(83,105,146,167),(84,106,147,168)], [(1,125,203,155),(2,126,204,156),(3,113,205,157),(4,114,206,158),(5,115,207,159),(6,116,208,160),(7,117,209,161),(8,118,210,162),(9,119,197,163),(10,120,198,164),(11,121,199,165),(12,122,200,166),(13,123,201,167),(14,124,202,168),(15,80,184,46),(16,81,185,47),(17,82,186,48),(18,83,187,49),(19,84,188,50),(20,71,189,51),(21,72,190,52),(22,73,191,53),(23,74,192,54),(24,75,193,55),(25,76,194,56),(26,77,195,43),(27,78,196,44),(28,79,183,45),(29,62,176,104),(30,63,177,105),(31,64,178,106),(32,65,179,107),(33,66,180,108),(34,67,181,109),(35,68,182,110),(36,69,169,111),(37,70,170,112),(38,57,171,99),(39,58,172,100),(40,59,173,101),(41,60,174,102),(42,61,175,103),(85,141,137,223),(86,142,138,224),(87,143,139,211),(88,144,140,212),(89,145,127,213),(90,146,128,214),(91,147,129,215),(92,148,130,216),(93,149,131,217),(94,150,132,218),(95,151,133,219),(96,152,134,220),(97,153,135,221),(98,154,136,222)]])
88 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 14 | 14 | 14 | 14 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | + | + | + | - | + | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | D4 | Q8 | D7 | C4○D4 | D14 | C4×D7 | C7⋊D4 | C4○D28 | D4×D7 | Q8×D7 | Q8⋊2D7 |
| kernel | D14⋊C4⋊6C4 | C14.C42 | C2×Dic7⋊C4 | C2×D14⋊C4 | C14×C4⋊C4 | D7×C22×C4 | D14⋊C4 | C2×Dic7 | C2×C28 | C22×D7 | C22×D7 | C2×C4⋊C4 | C2×C14 | C22×C4 | C2×C4 | C2×C4 | C22 | C22 | C22 | C22 |
| # reps | 1 | 2 | 1 | 2 | 1 | 1 | 8 | 2 | 2 | 2 | 2 | 3 | 4 | 9 | 12 | 12 | 12 | 6 | 3 | 3 |
Matrix representation of D14⋊C4⋊6C4 ►in GL6(𝔽29)
| 18 | 25 | 0 | 0 | 0 | 0 |
| 4 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 8 | 0 | 0 |
| 0 | 0 | 18 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 18 | 25 | 0 | 0 | 0 | 0 |
| 1 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 4 | 26 | 0 | 0 |
| 0 | 0 | 5 | 25 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 11 | 2 | 0 | 0 | 0 | 0 |
| 27 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
G:=sub<GL(6,GF(29))| [18,4,0,0,0,0,25,4,0,0,0,0,0,0,18,18,0,0,0,0,8,0,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[18,1,0,0,0,0,25,11,0,0,0,0,0,0,4,5,0,0,0,0,26,25,0,0,0,0,0,0,28,0,0,0,0,0,0,1],[11,27,0,0,0,0,2,18,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,1,0],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,17] >;
D14⋊C4⋊6C4 in GAP, Magma, Sage, TeX
D_{14}\rtimes C_4\rtimes_6C_4 % in TeX
G:=Group("D14:C4:6C4"); // GroupNames label
G:=SmallGroup(448,523);
// by ID
G=gap.SmallGroup(448,523);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,232,387,58,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^2=c^4=d^4=1,b*a*b=a^-1,a*c=c*a,a*d=d*a,c*b*c^-1=a^7*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations