metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14⋊C4⋊2C4, C14.3(C4×D4), C2.6(C4×D28), D14⋊2(C4⋊C4), C14.3C22≀C2, (C2×C4).112D28, (C2×C28).234D4, C22.62(D4×D7), (C22×D7).7Q8, C22.17(Q8×D7), (C22×D7).67D4, C2.C42⋊8D7, (C22×C4).17D14, C22.25(C2×D28), C2.2(C22⋊D28), C7⋊1(C23.8Q8), C14.C42⋊2C2, C2.2(D14⋊2Q8), C2.4(D14⋊Q8), (C2×Dic7).131D4, C14.25(C22⋊Q8), C2.8(Dic7⋊4D4), C2.4(D14.D4), C22.36(C4○D28), (C23×D7).85C22, C23.258(C22×D7), C22.37(D4⋊2D7), (C22×C28).333C22, (C22×C14).293C23, C14.9(C22.D4), (C22×Dic7).16C22, (C2×C4)⋊3(C4×D7), C2.8(D7×C4⋊C4), (C2×C28)⋊5(C2×C4), C14.6(C2×C4⋊C4), (C2×C4⋊Dic7)⋊1C2, C22.91(C2×C4×D7), (C2×D14⋊C4).3C2, (C2×Dic7)⋊3(C2×C4), (C2×C14).68(C2×Q8), (D7×C22×C4).15C2, (C2×Dic7⋊C4)⋊31C2, (C2×C14).202(C2×D4), (C2×C14).52(C22×C4), (C22×D7).30(C2×C4), (C2×C14).132(C4○D4), (C7×C2.C42)⋊15C2, SmallGroup(448,202)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14⋊C4⋊C4
G = < a,b,c,d | a14=b2=c4=d4=1, bab=a-1, ac=ca, ad=da, cbc-1=a7b, bd=db, dcd-1=a7c-1 >
Subgroups: 1180 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.C42, C2×C22⋊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, C4⋊Dic7, D14⋊C4, D14⋊C4, C2×C4×D7, C22×Dic7, C22×C28, C23×D7, C14.C42, C7×C2.C42, C2×Dic7⋊C4, C2×C4⋊Dic7, C2×D14⋊C4, D7×C22×C4, D14⋊C4⋊C4
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, D28, C22×D7, C23.8Q8, C2×C4×D7, C2×D28, C4○D28, D4×D7, D4⋊2D7, Q8×D7, C4×D28, Dic7⋊4D4, C22⋊D28, D14.D4, D7×C4⋊C4, D14⋊Q8, D14⋊2Q8, D14⋊C4⋊C4
►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 7)(2 6)(3 5)(8 14)(9 13)(10 12)(16 28)(17 27)(18 26)(19 25)(20 24)(21 23)(30 42)(31 41)(32 40)(33 39)(34 38)(35 37)(43 44)(45 56)(46 55)(47 54)(48 53)(49 52)(50 51)(57 58)(59 70)(60 69)(61 68)(62 67)(63 66)(64 65)(71 74)(72 73)(75 84)(76 83)(77 82)(78 81)(79 80)(85 96)(86 95)(87 94)(88 93)(89 92)(90 91)(97 98)(99 108)(100 107)(101 106)(102 105)(103 104)(109 112)(110 111)(114 126)(115 125)(116 124)(117 123)(118 122)(119 121)(127 135)(128 134)(129 133)(130 132)(136 140)(137 139)(141 151)(142 150)(143 149)(144 148)(145 147)(152 154)(155 168)(156 167)(157 166)(158 165)(159 164)(160 163)(161 162)(170 182)(171 181)(172 180)(173 179)(174 178)(175 177)(183 186)(184 185)(187 196)(188 195)(189 194)(190 193)(191 192)(197 199)(200 210)(201 209)(202 208)(203 207)(204 206)(211 222)(212 221)(213 220)(214 219)(215 218)(216 217)(223 224)
(1 192 19 91)(2 193 20 92)(3 194 21 93)(4 195 22 94)(5 196 23 95)(6 183 24 96)(7 184 25 97)(8 185 26 98)(9 186 27 85)(10 187 28 86)(11 188 15 87)(12 189 16 88)(13 190 17 89)(14 191 18 90)(29 83 198 61)(30 84 199 62)(31 71 200 63)(32 72 201 64)(33 73 202 65)(34 74 203 66)(35 75 204 67)(36 76 205 68)(37 77 206 69)(38 78 207 70)(39 79 208 57)(40 80 209 58)(41 81 210 59)(42 82 197 60)(43 179 161 142)(44 180 162 143)(45 181 163 144)(46 182 164 145)(47 169 165 146)(48 170 166 147)(49 171 167 148)(50 172 168 149)(51 173 155 150)(52 174 156 151)(53 175 157 152)(54 176 158 153)(55 177 159 154)(56 178 160 141)(99 137 219 119)(100 138 220 120)(101 139 221 121)(102 140 222 122)(103 127 223 123)(104 128 224 124)(105 129 211 125)(106 130 212 126)(107 131 213 113)(108 132 214 114)(109 133 215 115)(110 134 216 116)(111 135 217 117)(112 136 218 118)
(1 135 33 143)(2 136 34 144)(3 137 35 145)(4 138 36 146)(5 139 37 147)(6 140 38 148)(7 127 39 149)(8 128 40 150)(9 129 41 151)(10 130 42 152)(11 131 29 153)(12 132 30 154)(13 133 31 141)(14 134 32 142)(15 113 198 176)(16 114 199 177)(17 115 200 178)(18 116 201 179)(19 117 202 180)(20 118 203 181)(21 119 204 182)(22 120 205 169)(23 121 206 170)(24 122 207 171)(25 123 208 172)(26 124 209 173)(27 125 210 174)(28 126 197 175)(43 97 216 57)(44 98 217 58)(45 85 218 59)(46 86 219 60)(47 87 220 61)(48 88 221 62)(49 89 222 63)(50 90 223 64)(51 91 224 65)(52 92 211 66)(53 93 212 67)(54 94 213 68)(55 95 214 69)(56 96 215 70)(71 167 190 102)(72 168 191 103)(73 155 192 104)(74 156 193 105)(75 157 194 106)(76 158 195 107)(77 159 196 108)(78 160 183 109)(79 161 184 110)(80 162 185 111)(81 163 186 112)(82 164 187 99)(83 165 188 100)(84 166 189 101)
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), (1,7)(2,6)(3,5)(8,14)(9,13)(10,12)(16,28)(17,27)(18,26)(19,25)(20,24)(21,23)(30,42)(31,41)(32,40)(33,39)(34,38)(35,37)(43,44)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)(57,58)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)(71,74)(72,73)(75,84)(76,83)(77,82)(78,81)(79,80)(85,96)(86,95)(87,94)(88,93)(89,92)(90,91)(97,98)(99,108)(100,107)(101,106)(102,105)(103,104)(109,112)(110,111)(114,126)(115,125)(116,124)(117,123)(118,122)(119,121)(127,135)(128,134)(129,133)(130,132)(136,140)(137,139)(141,151)(142,150)(143,149)(144,148)(145,147)(152,154)(155,168)(156,167)(157,166)(158,165)(159,164)(160,163)(161,162)(170,182)(171,181)(172,180)(173,179)(174,178)(175,177)(183,186)(184,185)(187,196)(188,195)(189,194)(190,193)(191,192)(197,199)(200,210)(201,209)(202,208)(203,207)(204,206)(211,222)(212,221)(213,220)(214,219)(215,218)(216,217)(223,224), (1,192,19,91)(2,193,20,92)(3,194,21,93)(4,195,22,94)(5,196,23,95)(6,183,24,96)(7,184,25,97)(8,185,26,98)(9,186,27,85)(10,187,28,86)(11,188,15,87)(12,189,16,88)(13,190,17,89)(14,191,18,90)(29,83,198,61)(30,84,199,62)(31,71,200,63)(32,72,201,64)(33,73,202,65)(34,74,203,66)(35,75,204,67)(36,76,205,68)(37,77,206,69)(38,78,207,70)(39,79,208,57)(40,80,209,58)(41,81,210,59)(42,82,197,60)(43,179,161,142)(44,180,162,143)(45,181,163,144)(46,182,164,145)(47,169,165,146)(48,170,166,147)(49,171,167,148)(50,172,168,149)(51,173,155,150)(52,174,156,151)(53,175,157,152)(54,176,158,153)(55,177,159,154)(56,178,160,141)(99,137,219,119)(100,138,220,120)(101,139,221,121)(102,140,222,122)(103,127,223,123)(104,128,224,124)(105,129,211,125)(106,130,212,126)(107,131,213,113)(108,132,214,114)(109,133,215,115)(110,134,216,116)(111,135,217,117)(112,136,218,118), (1,135,33,143)(2,136,34,144)(3,137,35,145)(4,138,36,146)(5,139,37,147)(6,140,38,148)(7,127,39,149)(8,128,40,150)(9,129,41,151)(10,130,42,152)(11,131,29,153)(12,132,30,154)(13,133,31,141)(14,134,32,142)(15,113,198,176)(16,114,199,177)(17,115,200,178)(18,116,201,179)(19,117,202,180)(20,118,203,181)(21,119,204,182)(22,120,205,169)(23,121,206,170)(24,122,207,171)(25,123,208,172)(26,124,209,173)(27,125,210,174)(28,126,197,175)(43,97,216,57)(44,98,217,58)(45,85,218,59)(46,86,219,60)(47,87,220,61)(48,88,221,62)(49,89,222,63)(50,90,223,64)(51,91,224,65)(52,92,211,66)(53,93,212,67)(54,94,213,68)(55,95,214,69)(56,96,215,70)(71,167,190,102)(72,168,191,103)(73,155,192,104)(74,156,193,105)(75,157,194,106)(76,158,195,107)(77,159,196,108)(78,160,183,109)(79,161,184,110)(80,162,185,111)(81,163,186,112)(82,164,187,99)(83,165,188,100)(84,166,189,101)>;
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), (1,7)(2,6)(3,5)(8,14)(9,13)(10,12)(16,28)(17,27)(18,26)(19,25)(20,24)(21,23)(30,42)(31,41)(32,40)(33,39)(34,38)(35,37)(43,44)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)(57,58)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)(71,74)(72,73)(75,84)(76,83)(77,82)(78,81)(79,80)(85,96)(86,95)(87,94)(88,93)(89,92)(90,91)(97,98)(99,108)(100,107)(101,106)(102,105)(103,104)(109,112)(110,111)(114,126)(115,125)(116,124)(117,123)(118,122)(119,121)(127,135)(128,134)(129,133)(130,132)(136,140)(137,139)(141,151)(142,150)(143,149)(144,148)(145,147)(152,154)(155,168)(156,167)(157,166)(158,165)(159,164)(160,163)(161,162)(170,182)(171,181)(172,180)(173,179)(174,178)(175,177)(183,186)(184,185)(187,196)(188,195)(189,194)(190,193)(191,192)(197,199)(200,210)(201,209)(202,208)(203,207)(204,206)(211,222)(212,221)(213,220)(214,219)(215,218)(216,217)(223,224), (1,192,19,91)(2,193,20,92)(3,194,21,93)(4,195,22,94)(5,196,23,95)(6,183,24,96)(7,184,25,97)(8,185,26,98)(9,186,27,85)(10,187,28,86)(11,188,15,87)(12,189,16,88)(13,190,17,89)(14,191,18,90)(29,83,198,61)(30,84,199,62)(31,71,200,63)(32,72,201,64)(33,73,202,65)(34,74,203,66)(35,75,204,67)(36,76,205,68)(37,77,206,69)(38,78,207,70)(39,79,208,57)(40,80,209,58)(41,81,210,59)(42,82,197,60)(43,179,161,142)(44,180,162,143)(45,181,163,144)(46,182,164,145)(47,169,165,146)(48,170,166,147)(49,171,167,148)(50,172,168,149)(51,173,155,150)(52,174,156,151)(53,175,157,152)(54,176,158,153)(55,177,159,154)(56,178,160,141)(99,137,219,119)(100,138,220,120)(101,139,221,121)(102,140,222,122)(103,127,223,123)(104,128,224,124)(105,129,211,125)(106,130,212,126)(107,131,213,113)(108,132,214,114)(109,133,215,115)(110,134,216,116)(111,135,217,117)(112,136,218,118), (1,135,33,143)(2,136,34,144)(3,137,35,145)(4,138,36,146)(5,139,37,147)(6,140,38,148)(7,127,39,149)(8,128,40,150)(9,129,41,151)(10,130,42,152)(11,131,29,153)(12,132,30,154)(13,133,31,141)(14,134,32,142)(15,113,198,176)(16,114,199,177)(17,115,200,178)(18,116,201,179)(19,117,202,180)(20,118,203,181)(21,119,204,182)(22,120,205,169)(23,121,206,170)(24,122,207,171)(25,123,208,172)(26,124,209,173)(27,125,210,174)(28,126,197,175)(43,97,216,57)(44,98,217,58)(45,85,218,59)(46,86,219,60)(47,87,220,61)(48,88,221,62)(49,89,222,63)(50,90,223,64)(51,91,224,65)(52,92,211,66)(53,93,212,67)(54,94,213,68)(55,95,214,69)(56,96,215,70)(71,167,190,102)(72,168,191,103)(73,155,192,104)(74,156,193,105)(75,157,194,106)(76,158,195,107)(77,159,196,108)(78,160,183,109)(79,161,184,110)(80,162,185,111)(81,163,186,112)(82,164,187,99)(83,165,188,100)(84,166,189,101) );
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)], [(1,7),(2,6),(3,5),(8,14),(9,13),(10,12),(16,28),(17,27),(18,26),(19,25),(20,24),(21,23),(30,42),(31,41),(32,40),(33,39),(34,38),(35,37),(43,44),(45,56),(46,55),(47,54),(48,53),(49,52),(50,51),(57,58),(59,70),(60,69),(61,68),(62,67),(63,66),(64,65),(71,74),(72,73),(75,84),(76,83),(77,82),(78,81),(79,80),(85,96),(86,95),(87,94),(88,93),(89,92),(90,91),(97,98),(99,108),(100,107),(101,106),(102,105),(103,104),(109,112),(110,111),(114,126),(115,125),(116,124),(117,123),(118,122),(119,121),(127,135),(128,134),(129,133),(130,132),(136,140),(137,139),(141,151),(142,150),(143,149),(144,148),(145,147),(152,154),(155,168),(156,167),(157,166),(158,165),(159,164),(160,163),(161,162),(170,182),(171,181),(172,180),(173,179),(174,178),(175,177),(183,186),(184,185),(187,196),(188,195),(189,194),(190,193),(191,192),(197,199),(200,210),(201,209),(202,208),(203,207),(204,206),(211,222),(212,221),(213,220),(214,219),(215,218),(216,217),(223,224)], [(1,192,19,91),(2,193,20,92),(3,194,21,93),(4,195,22,94),(5,196,23,95),(6,183,24,96),(7,184,25,97),(8,185,26,98),(9,186,27,85),(10,187,28,86),(11,188,15,87),(12,189,16,88),(13,190,17,89),(14,191,18,90),(29,83,198,61),(30,84,199,62),(31,71,200,63),(32,72,201,64),(33,73,202,65),(34,74,203,66),(35,75,204,67),(36,76,205,68),(37,77,206,69),(38,78,207,70),(39,79,208,57),(40,80,209,58),(41,81,210,59),(42,82,197,60),(43,179,161,142),(44,180,162,143),(45,181,163,144),(46,182,164,145),(47,169,165,146),(48,170,166,147),(49,171,167,148),(50,172,168,149),(51,173,155,150),(52,174,156,151),(53,175,157,152),(54,176,158,153),(55,177,159,154),(56,178,160,141),(99,137,219,119),(100,138,220,120),(101,139,221,121),(102,140,222,122),(103,127,223,123),(104,128,224,124),(105,129,211,125),(106,130,212,126),(107,131,213,113),(108,132,214,114),(109,133,215,115),(110,134,216,116),(111,135,217,117),(112,136,218,118)], [(1,135,33,143),(2,136,34,144),(3,137,35,145),(4,138,36,146),(5,139,37,147),(6,140,38,148),(7,127,39,149),(8,128,40,150),(9,129,41,151),(10,130,42,152),(11,131,29,153),(12,132,30,154),(13,133,31,141),(14,134,32,142),(15,113,198,176),(16,114,199,177),(17,115,200,178),(18,116,201,179),(19,117,202,180),(20,118,203,181),(21,119,204,182),(22,120,205,169),(23,121,206,170),(24,122,207,171),(25,123,208,172),(26,124,209,173),(27,125,210,174),(28,126,197,175),(43,97,216,57),(44,98,217,58),(45,85,218,59),(46,86,219,60),(47,87,220,61),(48,88,221,62),(49,89,222,63),(50,90,223,64),(51,91,224,65),(52,92,211,66),(53,93,212,67),(54,94,213,68),(55,95,214,69),(56,96,215,70),(71,167,190,102),(72,168,191,103),(73,155,192,104),(74,156,193,105),(75,157,194,106),(76,158,195,107),(77,159,196,108),(78,160,183,109),(79,161,184,110),(80,162,185,111),(81,163,186,112),(82,164,187,99),(83,165,188,100),(84,166,189,101)]])
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 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | + | + | + | + | - | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | D4 | Q8 | D7 | C4○D4 | D14 | C4×D7 | D28 | C4○D28 | D4×D7 | D4⋊2D7 | Q8×D7 |
| kernel | D14⋊C4⋊C4 | C14.C42 | C7×C2.C42 | C2×Dic7⋊C4 | C2×C4⋊Dic7 | C2×D14⋊C4 | D7×C22×C4 | D14⋊C4 | C2×Dic7 | C2×C28 | C22×D7 | C22×D7 | C2.C42 | C2×C14 | C22×C4 | C2×C4 | C2×C4 | C22 | C22 | C22 | C22 |
| # reps | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 8 | 2 | 2 | 2 | 2 | 3 | 4 | 9 | 12 | 12 | 12 | 6 | 3 | 3 |
Matrix representation of D14⋊C4⋊C4 ►in GL6(𝔽29)
| 18 | 25 | 0 | 0 | 0 | 0 |
| 4 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 25 | 0 | 0 |
| 0 | 0 | 4 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 11 | 4 | 0 | 0 | 0 | 0 |
| 28 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 4 | 0 | 0 |
| 0 | 0 | 28 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 9 | 28 |
| 13 | 5 | 0 | 0 | 0 | 0 |
| 24 | 16 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 24 | 0 | 0 |
| 0 | 0 | 5 | 13 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 27 |
| 0 | 0 | 0 | 0 | 11 | 20 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 21 | 17 |
G:=sub<GL(6,GF(29))| [18,4,0,0,0,0,25,4,0,0,0,0,0,0,18,4,0,0,0,0,25,4,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[11,28,0,0,0,0,4,18,0,0,0,0,0,0,11,28,0,0,0,0,4,18,0,0,0,0,0,0,1,9,0,0,0,0,0,28],[13,24,0,0,0,0,5,16,0,0,0,0,0,0,16,5,0,0,0,0,24,13,0,0,0,0,0,0,9,11,0,0,0,0,27,20],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,21,0,0,0,0,0,17] >;
D14⋊C4⋊C4 in GAP, Magma, Sage, TeX
D_{14}\rtimes C_4\rtimes C_4 % in TeX
G:=Group("D14:C4:C4"); // GroupNames label
G:=SmallGroup(448,202);
// by ID
G=gap.SmallGroup(448,202);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,344,387,58,18822]);
// 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=a^7*c^-1>;
// generators/relations