metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14⋊1(C4⋊C4), C22.61(D4×D7), (C22×D7).6Q8, C22.16(Q8×D7), C14.4(C4⋊D4), (C22×D7).45D4, C2.C42⋊2D7, (C22×C4).16D14, C2.3(D14⋊D4), C7⋊1(C23.7Q8), Dic7⋊2(C22⋊C4), C2.3(D14⋊Q8), (C2×Dic7).130D4, C2.9(C42⋊D7), C14.24(C22⋊Q8), C14.C42⋊36C2, C14.5(C42⋊C2), C22.35(C4○D28), (C22×C28).13C22, (C23×D7).84C22, C23.257(C22×D7), (C22×C14).292C23, (C22×Dic7).15C22, (C2×C4×D7)⋊11C4, C2.7(D7×C4⋊C4), C14.5(C2×C4⋊C4), C2.8(D7×C22⋊C4), C22.90(C2×C4×D7), (C2×Dic7⋊C4)⋊1C2, (C2×D14⋊C4).2C2, (C2×C4).125(C4×D7), C14.6(C2×C22⋊C4), (C2×C14).67(C2×Q8), (D7×C22×C4).14C2, (C2×C28).143(C2×C4), (C2×C14).201(C2×D4), (C2×C14).58(C4○D4), (C2×C14).51(C22×C4), (C2×Dic7).78(C2×C4), (C22×D7).49(C2×C4), (C7×C2.C42)⋊20C2, SmallGroup(448,201)
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=cac-1=a-1, ad=da, cbc-1=a12b, dbd-1=a7b, dcd-1=c-1 >
Subgroups: 1180 in 234 conjugacy classes, 79 normal (25 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, C23, C23, D7, C14, C14, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C24, Dic7, Dic7, C28, D14, D14, C2×C14, 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, C23.7Q8, Dic7⋊C4, D14⋊C4, C2×C4×D7, C2×C4×D7, C22×Dic7, C22×Dic7, C22×C28, C22×C28, C23×D7, C14.C42, C7×C2.C42, C2×Dic7⋊C4, C2×D14⋊C4, D7×C22×C4, D14⋊(C4⋊C4)
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D7, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, D14, C2×C22⋊C4, C2×C4⋊C4, C42⋊C2, C4⋊D4, C22⋊Q8, C4×D7, C22×D7, C23.7Q8, C2×C4×D7, C4○D28, D4×D7, Q8×D7, C42⋊D7, D7×C22⋊C4, D14⋊D4, D7×C4⋊C4, D14⋊Q8, 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 95)(2 94)(3 93)(4 92)(5 91)(6 90)(7 89)(8 88)(9 87)(10 86)(11 85)(12 98)(13 97)(14 96)(15 165)(16 164)(17 163)(18 162)(19 161)(20 160)(21 159)(22 158)(23 157)(24 156)(25 155)(26 168)(27 167)(28 166)(29 118)(30 117)(31 116)(32 115)(33 114)(34 113)(35 126)(36 125)(37 124)(38 123)(39 122)(40 121)(41 120)(42 119)(43 186)(44 185)(45 184)(46 183)(47 196)(48 195)(49 194)(50 193)(51 192)(52 191)(53 190)(54 189)(55 188)(56 187)(57 128)(58 127)(59 140)(60 139)(61 138)(62 137)(63 136)(64 135)(65 134)(66 133)(67 132)(68 131)(69 130)(70 129)(71 152)(72 151)(73 150)(74 149)(75 148)(76 147)(77 146)(78 145)(79 144)(80 143)(81 142)(82 141)(83 154)(84 153)(99 198)(100 197)(101 210)(102 209)(103 208)(104 207)(105 206)(106 205)(107 204)(108 203)(109 202)(110 201)(111 200)(112 199)(169 224)(170 223)(171 222)(172 221)(173 220)(174 219)(175 218)(176 217)(177 216)(178 215)(179 214)(180 213)(181 212)(182 211)
(1 178 89 223)(2 177 90 222)(3 176 91 221)(4 175 92 220)(5 174 93 219)(6 173 94 218)(7 172 95 217)(8 171 96 216)(9 170 97 215)(10 169 98 214)(11 182 85 213)(12 181 86 212)(13 180 87 211)(14 179 88 224)(15 80 164 146)(16 79 165 145)(17 78 166 144)(18 77 167 143)(19 76 168 142)(20 75 155 141)(21 74 156 154)(22 73 157 153)(23 72 158 152)(24 71 159 151)(25 84 160 150)(26 83 161 149)(27 82 162 148)(28 81 163 147)(29 99 123 209)(30 112 124 208)(31 111 125 207)(32 110 126 206)(33 109 113 205)(34 108 114 204)(35 107 115 203)(36 106 116 202)(37 105 117 201)(38 104 118 200)(39 103 119 199)(40 102 120 198)(41 101 121 197)(42 100 122 210)(43 139 184 64)(44 138 185 63)(45 137 186 62)(46 136 187 61)(47 135 188 60)(48 134 189 59)(49 133 190 58)(50 132 191 57)(51 131 192 70)(52 130 193 69)(53 129 194 68)(54 128 195 67)(55 127 196 66)(56 140 183 65)
(1 41 134 152)(2 42 135 153)(3 29 136 154)(4 30 137 141)(5 31 138 142)(6 32 139 143)(7 33 140 144)(8 34 127 145)(9 35 128 146)(10 36 129 147)(11 37 130 148)(12 38 131 149)(13 39 132 150)(14 40 133 151)(15 215 107 54)(16 216 108 55)(17 217 109 56)(18 218 110 43)(19 219 111 44)(20 220 112 45)(21 221 99 46)(22 222 100 47)(23 223 101 48)(24 224 102 49)(25 211 103 50)(26 212 104 51)(27 213 105 52)(28 214 106 53)(57 84 87 119)(58 71 88 120)(59 72 89 121)(60 73 90 122)(61 74 91 123)(62 75 92 124)(63 76 93 125)(64 77 94 126)(65 78 95 113)(66 79 96 114)(67 80 97 115)(68 81 98 116)(69 82 85 117)(70 83 86 118)(155 175 208 186)(156 176 209 187)(157 177 210 188)(158 178 197 189)(159 179 198 190)(160 180 199 191)(161 181 200 192)(162 182 201 193)(163 169 202 194)(164 170 203 195)(165 171 204 196)(166 172 205 183)(167 173 206 184)(168 174 207 185)
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), (1,95)(2,94)(3,93)(4,92)(5,91)(6,90)(7,89)(8,88)(9,87)(10,86)(11,85)(12,98)(13,97)(14,96)(15,165)(16,164)(17,163)(18,162)(19,161)(20,160)(21,159)(22,158)(23,157)(24,156)(25,155)(26,168)(27,167)(28,166)(29,118)(30,117)(31,116)(32,115)(33,114)(34,113)(35,126)(36,125)(37,124)(38,123)(39,122)(40,121)(41,120)(42,119)(43,186)(44,185)(45,184)(46,183)(47,196)(48,195)(49,194)(50,193)(51,192)(52,191)(53,190)(54,189)(55,188)(56,187)(57,128)(58,127)(59,140)(60,139)(61,138)(62,137)(63,136)(64,135)(65,134)(66,133)(67,132)(68,131)(69,130)(70,129)(71,152)(72,151)(73,150)(74,149)(75,148)(76,147)(77,146)(78,145)(79,144)(80,143)(81,142)(82,141)(83,154)(84,153)(99,198)(100,197)(101,210)(102,209)(103,208)(104,207)(105,206)(106,205)(107,204)(108,203)(109,202)(110,201)(111,200)(112,199)(169,224)(170,223)(171,222)(172,221)(173,220)(174,219)(175,218)(176,217)(177,216)(178,215)(179,214)(180,213)(181,212)(182,211), (1,178,89,223)(2,177,90,222)(3,176,91,221)(4,175,92,220)(5,174,93,219)(6,173,94,218)(7,172,95,217)(8,171,96,216)(9,170,97,215)(10,169,98,214)(11,182,85,213)(12,181,86,212)(13,180,87,211)(14,179,88,224)(15,80,164,146)(16,79,165,145)(17,78,166,144)(18,77,167,143)(19,76,168,142)(20,75,155,141)(21,74,156,154)(22,73,157,153)(23,72,158,152)(24,71,159,151)(25,84,160,150)(26,83,161,149)(27,82,162,148)(28,81,163,147)(29,99,123,209)(30,112,124,208)(31,111,125,207)(32,110,126,206)(33,109,113,205)(34,108,114,204)(35,107,115,203)(36,106,116,202)(37,105,117,201)(38,104,118,200)(39,103,119,199)(40,102,120,198)(41,101,121,197)(42,100,122,210)(43,139,184,64)(44,138,185,63)(45,137,186,62)(46,136,187,61)(47,135,188,60)(48,134,189,59)(49,133,190,58)(50,132,191,57)(51,131,192,70)(52,130,193,69)(53,129,194,68)(54,128,195,67)(55,127,196,66)(56,140,183,65), (1,41,134,152)(2,42,135,153)(3,29,136,154)(4,30,137,141)(5,31,138,142)(6,32,139,143)(7,33,140,144)(8,34,127,145)(9,35,128,146)(10,36,129,147)(11,37,130,148)(12,38,131,149)(13,39,132,150)(14,40,133,151)(15,215,107,54)(16,216,108,55)(17,217,109,56)(18,218,110,43)(19,219,111,44)(20,220,112,45)(21,221,99,46)(22,222,100,47)(23,223,101,48)(24,224,102,49)(25,211,103,50)(26,212,104,51)(27,213,105,52)(28,214,106,53)(57,84,87,119)(58,71,88,120)(59,72,89,121)(60,73,90,122)(61,74,91,123)(62,75,92,124)(63,76,93,125)(64,77,94,126)(65,78,95,113)(66,79,96,114)(67,80,97,115)(68,81,98,116)(69,82,85,117)(70,83,86,118)(155,175,208,186)(156,176,209,187)(157,177,210,188)(158,178,197,189)(159,179,198,190)(160,180,199,191)(161,181,200,192)(162,182,201,193)(163,169,202,194)(164,170,203,195)(165,171,204,196)(166,172,205,183)(167,173,206,184)(168,174,207,185)>;
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), (1,95)(2,94)(3,93)(4,92)(5,91)(6,90)(7,89)(8,88)(9,87)(10,86)(11,85)(12,98)(13,97)(14,96)(15,165)(16,164)(17,163)(18,162)(19,161)(20,160)(21,159)(22,158)(23,157)(24,156)(25,155)(26,168)(27,167)(28,166)(29,118)(30,117)(31,116)(32,115)(33,114)(34,113)(35,126)(36,125)(37,124)(38,123)(39,122)(40,121)(41,120)(42,119)(43,186)(44,185)(45,184)(46,183)(47,196)(48,195)(49,194)(50,193)(51,192)(52,191)(53,190)(54,189)(55,188)(56,187)(57,128)(58,127)(59,140)(60,139)(61,138)(62,137)(63,136)(64,135)(65,134)(66,133)(67,132)(68,131)(69,130)(70,129)(71,152)(72,151)(73,150)(74,149)(75,148)(76,147)(77,146)(78,145)(79,144)(80,143)(81,142)(82,141)(83,154)(84,153)(99,198)(100,197)(101,210)(102,209)(103,208)(104,207)(105,206)(106,205)(107,204)(108,203)(109,202)(110,201)(111,200)(112,199)(169,224)(170,223)(171,222)(172,221)(173,220)(174,219)(175,218)(176,217)(177,216)(178,215)(179,214)(180,213)(181,212)(182,211), (1,178,89,223)(2,177,90,222)(3,176,91,221)(4,175,92,220)(5,174,93,219)(6,173,94,218)(7,172,95,217)(8,171,96,216)(9,170,97,215)(10,169,98,214)(11,182,85,213)(12,181,86,212)(13,180,87,211)(14,179,88,224)(15,80,164,146)(16,79,165,145)(17,78,166,144)(18,77,167,143)(19,76,168,142)(20,75,155,141)(21,74,156,154)(22,73,157,153)(23,72,158,152)(24,71,159,151)(25,84,160,150)(26,83,161,149)(27,82,162,148)(28,81,163,147)(29,99,123,209)(30,112,124,208)(31,111,125,207)(32,110,126,206)(33,109,113,205)(34,108,114,204)(35,107,115,203)(36,106,116,202)(37,105,117,201)(38,104,118,200)(39,103,119,199)(40,102,120,198)(41,101,121,197)(42,100,122,210)(43,139,184,64)(44,138,185,63)(45,137,186,62)(46,136,187,61)(47,135,188,60)(48,134,189,59)(49,133,190,58)(50,132,191,57)(51,131,192,70)(52,130,193,69)(53,129,194,68)(54,128,195,67)(55,127,196,66)(56,140,183,65), (1,41,134,152)(2,42,135,153)(3,29,136,154)(4,30,137,141)(5,31,138,142)(6,32,139,143)(7,33,140,144)(8,34,127,145)(9,35,128,146)(10,36,129,147)(11,37,130,148)(12,38,131,149)(13,39,132,150)(14,40,133,151)(15,215,107,54)(16,216,108,55)(17,217,109,56)(18,218,110,43)(19,219,111,44)(20,220,112,45)(21,221,99,46)(22,222,100,47)(23,223,101,48)(24,224,102,49)(25,211,103,50)(26,212,104,51)(27,213,105,52)(28,214,106,53)(57,84,87,119)(58,71,88,120)(59,72,89,121)(60,73,90,122)(61,74,91,123)(62,75,92,124)(63,76,93,125)(64,77,94,126)(65,78,95,113)(66,79,96,114)(67,80,97,115)(68,81,98,116)(69,82,85,117)(70,83,86,118)(155,175,208,186)(156,176,209,187)(157,177,210,188)(158,178,197,189)(159,179,198,190)(160,180,199,191)(161,181,200,192)(162,182,201,193)(163,169,202,194)(164,170,203,195)(165,171,204,196)(166,172,205,183)(167,173,206,184)(168,174,207,185) );
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)], [(1,95),(2,94),(3,93),(4,92),(5,91),(6,90),(7,89),(8,88),(9,87),(10,86),(11,85),(12,98),(13,97),(14,96),(15,165),(16,164),(17,163),(18,162),(19,161),(20,160),(21,159),(22,158),(23,157),(24,156),(25,155),(26,168),(27,167),(28,166),(29,118),(30,117),(31,116),(32,115),(33,114),(34,113),(35,126),(36,125),(37,124),(38,123),(39,122),(40,121),(41,120),(42,119),(43,186),(44,185),(45,184),(46,183),(47,196),(48,195),(49,194),(50,193),(51,192),(52,191),(53,190),(54,189),(55,188),(56,187),(57,128),(58,127),(59,140),(60,139),(61,138),(62,137),(63,136),(64,135),(65,134),(66,133),(67,132),(68,131),(69,130),(70,129),(71,152),(72,151),(73,150),(74,149),(75,148),(76,147),(77,146),(78,145),(79,144),(80,143),(81,142),(82,141),(83,154),(84,153),(99,198),(100,197),(101,210),(102,209),(103,208),(104,207),(105,206),(106,205),(107,204),(108,203),(109,202),(110,201),(111,200),(112,199),(169,224),(170,223),(171,222),(172,221),(173,220),(174,219),(175,218),(176,217),(177,216),(178,215),(179,214),(180,213),(181,212),(182,211)], [(1,178,89,223),(2,177,90,222),(3,176,91,221),(4,175,92,220),(5,174,93,219),(6,173,94,218),(7,172,95,217),(8,171,96,216),(9,170,97,215),(10,169,98,214),(11,182,85,213),(12,181,86,212),(13,180,87,211),(14,179,88,224),(15,80,164,146),(16,79,165,145),(17,78,166,144),(18,77,167,143),(19,76,168,142),(20,75,155,141),(21,74,156,154),(22,73,157,153),(23,72,158,152),(24,71,159,151),(25,84,160,150),(26,83,161,149),(27,82,162,148),(28,81,163,147),(29,99,123,209),(30,112,124,208),(31,111,125,207),(32,110,126,206),(33,109,113,205),(34,108,114,204),(35,107,115,203),(36,106,116,202),(37,105,117,201),(38,104,118,200),(39,103,119,199),(40,102,120,198),(41,101,121,197),(42,100,122,210),(43,139,184,64),(44,138,185,63),(45,137,186,62),(46,136,187,61),(47,135,188,60),(48,134,189,59),(49,133,190,58),(50,132,191,57),(51,131,192,70),(52,130,193,69),(53,129,194,68),(54,128,195,67),(55,127,196,66),(56,140,183,65)], [(1,41,134,152),(2,42,135,153),(3,29,136,154),(4,30,137,141),(5,31,138,142),(6,32,139,143),(7,33,140,144),(8,34,127,145),(9,35,128,146),(10,36,129,147),(11,37,130,148),(12,38,131,149),(13,39,132,150),(14,40,133,151),(15,215,107,54),(16,216,108,55),(17,217,109,56),(18,218,110,43),(19,219,111,44),(20,220,112,45),(21,221,99,46),(22,222,100,47),(23,223,101,48),(24,224,102,49),(25,211,103,50),(26,212,104,51),(27,213,105,52),(28,214,106,53),(57,84,87,119),(58,71,88,120),(59,72,89,121),(60,73,90,122),(61,74,91,123),(62,75,92,124),(63,76,93,125),(64,77,94,126),(65,78,95,113),(66,79,96,114),(67,80,97,115),(68,81,98,116),(69,82,85,117),(70,83,86,118),(155,175,208,186),(156,176,209,187),(157,177,210,188),(158,178,197,189),(159,179,198,190),(160,180,199,191),(161,181,200,192),(162,182,201,193),(163,169,202,194),(164,170,203,195),(165,171,204,196),(166,172,205,183),(167,173,206,184),(168,174,207,185)]])
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 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | + | + | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | Q8 | D7 | C4○D4 | D14 | C4×D7 | C4○D28 | D4×D7 | Q8×D7 |
| kernel | D14⋊(C4⋊C4) | C14.C42 | C7×C2.C42 | C2×Dic7⋊C4 | C2×D14⋊C4 | D7×C22×C4 | C2×C4×D7 | C2×Dic7 | C22×D7 | C22×D7 | C2.C42 | C2×C14 | C22×C4 | C2×C4 | C22 | C22 | C22 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 8 | 4 | 2 | 2 | 3 | 4 | 9 | 12 | 24 | 9 | 3 |
Matrix representation of D14⋊(C4⋊C4) ►in GL5(𝔽29)
| 1 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 3 | 8 |
| 0 | 0 | 0 | 21 | 8 |
| 28 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 |
| 0 | 0 | 0 | 28 | 0 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 20 | 22 |
| 0 | 0 | 0 | 20 | 9 |
| 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 27 | 18 |
| 0 | 0 | 0 | 11 | 2 |
G:=sub<GL(5,GF(29))| [1,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,3,21,0,0,0,8,8],[28,0,0,0,0,0,1,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,28,0],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,20,20,0,0,0,22,9],[12,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,27,11,0,0,0,18,2] >;
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(448,201);
// by ID
G=gap.SmallGroup(448,201);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,1094,387,58,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^2=c^4=d^4=1,b*a*b=c*a*c^-1=a^-1,a*d=d*a,c*b*c^-1=a^12*b,d*b*d^-1=a^7*b,d*c*d^-1=c^-1>;
// generators/relations