C14xC4:1D4 - GroupNames

G = C₁₄×C₄⋊₁D₄ order 448 = 2⁶·7

Direct product of C₁₄ and C₄⋊₁D₄

direct product, metabelian, nilpotent (class 2), monomial, 2-elementary

Aliases: C₁₄×C₄⋊₁D₄, C₄⋊₁(D₄×C₁₄), C₂₈⋊₁₂(C₂×D₄), (C₂×C₂₈)⋊₃₃D₄, (C₂×C₄²)⋊₁₁C₁₄, C₄²⋊₁₈(C₂×C₁₄), (C₄×C₂₈)⋊₅₉C₂², (C₂²×D₄)⋊₅C₁₄, (D₄×C₁₄)⋊₆₃C₂², C₂⁴.₁₈(C₂×C₁₄), C₂².₆₃(D₄×C₁₄), (C₂×C₂₈).₉₆₁C₂³, (C₂×C₁₄).₃₅₀C₂⁴, C₁₄.₁₈₆(C₂²×D₄), C₂³.₈(C₂²×C₁₄), C₂².₂₄(C₂³×C₁₄), (C₂²×C₁₄).₈₈C₂³, (C₂³×C₁₄).₁₅C₂², (C₂²×C₂₈).₅₉₆C₂², (C₂×C₄×C₂₈)⋊₂₄C₂, (C₂×C₄)⋊₇(C₇×D₄), (D₄×C₂×C₁₄)⋊₂₀C₂, C₂.₁₀(D₄×C₂×C₁₄), (C₂×D₄)⋊₁₁(C₂×C₁₄), (C₂×C₁₄).₆₈₄(C₂×D₄), (C₂²×C₄).₁₂₄(C₂×C₁₄), (C₂×C₄).₁₃₆(C₂²×C₁₄), SmallGroup(448,1313)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series

C₁ — C₂² — C₁₄×C₄⋊₁D₄

Chief series

C₁ — C₂ — C₂² — C₂×C₁₄ — C₂²×C₁₄ — D₄×C₁₄ — C₇×C₄⋊₁D₄ — C₁₄×C₄⋊₁D₄

Lower central

C₁ — C₂² — C₁₄×C₄⋊₁D₄

Upper central

C₁ — C₂²×C₁₄ — C₁₄×C₄⋊₁D₄

Generators and relations for C₁₄×C₄⋊₁D₄
G = < a,b,c,d | a¹⁴=b⁴=c⁴=d²=1, ab=ba, ac=ca, ad=da, bc=cb, dbd=b^-1, dcd=c^-1 >

Subgroups: 882 in 498 conjugacy classes, 210 normal (10 characteristic)
C₁, C₂, C₂, C₄, C₂², C₂², C₂², C₇, C₂×C₄, D₄, C₂³, C₂³, C₂³, C₁₄, C₁₄, C₄², C₂²×C₄, C₂×D₄, C₂×D₄, C₂⁴, C₂₈, C₂×C₁₄, C₂×C₁₄, C₂×C₁₄, C₂×C₄², C₄⋊₁D₄, C₂²×D₄, C₂×C₂₈, C₇×D₄, C₂²×C₁₄, C₂²×C₁₄, C₂²×C₁₄, C₂×C₄⋊₁D₄, C₄×C₂₈, C₂²×C₂₈, D₄×C₁₄, D₄×C₁₄, C₂³×C₁₄, C₂×C₄×C₂₈, C₇×C₄⋊₁D₄, D₄×C₂×C₁₄, C₁₄×C₄⋊₁D₄
Quotients: C₁, C₂, C₂², C₇, D₄, C₂³, C₁₄, C₂×D₄, C₂⁴, C₂×C₁₄, C₄⋊₁D₄, C₂²×D₄, C₇×D₄, C₂²×C₁₄, C₂×C₄⋊₁D₄, D₄×C₁₄, C₂³×C₁₄, C₇×C₄⋊₁D₄, D₄×C₂×C₁₄, C₁₄×C₄⋊₁D₄

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

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

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

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

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

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

196 conjugacy classes

class	1	2A	···	2G	2H	···	2O	4A	···	4L	7A	···	7F	14A	···	14AP	14AQ	···	14CL	28A	···	28BT
order	1	2	···	2	2	···	2	4	···	4	7	···	7	14	···	14	14	···	14	28	···	28
size	1	1	···	1	4	···	4	2	···	2	1	···	1	1	···	1	4	···	4	2	···	2

196 irreducible representations

dim	1	1	1	1	1	1	1	1	2	2
type	+	+	+	+					+
image	C₁	C₂	C₂	C₂	C₇	C₁₄	C₁₄	C₁₄	D₄	C₇×D₄
kernel	C₁₄×C₄⋊₁D₄	C₂×C₄×C₂₈	C₇×C₄⋊₁D₄	D₄×C₂×C₁₄	C₂×C₄⋊₁D₄	C₂×C₄²	C₄⋊₁D₄	C₂²×D₄	C₂×C₂₈	C₂×C₄
# reps	1	1	8	6	6	6	48	36	12	72

Matrix representation of C₁₄×C₄⋊₁D₄ ►in GL₆(𝔽₂₉)

6	0	0	0	0	0
0	6	0	0	0	0
0	0	7	0	0	0
0	0	0	7	0	0
0	0	0	0	13	0
0	0	0	0	0	13

1	2	0	0	0	0
28	28	0	0	0	0
0	0	28	2	0	0
0	0	28	1	0	0
0	0	0	0	28	0
0	0	0	0	0	28

28	0	0	0	0	0
0	28	0	0	0	0
0	0	1	0	0	0
0	0	0	1	0	0
0	0	0	0	1	2
0	0	0	0	28	28

28	27	0	0	0	0
0	1	0	0	0	0
0	0	1	27	0	0
0	0	0	28	0	0
0	0	0	0	28	27
0	0	0	0	0	1

G:=sub<GL(6,GF(29))| [6,0,0,0,0,0,0,6,0,0,0,0,0,0,7,0,0,0,0,0,0,7,0,0,0,0,0,0,13,0,0,0,0,0,0,13],[1,28,0,0,0,0,2,28,0,0,0,0,0,0,28,28,0,0,0,0,2,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,28,0,0,0,0,2,28],[28,0,0,0,0,0,27,1,0,0,0,0,0,0,1,0,0,0,0,0,27,28,0,0,0,0,0,0,28,0,0,0,0,0,27,1] >;

C₁₄×C₄⋊₁D₄ in GAP, Magma, Sage, TeX

C_{14}\times C_4\rtimes_1D_4

% in TeX

G:=Group("C14xC4:1D4");

// GroupNames label

G:=SmallGroup(448,1313);

// by ID

G=gap.SmallGroup(448,1313);

# by ID

G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,1597,792,4790,1192]);

// Polycyclic

G:=Group<a,b,c,d|a^14=b^4=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d=b^-1,d*c*d=c^-1>;

// generators/relations

G = C14×C4⋊1D4 order 448 = 26·7

Direct product of C14 and C4⋊1D4

G = C₁₄×C₄⋊₁D₄ order 448 = 2⁶·7

Direct product of C₁₄ and C₄⋊₁D₄