G = C14.1442+ 1+4 order 448 = 26·7
53rd non-split extension by C14 of 2+ 1+4 acting via 2+ 1+4/C4○D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.1442+ 1+4, C14.1062- 1+4, C4○D4⋊5Dic7, D4⋊8(C2×Dic7), Q8⋊7(C2×Dic7), (Q8×Dic7)⋊28C2, (D4×Dic7)⋊41C2, (C2×D4).253D14, C14.51(C23×C4), (C2×Q8).209D14, C2.5(D4⋊8D14), C28.100(C22×C4), (C2×C14).313C24, (C2×C28).560C23, (C22×C4).286D14, C2.13(C23×Dic7), C4.22(C22×Dic7), C22.49(C23×D7), (D4×C14).275C22, C4⋊Dic7.392C22, (Q8×C14).242C22, C23.210(C22×D7), C2.5(D4.10D14), C23.21D14⋊37C2, C22.4(C22×Dic7), (C22×C14).239C23, (C22×C28).295C22, C7⋊5(C23.33C23), (C2×Dic7).292C23, (C4×Dic7).175C22, C23.D7.135C22, (C22×Dic7).167C22, (C7×C4○D4)⋊6C4, (C2×C28)⋊17(C2×C4), (C7×D4)⋊22(C2×C4), (C7×Q8)⋊20(C2×C4), (C2×C4)⋊5(C2×Dic7), (C2×C4⋊Dic7)⋊47C2, (C2×C4○D4).12D7, (C14×C4○D4).14C2, (C2×C14).31(C22×C4), (C2×C4).638(C22×D7), SmallGroup(448,1280)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.1442+ 1+4
G = < a,b,c,d,e | a14=b4=c2=1, d2=b2, e2=a7, ab=ba, ac=ca, ad=da, eae-1=a-1, cbc=b-1, bd=db, be=eb, cd=dc, ce=ec, ede-1=b2d >
Subgroups: 916 in 294 conjugacy classes, 191 normal (18 characteristic)
C1, C2 [×3], C2 [×6], C4 [×8], C4 [×8], C22, C22 [×6], C22 [×6], C7, C2×C4, C2×C4 [×15], C2×C4 [×14], D4 [×12], Q8 [×4], C23 [×3], C14 [×3], C14 [×6], C42 [×6], C22⋊C4 [×6], C4⋊C4 [×10], C22×C4 [×3], C22×C4 [×6], C2×D4 [×3], C2×Q8, C4○D4 [×8], Dic7 [×8], C28 [×8], C2×C14, C2×C14 [×6], C2×C14 [×6], C2×C4⋊C4 [×3], C42⋊C2 [×3], C4×D4 [×6], C4×Q8 [×2], C2×C4○D4, C2×Dic7 [×8], C2×Dic7 [×6], C2×C28, C2×C28 [×15], C7×D4 [×12], C7×Q8 [×4], C22×C14 [×3], C23.33C23, C4×Dic7 [×6], C4⋊Dic7, C4⋊Dic7 [×9], C23.D7 [×6], C22×Dic7 [×6], C22×C28 [×3], D4×C14 [×3], Q8×C14, C7×C4○D4 [×8], C2×C4⋊Dic7 [×3], C23.21D14 [×3], D4×Dic7 [×6], Q8×Dic7 [×2], C14×C4○D4, C14.1442+ 1+4
Quotients: C1, C2 [×15], C4 [×8], C22 [×35], C2×C4 [×28], C23 [×15], D7, C22×C4 [×14], C24, Dic7 [×8], D14 [×7], C23×C4, 2+ 1+4, 2- 1+4, C2×Dic7 [×28], C22×D7 [×7], C23.33C23, C22×Dic7 [×14], C23×D7, D4⋊8D14, D4.10D14, C23×Dic7, C14.1442+ 1+4
►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)
(1 105 134 162)(2 106 135 163)(3 107 136 164)(4 108 137 165)(5 109 138 166)(6 110 139 167)(7 111 140 168)(8 112 127 155)(9 99 128 156)(10 100 129 157)(11 101 130 158)(12 102 131 159)(13 103 132 160)(14 104 133 161)(15 29 121 148)(16 30 122 149)(17 31 123 150)(18 32 124 151)(19 33 125 152)(20 34 126 153)(21 35 113 154)(22 36 114 141)(23 37 115 142)(24 38 116 143)(25 39 117 144)(26 40 118 145)(27 41 119 146)(28 42 120 147)(43 186 209 57)(44 187 210 58)(45 188 197 59)(46 189 198 60)(47 190 199 61)(48 191 200 62)(49 192 201 63)(50 193 202 64)(51 194 203 65)(52 195 204 66)(53 196 205 67)(54 183 206 68)(55 184 207 69)(56 185 208 70)(71 90 220 174)(72 91 221 175)(73 92 222 176)(74 93 223 177)(75 94 224 178)(76 95 211 179)(77 96 212 180)(78 97 213 181)(79 98 214 182)(80 85 215 169)(81 86 216 170)(82 87 217 171)(83 88 218 172)(84 89 219 173)
(15 121)(16 122)(17 123)(18 124)(19 125)(20 126)(21 113)(22 114)(23 115)(24 116)(25 117)(26 118)(27 119)(28 120)(57 186)(58 187)(59 188)(60 189)(61 190)(62 191)(63 192)(64 193)(65 194)(66 195)(67 196)(68 183)(69 184)(70 185)(85 169)(86 170)(87 171)(88 172)(89 173)(90 174)(91 175)(92 176)(93 177)(94 178)(95 179)(96 180)(97 181)(98 182)(99 156)(100 157)(101 158)(102 159)(103 160)(104 161)(105 162)(106 163)(107 164)(108 165)(109 166)(110 167)(111 168)(112 155)
(1 218 134 83)(2 219 135 84)(3 220 136 71)(4 221 137 72)(5 222 138 73)(6 223 139 74)(7 224 140 75)(8 211 127 76)(9 212 128 77)(10 213 129 78)(11 214 130 79)(12 215 131 80)(13 216 132 81)(14 217 133 82)(15 65 121 194)(16 66 122 195)(17 67 123 196)(18 68 124 183)(19 69 125 184)(20 70 126 185)(21 57 113 186)(22 58 114 187)(23 59 115 188)(24 60 116 189)(25 61 117 190)(26 62 118 191)(27 63 119 192)(28 64 120 193)(29 51 148 203)(30 52 149 204)(31 53 150 205)(32 54 151 206)(33 55 152 207)(34 56 153 208)(35 43 154 209)(36 44 141 210)(37 45 142 197)(38 46 143 198)(39 47 144 199)(40 48 145 200)(41 49 146 201)(42 50 147 202)(85 102 169 159)(86 103 170 160)(87 104 171 161)(88 105 172 162)(89 106 173 163)(90 107 174 164)(91 108 175 165)(92 109 176 166)(93 110 177 167)(94 111 178 168)(95 112 179 155)(96 99 180 156)(97 100 181 157)(98 101 182 158)
(1 142 8 149)(2 141 9 148)(3 154 10 147)(4 153 11 146)(5 152 12 145)(6 151 13 144)(7 150 14 143)(15 106 22 99)(16 105 23 112)(17 104 24 111)(18 103 25 110)(19 102 26 109)(20 101 27 108)(21 100 28 107)(29 135 36 128)(30 134 37 127)(31 133 38 140)(32 132 39 139)(33 131 40 138)(34 130 41 137)(35 129 42 136)(43 213 50 220)(44 212 51 219)(45 211 52 218)(46 224 53 217)(47 223 54 216)(48 222 55 215)(49 221 56 214)(57 97 64 90)(58 96 65 89)(59 95 66 88)(60 94 67 87)(61 93 68 86)(62 92 69 85)(63 91 70 98)(71 209 78 202)(72 208 79 201)(73 207 80 200)(74 206 81 199)(75 205 82 198)(76 204 83 197)(77 203 84 210)(113 157 120 164)(114 156 121 163)(115 155 122 162)(116 168 123 161)(117 167 124 160)(118 166 125 159)(119 165 126 158)(169 191 176 184)(170 190 177 183)(171 189 178 196)(172 188 179 195)(173 187 180 194)(174 186 181 193)(175 185 182 192)
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), (1,105,134,162)(2,106,135,163)(3,107,136,164)(4,108,137,165)(5,109,138,166)(6,110,139,167)(7,111,140,168)(8,112,127,155)(9,99,128,156)(10,100,129,157)(11,101,130,158)(12,102,131,159)(13,103,132,160)(14,104,133,161)(15,29,121,148)(16,30,122,149)(17,31,123,150)(18,32,124,151)(19,33,125,152)(20,34,126,153)(21,35,113,154)(22,36,114,141)(23,37,115,142)(24,38,116,143)(25,39,117,144)(26,40,118,145)(27,41,119,146)(28,42,120,147)(43,186,209,57)(44,187,210,58)(45,188,197,59)(46,189,198,60)(47,190,199,61)(48,191,200,62)(49,192,201,63)(50,193,202,64)(51,194,203,65)(52,195,204,66)(53,196,205,67)(54,183,206,68)(55,184,207,69)(56,185,208,70)(71,90,220,174)(72,91,221,175)(73,92,222,176)(74,93,223,177)(75,94,224,178)(76,95,211,179)(77,96,212,180)(78,97,213,181)(79,98,214,182)(80,85,215,169)(81,86,216,170)(82,87,217,171)(83,88,218,172)(84,89,219,173), (15,121)(16,122)(17,123)(18,124)(19,125)(20,126)(21,113)(22,114)(23,115)(24,116)(25,117)(26,118)(27,119)(28,120)(57,186)(58,187)(59,188)(60,189)(61,190)(62,191)(63,192)(64,193)(65,194)(66,195)(67,196)(68,183)(69,184)(70,185)(85,169)(86,170)(87,171)(88,172)(89,173)(90,174)(91,175)(92,176)(93,177)(94,178)(95,179)(96,180)(97,181)(98,182)(99,156)(100,157)(101,158)(102,159)(103,160)(104,161)(105,162)(106,163)(107,164)(108,165)(109,166)(110,167)(111,168)(112,155), (1,218,134,83)(2,219,135,84)(3,220,136,71)(4,221,137,72)(5,222,138,73)(6,223,139,74)(7,224,140,75)(8,211,127,76)(9,212,128,77)(10,213,129,78)(11,214,130,79)(12,215,131,80)(13,216,132,81)(14,217,133,82)(15,65,121,194)(16,66,122,195)(17,67,123,196)(18,68,124,183)(19,69,125,184)(20,70,126,185)(21,57,113,186)(22,58,114,187)(23,59,115,188)(24,60,116,189)(25,61,117,190)(26,62,118,191)(27,63,119,192)(28,64,120,193)(29,51,148,203)(30,52,149,204)(31,53,150,205)(32,54,151,206)(33,55,152,207)(34,56,153,208)(35,43,154,209)(36,44,141,210)(37,45,142,197)(38,46,143,198)(39,47,144,199)(40,48,145,200)(41,49,146,201)(42,50,147,202)(85,102,169,159)(86,103,170,160)(87,104,171,161)(88,105,172,162)(89,106,173,163)(90,107,174,164)(91,108,175,165)(92,109,176,166)(93,110,177,167)(94,111,178,168)(95,112,179,155)(96,99,180,156)(97,100,181,157)(98,101,182,158), (1,142,8,149)(2,141,9,148)(3,154,10,147)(4,153,11,146)(5,152,12,145)(6,151,13,144)(7,150,14,143)(15,106,22,99)(16,105,23,112)(17,104,24,111)(18,103,25,110)(19,102,26,109)(20,101,27,108)(21,100,28,107)(29,135,36,128)(30,134,37,127)(31,133,38,140)(32,132,39,139)(33,131,40,138)(34,130,41,137)(35,129,42,136)(43,213,50,220)(44,212,51,219)(45,211,52,218)(46,224,53,217)(47,223,54,216)(48,222,55,215)(49,221,56,214)(57,97,64,90)(58,96,65,89)(59,95,66,88)(60,94,67,87)(61,93,68,86)(62,92,69,85)(63,91,70,98)(71,209,78,202)(72,208,79,201)(73,207,80,200)(74,206,81,199)(75,205,82,198)(76,204,83,197)(77,203,84,210)(113,157,120,164)(114,156,121,163)(115,155,122,162)(116,168,123,161)(117,167,124,160)(118,166,125,159)(119,165,126,158)(169,191,176,184)(170,190,177,183)(171,189,178,196)(172,188,179,195)(173,187,180,194)(174,186,181,193)(175,185,182,192)>;
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), (1,105,134,162)(2,106,135,163)(3,107,136,164)(4,108,137,165)(5,109,138,166)(6,110,139,167)(7,111,140,168)(8,112,127,155)(9,99,128,156)(10,100,129,157)(11,101,130,158)(12,102,131,159)(13,103,132,160)(14,104,133,161)(15,29,121,148)(16,30,122,149)(17,31,123,150)(18,32,124,151)(19,33,125,152)(20,34,126,153)(21,35,113,154)(22,36,114,141)(23,37,115,142)(24,38,116,143)(25,39,117,144)(26,40,118,145)(27,41,119,146)(28,42,120,147)(43,186,209,57)(44,187,210,58)(45,188,197,59)(46,189,198,60)(47,190,199,61)(48,191,200,62)(49,192,201,63)(50,193,202,64)(51,194,203,65)(52,195,204,66)(53,196,205,67)(54,183,206,68)(55,184,207,69)(56,185,208,70)(71,90,220,174)(72,91,221,175)(73,92,222,176)(74,93,223,177)(75,94,224,178)(76,95,211,179)(77,96,212,180)(78,97,213,181)(79,98,214,182)(80,85,215,169)(81,86,216,170)(82,87,217,171)(83,88,218,172)(84,89,219,173), (15,121)(16,122)(17,123)(18,124)(19,125)(20,126)(21,113)(22,114)(23,115)(24,116)(25,117)(26,118)(27,119)(28,120)(57,186)(58,187)(59,188)(60,189)(61,190)(62,191)(63,192)(64,193)(65,194)(66,195)(67,196)(68,183)(69,184)(70,185)(85,169)(86,170)(87,171)(88,172)(89,173)(90,174)(91,175)(92,176)(93,177)(94,178)(95,179)(96,180)(97,181)(98,182)(99,156)(100,157)(101,158)(102,159)(103,160)(104,161)(105,162)(106,163)(107,164)(108,165)(109,166)(110,167)(111,168)(112,155), (1,218,134,83)(2,219,135,84)(3,220,136,71)(4,221,137,72)(5,222,138,73)(6,223,139,74)(7,224,140,75)(8,211,127,76)(9,212,128,77)(10,213,129,78)(11,214,130,79)(12,215,131,80)(13,216,132,81)(14,217,133,82)(15,65,121,194)(16,66,122,195)(17,67,123,196)(18,68,124,183)(19,69,125,184)(20,70,126,185)(21,57,113,186)(22,58,114,187)(23,59,115,188)(24,60,116,189)(25,61,117,190)(26,62,118,191)(27,63,119,192)(28,64,120,193)(29,51,148,203)(30,52,149,204)(31,53,150,205)(32,54,151,206)(33,55,152,207)(34,56,153,208)(35,43,154,209)(36,44,141,210)(37,45,142,197)(38,46,143,198)(39,47,144,199)(40,48,145,200)(41,49,146,201)(42,50,147,202)(85,102,169,159)(86,103,170,160)(87,104,171,161)(88,105,172,162)(89,106,173,163)(90,107,174,164)(91,108,175,165)(92,109,176,166)(93,110,177,167)(94,111,178,168)(95,112,179,155)(96,99,180,156)(97,100,181,157)(98,101,182,158), (1,142,8,149)(2,141,9,148)(3,154,10,147)(4,153,11,146)(5,152,12,145)(6,151,13,144)(7,150,14,143)(15,106,22,99)(16,105,23,112)(17,104,24,111)(18,103,25,110)(19,102,26,109)(20,101,27,108)(21,100,28,107)(29,135,36,128)(30,134,37,127)(31,133,38,140)(32,132,39,139)(33,131,40,138)(34,130,41,137)(35,129,42,136)(43,213,50,220)(44,212,51,219)(45,211,52,218)(46,224,53,217)(47,223,54,216)(48,222,55,215)(49,221,56,214)(57,97,64,90)(58,96,65,89)(59,95,66,88)(60,94,67,87)(61,93,68,86)(62,92,69,85)(63,91,70,98)(71,209,78,202)(72,208,79,201)(73,207,80,200)(74,206,81,199)(75,205,82,198)(76,204,83,197)(77,203,84,210)(113,157,120,164)(114,156,121,163)(115,155,122,162)(116,168,123,161)(117,167,124,160)(118,166,125,159)(119,165,126,158)(169,191,176,184)(170,190,177,183)(171,189,178,196)(172,188,179,195)(173,187,180,194)(174,186,181,193)(175,185,182,192) );
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)], [(1,105,134,162),(2,106,135,163),(3,107,136,164),(4,108,137,165),(5,109,138,166),(6,110,139,167),(7,111,140,168),(8,112,127,155),(9,99,128,156),(10,100,129,157),(11,101,130,158),(12,102,131,159),(13,103,132,160),(14,104,133,161),(15,29,121,148),(16,30,122,149),(17,31,123,150),(18,32,124,151),(19,33,125,152),(20,34,126,153),(21,35,113,154),(22,36,114,141),(23,37,115,142),(24,38,116,143),(25,39,117,144),(26,40,118,145),(27,41,119,146),(28,42,120,147),(43,186,209,57),(44,187,210,58),(45,188,197,59),(46,189,198,60),(47,190,199,61),(48,191,200,62),(49,192,201,63),(50,193,202,64),(51,194,203,65),(52,195,204,66),(53,196,205,67),(54,183,206,68),(55,184,207,69),(56,185,208,70),(71,90,220,174),(72,91,221,175),(73,92,222,176),(74,93,223,177),(75,94,224,178),(76,95,211,179),(77,96,212,180),(78,97,213,181),(79,98,214,182),(80,85,215,169),(81,86,216,170),(82,87,217,171),(83,88,218,172),(84,89,219,173)], [(15,121),(16,122),(17,123),(18,124),(19,125),(20,126),(21,113),(22,114),(23,115),(24,116),(25,117),(26,118),(27,119),(28,120),(57,186),(58,187),(59,188),(60,189),(61,190),(62,191),(63,192),(64,193),(65,194),(66,195),(67,196),(68,183),(69,184),(70,185),(85,169),(86,170),(87,171),(88,172),(89,173),(90,174),(91,175),(92,176),(93,177),(94,178),(95,179),(96,180),(97,181),(98,182),(99,156),(100,157),(101,158),(102,159),(103,160),(104,161),(105,162),(106,163),(107,164),(108,165),(109,166),(110,167),(111,168),(112,155)], [(1,218,134,83),(2,219,135,84),(3,220,136,71),(4,221,137,72),(5,222,138,73),(6,223,139,74),(7,224,140,75),(8,211,127,76),(9,212,128,77),(10,213,129,78),(11,214,130,79),(12,215,131,80),(13,216,132,81),(14,217,133,82),(15,65,121,194),(16,66,122,195),(17,67,123,196),(18,68,124,183),(19,69,125,184),(20,70,126,185),(21,57,113,186),(22,58,114,187),(23,59,115,188),(24,60,116,189),(25,61,117,190),(26,62,118,191),(27,63,119,192),(28,64,120,193),(29,51,148,203),(30,52,149,204),(31,53,150,205),(32,54,151,206),(33,55,152,207),(34,56,153,208),(35,43,154,209),(36,44,141,210),(37,45,142,197),(38,46,143,198),(39,47,144,199),(40,48,145,200),(41,49,146,201),(42,50,147,202),(85,102,169,159),(86,103,170,160),(87,104,171,161),(88,105,172,162),(89,106,173,163),(90,107,174,164),(91,108,175,165),(92,109,176,166),(93,110,177,167),(94,111,178,168),(95,112,179,155),(96,99,180,156),(97,100,181,157),(98,101,182,158)], [(1,142,8,149),(2,141,9,148),(3,154,10,147),(4,153,11,146),(5,152,12,145),(6,151,13,144),(7,150,14,143),(15,106,22,99),(16,105,23,112),(17,104,24,111),(18,103,25,110),(19,102,26,109),(20,101,27,108),(21,100,28,107),(29,135,36,128),(30,134,37,127),(31,133,38,140),(32,132,39,139),(33,131,40,138),(34,130,41,137),(35,129,42,136),(43,213,50,220),(44,212,51,219),(45,211,52,218),(46,224,53,217),(47,223,54,216),(48,222,55,215),(49,221,56,214),(57,97,64,90),(58,96,65,89),(59,95,66,88),(60,94,67,87),(61,93,68,86),(62,92,69,85),(63,91,70,98),(71,209,78,202),(72,208,79,201),(73,207,80,200),(74,206,81,199),(75,205,82,198),(76,204,83,197),(77,203,84,210),(113,157,120,164),(114,156,121,163),(115,155,122,162),(116,168,123,161),(117,167,124,160),(118,166,125,159),(119,165,126,158),(169,191,176,184),(170,190,177,183),(171,189,178,196),(172,188,179,195),(173,187,180,194),(174,186,181,193),(175,185,182,192)])
94 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | ··· | 2I | 4A | ··· | 4H | 4I | ··· | 4X | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14AA | 28A | ··· | 28L | 28M | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 14 | ··· | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
94 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | + | - | + | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | D7 | D14 | D14 | D14 | Dic7 | 2+ 1+4 | 2- 1+4 | D4⋊8D14 | D4.10D14 |
| kernel | C14.1442+ 1+4 | C2×C4⋊Dic7 | C23.21D14 | D4×Dic7 | Q8×Dic7 | C14×C4○D4 | C7×C4○D4 | C2×C4○D4 | C22×C4 | C2×D4 | C2×Q8 | C4○D4 | C14 | C14 | C2 | C2 |
| # reps | 1 | 3 | 3 | 6 | 2 | 1 | 16 | 3 | 9 | 9 | 3 | 24 | 1 | 1 | 6 | 6 |
Matrix representation of C14.1442+ 1+4 ►in GL6(𝔽29)
| 4 | 4 | 0 | 0 | 0 | 0 |
| 25 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 8 | 0 | 0 |
| 0 | 0 | 21 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 8 |
| 0 | 0 | 0 | 0 | 13 | 2 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 18 | 8 | 21 |
| 0 | 0 | 11 | 27 | 17 | 14 |
| 0 | 0 | 0 | 0 | 3 | 11 |
| 0 | 0 | 0 | 0 | 7 | 26 |
| 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 | 14 | 28 | 0 |
| 0 | 0 | 15 | 4 | 0 | 28 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 11 | 0 | 0 |
| 0 | 0 | 18 | 2 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 11 |
| 0 | 0 | 0 | 0 | 7 | 26 |
| 2 | 11 | 0 | 0 | 0 | 0 |
| 18 | 27 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 16 | 0 | 0 |
| 0 | 0 | 2 | 24 | 0 | 0 |
| 0 | 0 | 28 | 17 | 21 | 2 |
| 0 | 0 | 25 | 17 | 11 | 8 |
G:=sub<GL(6,GF(29))| [4,25,0,0,0,0,4,18,0,0,0,0,0,0,8,21,0,0,0,0,8,3,0,0,0,0,0,0,9,13,0,0,0,0,8,2],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,2,11,0,0,0,0,18,27,0,0,0,0,8,17,3,7,0,0,21,14,11,26],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,15,0,0,0,1,14,4,0,0,0,0,28,0,0,0,0,0,0,28],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,27,18,0,0,0,0,11,2,0,0,0,0,0,0,3,7,0,0,0,0,11,26],[2,18,0,0,0,0,11,27,0,0,0,0,0,0,5,2,28,25,0,0,16,24,17,17,0,0,0,0,21,11,0,0,0,0,2,8] >;
C14.1442+ 1+4 in GAP, Magma, Sage, TeX
C_{14}._{144}2_+^{1+4} % in TeX
G:=Group("C14.144ES+(2,2)"); // GroupNames label
G:=SmallGroup(448,1280);
// by ID
G=gap.SmallGroup(448,1280);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,387,1123,136,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=c^2=1,d^2=b^2,e^2=a^7,a*b=b*a,a*c=c*a,a*d=d*a,e*a*e^-1=a^-1,c*b*c=b^-1,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=b^2*d>;
// generators/relations