G = C14.22- 1+4 order 448 = 26·7
2nd non-split extension by C14 of 2- 1+4 acting via 2- 1+4/C2×Q8=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.22- 1+4, C14.82+ 1+4, C4○D28⋊9C4, D28⋊23(C2×C4), D28⋊C4⋊8C2, C4⋊C4.305D14, Dic14⋊22(C2×C4), Dic7⋊3Q8⋊8C2, C28.89(C22×C4), C14.14(C23×C4), (C2×C14).48C24, D14.3(C22×C4), C2.2(D4⋊6D14), (C2×C28).486C23, (C22×C4).176D14, Dic7.5(C22×C4), C22.24(C23×D7), D14⋊C4.116C22, (C2×D28).253C22, C4⋊Dic7.359C22, (C4×Dic7).63C22, C23.224(C22×D7), C23.21D14⋊22C2, Dic7⋊C4.129C22, (C22×C14).397C23, (C22×C28).216C22, C2.1(Q8.10D14), C7⋊1(C23.33C23), (C2×Dic7).186C23, (C22×D7).155C23, C23.D7.141C22, (C2×Dic14).281C22, (D7×C4⋊C4)⋊8C2, (C2×C4)⋊5(C4×D7), C4.92(C2×C4×D7), (C2×C28)⋊9(C2×C4), (C2×C4⋊C4)⋊13D7, (C4×D7)⋊1(C2×C4), (C14×C4⋊C4)⋊10C2, C4⋊C4⋊7D7⋊8C2, (C4×C7⋊D4)⋊35C2, C7⋊D4⋊10(C2×C4), C2.16(D7×C22×C4), C22.10(C2×C4×D7), (C2×C4○D28).16C2, (C2×C4×D7).189C22, (C7×C4⋊C4).294C22, (C2×C4).267(C22×D7), (C2×C14).153(C22×C4), (C2×C7⋊D4).146C22, SmallGroup(448,957)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.22- 1+4
G = < a,b,c,d,e | a14=b4=1, c2=a7, d2=e2=b2, bab-1=cac-1=a-1, ad=da, ae=ea, cbc-1=a7b-1, bd=db, be=eb, cd=dc, ce=ec, ede-1=a7b2d >
Subgroups: 1156 in 294 conjugacy classes, 151 normal (27 characteristic)
C1, C2 [×3], C2 [×6], C4 [×4], C4 [×12], C22, C22 [×2], C22 [×10], C7, C2×C4 [×2], C2×C4 [×8], C2×C4 [×20], D4 [×12], Q8 [×4], C23, C23 [×2], D7 [×4], C14 [×3], C14 [×2], C42 [×6], C22⋊C4 [×6], C4⋊C4 [×4], C4⋊C4 [×6], C22×C4, C22×C4 [×2], C22×C4 [×6], C2×D4 [×3], C2×Q8, C4○D4 [×8], Dic7 [×4], Dic7 [×4], C28 [×4], C28 [×4], D14 [×4], D14 [×4], C2×C14, C2×C14 [×2], C2×C14 [×2], C2×C4⋊C4, C2×C4⋊C4 [×2], C42⋊C2 [×3], C4×D4 [×6], C4×Q8 [×2], C2×C4○D4, Dic14 [×4], C4×D7 [×8], C4×D7 [×4], D28 [×4], C2×Dic7 [×6], C7⋊D4 [×8], C2×C28 [×2], C2×C28 [×8], C2×C28 [×2], C22×D7 [×2], C22×C14, C23.33C23, C4×Dic7 [×6], Dic7⋊C4 [×4], C4⋊Dic7 [×2], D14⋊C4 [×4], C23.D7 [×2], C7×C4⋊C4 [×4], C2×Dic14, C2×C4×D7 [×6], C2×D28, C4○D28 [×8], C2×C7⋊D4 [×2], C22×C28, C22×C28 [×2], Dic7⋊3Q8 [×2], D7×C4⋊C4 [×2], C4⋊C4⋊7D7 [×2], D28⋊C4 [×2], C23.21D14, C4×C7⋊D4 [×4], C14×C4⋊C4, C2×C4○D28, C14.22- 1+4
Quotients: C1, C2 [×15], C4 [×8], C22 [×35], C2×C4 [×28], C23 [×15], D7, C22×C4 [×14], C24, D14 [×7], C23×C4, 2+ 1+4, 2- 1+4, C4×D7 [×4], C22×D7 [×7], C23.33C23, C2×C4×D7 [×6], C23×D7, D7×C22×C4, D4⋊6D14, Q8.10D14, C14.22- 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)
(1 183 44 156)(2 196 45 155)(3 195 46 168)(4 194 47 167)(5 193 48 166)(6 192 49 165)(7 191 50 164)(8 190 51 163)(9 189 52 162)(10 188 53 161)(11 187 54 160)(12 186 55 159)(13 185 56 158)(14 184 43 157)(15 38 205 103)(16 37 206 102)(17 36 207 101)(18 35 208 100)(19 34 209 99)(20 33 210 112)(21 32 197 111)(22 31 198 110)(23 30 199 109)(24 29 200 108)(25 42 201 107)(26 41 202 106)(27 40 203 105)(28 39 204 104)(57 147 94 113)(58 146 95 126)(59 145 96 125)(60 144 97 124)(61 143 98 123)(62 142 85 122)(63 141 86 121)(64 154 87 120)(65 153 88 119)(66 152 89 118)(67 151 90 117)(68 150 91 116)(69 149 92 115)(70 148 93 114)(71 170 213 135)(72 169 214 134)(73 182 215 133)(74 181 216 132)(75 180 217 131)(76 179 218 130)(77 178 219 129)(78 177 220 128)(79 176 221 127)(80 175 222 140)(81 174 223 139)(82 173 224 138)(83 172 211 137)(84 171 212 136)
(1 125 8 118)(2 124 9 117)(3 123 10 116)(4 122 11 115)(5 121 12 114)(6 120 13 113)(7 119 14 126)(15 177 22 170)(16 176 23 169)(17 175 24 182)(18 174 25 181)(19 173 26 180)(20 172 27 179)(21 171 28 178)(29 80 36 73)(30 79 37 72)(31 78 38 71)(32 77 39 84)(33 76 40 83)(34 75 41 82)(35 74 42 81)(43 146 50 153)(44 145 51 152)(45 144 52 151)(46 143 53 150)(47 142 54 149)(48 141 55 148)(49 154 56 147)(57 158 64 165)(58 157 65 164)(59 156 66 163)(60 155 67 162)(61 168 68 161)(62 167 69 160)(63 166 70 159)(85 194 92 187)(86 193 93 186)(87 192 94 185)(88 191 95 184)(89 190 96 183)(90 189 97 196)(91 188 98 195)(99 217 106 224)(100 216 107 223)(101 215 108 222)(102 214 109 221)(103 213 110 220)(104 212 111 219)(105 211 112 218)(127 199 134 206)(128 198 135 205)(129 197 136 204)(130 210 137 203)(131 209 138 202)(132 208 139 201)(133 207 140 200)
(1 190 44 163)(2 191 45 164)(3 192 46 165)(4 193 47 166)(5 194 48 167)(6 195 49 168)(7 196 50 155)(8 183 51 156)(9 184 52 157)(10 185 53 158)(11 186 54 159)(12 187 55 160)(13 188 56 161)(14 189 43 162)(15 107 205 42)(16 108 206 29)(17 109 207 30)(18 110 208 31)(19 111 209 32)(20 112 210 33)(21 99 197 34)(22 100 198 35)(23 101 199 36)(24 102 200 37)(25 103 201 38)(26 104 202 39)(27 105 203 40)(28 106 204 41)(57 123 94 143)(58 124 95 144)(59 125 96 145)(60 126 97 146)(61 113 98 147)(62 114 85 148)(63 115 86 149)(64 116 87 150)(65 117 88 151)(66 118 89 152)(67 119 90 153)(68 120 91 154)(69 121 92 141)(70 122 93 142)(71 181 213 132)(72 182 214 133)(73 169 215 134)(74 170 216 135)(75 171 217 136)(76 172 218 137)(77 173 219 138)(78 174 220 139)(79 175 221 140)(80 176 222 127)(81 177 223 128)(82 178 224 129)(83 179 211 130)(84 180 212 131)
(1 20 44 210)(2 21 45 197)(3 22 46 198)(4 23 47 199)(5 24 48 200)(6 25 49 201)(7 26 50 202)(8 27 51 203)(9 28 52 204)(10 15 53 205)(11 16 54 206)(12 17 55 207)(13 18 56 208)(14 19 43 209)(29 166 108 193)(30 167 109 194)(31 168 110 195)(32 155 111 196)(33 156 112 183)(34 157 99 184)(35 158 100 185)(36 159 101 186)(37 160 102 187)(38 161 103 188)(39 162 104 189)(40 163 105 190)(41 164 106 191)(42 165 107 192)(57 223 94 81)(58 224 95 82)(59 211 96 83)(60 212 97 84)(61 213 98 71)(62 214 85 72)(63 215 86 73)(64 216 87 74)(65 217 88 75)(66 218 89 76)(67 219 90 77)(68 220 91 78)(69 221 92 79)(70 222 93 80)(113 174 147 139)(114 175 148 140)(115 176 149 127)(116 177 150 128)(117 178 151 129)(118 179 152 130)(119 180 153 131)(120 181 154 132)(121 182 141 133)(122 169 142 134)(123 170 143 135)(124 171 144 136)(125 172 145 137)(126 173 146 138)
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), (1,183,44,156)(2,196,45,155)(3,195,46,168)(4,194,47,167)(5,193,48,166)(6,192,49,165)(7,191,50,164)(8,190,51,163)(9,189,52,162)(10,188,53,161)(11,187,54,160)(12,186,55,159)(13,185,56,158)(14,184,43,157)(15,38,205,103)(16,37,206,102)(17,36,207,101)(18,35,208,100)(19,34,209,99)(20,33,210,112)(21,32,197,111)(22,31,198,110)(23,30,199,109)(24,29,200,108)(25,42,201,107)(26,41,202,106)(27,40,203,105)(28,39,204,104)(57,147,94,113)(58,146,95,126)(59,145,96,125)(60,144,97,124)(61,143,98,123)(62,142,85,122)(63,141,86,121)(64,154,87,120)(65,153,88,119)(66,152,89,118)(67,151,90,117)(68,150,91,116)(69,149,92,115)(70,148,93,114)(71,170,213,135)(72,169,214,134)(73,182,215,133)(74,181,216,132)(75,180,217,131)(76,179,218,130)(77,178,219,129)(78,177,220,128)(79,176,221,127)(80,175,222,140)(81,174,223,139)(82,173,224,138)(83,172,211,137)(84,171,212,136), (1,125,8,118)(2,124,9,117)(3,123,10,116)(4,122,11,115)(5,121,12,114)(6,120,13,113)(7,119,14,126)(15,177,22,170)(16,176,23,169)(17,175,24,182)(18,174,25,181)(19,173,26,180)(20,172,27,179)(21,171,28,178)(29,80,36,73)(30,79,37,72)(31,78,38,71)(32,77,39,84)(33,76,40,83)(34,75,41,82)(35,74,42,81)(43,146,50,153)(44,145,51,152)(45,144,52,151)(46,143,53,150)(47,142,54,149)(48,141,55,148)(49,154,56,147)(57,158,64,165)(58,157,65,164)(59,156,66,163)(60,155,67,162)(61,168,68,161)(62,167,69,160)(63,166,70,159)(85,194,92,187)(86,193,93,186)(87,192,94,185)(88,191,95,184)(89,190,96,183)(90,189,97,196)(91,188,98,195)(99,217,106,224)(100,216,107,223)(101,215,108,222)(102,214,109,221)(103,213,110,220)(104,212,111,219)(105,211,112,218)(127,199,134,206)(128,198,135,205)(129,197,136,204)(130,210,137,203)(131,209,138,202)(132,208,139,201)(133,207,140,200), (1,190,44,163)(2,191,45,164)(3,192,46,165)(4,193,47,166)(5,194,48,167)(6,195,49,168)(7,196,50,155)(8,183,51,156)(9,184,52,157)(10,185,53,158)(11,186,54,159)(12,187,55,160)(13,188,56,161)(14,189,43,162)(15,107,205,42)(16,108,206,29)(17,109,207,30)(18,110,208,31)(19,111,209,32)(20,112,210,33)(21,99,197,34)(22,100,198,35)(23,101,199,36)(24,102,200,37)(25,103,201,38)(26,104,202,39)(27,105,203,40)(28,106,204,41)(57,123,94,143)(58,124,95,144)(59,125,96,145)(60,126,97,146)(61,113,98,147)(62,114,85,148)(63,115,86,149)(64,116,87,150)(65,117,88,151)(66,118,89,152)(67,119,90,153)(68,120,91,154)(69,121,92,141)(70,122,93,142)(71,181,213,132)(72,182,214,133)(73,169,215,134)(74,170,216,135)(75,171,217,136)(76,172,218,137)(77,173,219,138)(78,174,220,139)(79,175,221,140)(80,176,222,127)(81,177,223,128)(82,178,224,129)(83,179,211,130)(84,180,212,131), (1,20,44,210)(2,21,45,197)(3,22,46,198)(4,23,47,199)(5,24,48,200)(6,25,49,201)(7,26,50,202)(8,27,51,203)(9,28,52,204)(10,15,53,205)(11,16,54,206)(12,17,55,207)(13,18,56,208)(14,19,43,209)(29,166,108,193)(30,167,109,194)(31,168,110,195)(32,155,111,196)(33,156,112,183)(34,157,99,184)(35,158,100,185)(36,159,101,186)(37,160,102,187)(38,161,103,188)(39,162,104,189)(40,163,105,190)(41,164,106,191)(42,165,107,192)(57,223,94,81)(58,224,95,82)(59,211,96,83)(60,212,97,84)(61,213,98,71)(62,214,85,72)(63,215,86,73)(64,216,87,74)(65,217,88,75)(66,218,89,76)(67,219,90,77)(68,220,91,78)(69,221,92,79)(70,222,93,80)(113,174,147,139)(114,175,148,140)(115,176,149,127)(116,177,150,128)(117,178,151,129)(118,179,152,130)(119,180,153,131)(120,181,154,132)(121,182,141,133)(122,169,142,134)(123,170,143,135)(124,171,144,136)(125,172,145,137)(126,173,146,138)>;
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), (1,183,44,156)(2,196,45,155)(3,195,46,168)(4,194,47,167)(5,193,48,166)(6,192,49,165)(7,191,50,164)(8,190,51,163)(9,189,52,162)(10,188,53,161)(11,187,54,160)(12,186,55,159)(13,185,56,158)(14,184,43,157)(15,38,205,103)(16,37,206,102)(17,36,207,101)(18,35,208,100)(19,34,209,99)(20,33,210,112)(21,32,197,111)(22,31,198,110)(23,30,199,109)(24,29,200,108)(25,42,201,107)(26,41,202,106)(27,40,203,105)(28,39,204,104)(57,147,94,113)(58,146,95,126)(59,145,96,125)(60,144,97,124)(61,143,98,123)(62,142,85,122)(63,141,86,121)(64,154,87,120)(65,153,88,119)(66,152,89,118)(67,151,90,117)(68,150,91,116)(69,149,92,115)(70,148,93,114)(71,170,213,135)(72,169,214,134)(73,182,215,133)(74,181,216,132)(75,180,217,131)(76,179,218,130)(77,178,219,129)(78,177,220,128)(79,176,221,127)(80,175,222,140)(81,174,223,139)(82,173,224,138)(83,172,211,137)(84,171,212,136), (1,125,8,118)(2,124,9,117)(3,123,10,116)(4,122,11,115)(5,121,12,114)(6,120,13,113)(7,119,14,126)(15,177,22,170)(16,176,23,169)(17,175,24,182)(18,174,25,181)(19,173,26,180)(20,172,27,179)(21,171,28,178)(29,80,36,73)(30,79,37,72)(31,78,38,71)(32,77,39,84)(33,76,40,83)(34,75,41,82)(35,74,42,81)(43,146,50,153)(44,145,51,152)(45,144,52,151)(46,143,53,150)(47,142,54,149)(48,141,55,148)(49,154,56,147)(57,158,64,165)(58,157,65,164)(59,156,66,163)(60,155,67,162)(61,168,68,161)(62,167,69,160)(63,166,70,159)(85,194,92,187)(86,193,93,186)(87,192,94,185)(88,191,95,184)(89,190,96,183)(90,189,97,196)(91,188,98,195)(99,217,106,224)(100,216,107,223)(101,215,108,222)(102,214,109,221)(103,213,110,220)(104,212,111,219)(105,211,112,218)(127,199,134,206)(128,198,135,205)(129,197,136,204)(130,210,137,203)(131,209,138,202)(132,208,139,201)(133,207,140,200), (1,190,44,163)(2,191,45,164)(3,192,46,165)(4,193,47,166)(5,194,48,167)(6,195,49,168)(7,196,50,155)(8,183,51,156)(9,184,52,157)(10,185,53,158)(11,186,54,159)(12,187,55,160)(13,188,56,161)(14,189,43,162)(15,107,205,42)(16,108,206,29)(17,109,207,30)(18,110,208,31)(19,111,209,32)(20,112,210,33)(21,99,197,34)(22,100,198,35)(23,101,199,36)(24,102,200,37)(25,103,201,38)(26,104,202,39)(27,105,203,40)(28,106,204,41)(57,123,94,143)(58,124,95,144)(59,125,96,145)(60,126,97,146)(61,113,98,147)(62,114,85,148)(63,115,86,149)(64,116,87,150)(65,117,88,151)(66,118,89,152)(67,119,90,153)(68,120,91,154)(69,121,92,141)(70,122,93,142)(71,181,213,132)(72,182,214,133)(73,169,215,134)(74,170,216,135)(75,171,217,136)(76,172,218,137)(77,173,219,138)(78,174,220,139)(79,175,221,140)(80,176,222,127)(81,177,223,128)(82,178,224,129)(83,179,211,130)(84,180,212,131), (1,20,44,210)(2,21,45,197)(3,22,46,198)(4,23,47,199)(5,24,48,200)(6,25,49,201)(7,26,50,202)(8,27,51,203)(9,28,52,204)(10,15,53,205)(11,16,54,206)(12,17,55,207)(13,18,56,208)(14,19,43,209)(29,166,108,193)(30,167,109,194)(31,168,110,195)(32,155,111,196)(33,156,112,183)(34,157,99,184)(35,158,100,185)(36,159,101,186)(37,160,102,187)(38,161,103,188)(39,162,104,189)(40,163,105,190)(41,164,106,191)(42,165,107,192)(57,223,94,81)(58,224,95,82)(59,211,96,83)(60,212,97,84)(61,213,98,71)(62,214,85,72)(63,215,86,73)(64,216,87,74)(65,217,88,75)(66,218,89,76)(67,219,90,77)(68,220,91,78)(69,221,92,79)(70,222,93,80)(113,174,147,139)(114,175,148,140)(115,176,149,127)(116,177,150,128)(117,178,151,129)(118,179,152,130)(119,180,153,131)(120,181,154,132)(121,182,141,133)(122,169,142,134)(123,170,143,135)(124,171,144,136)(125,172,145,137)(126,173,146,138) );
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)], [(1,183,44,156),(2,196,45,155),(3,195,46,168),(4,194,47,167),(5,193,48,166),(6,192,49,165),(7,191,50,164),(8,190,51,163),(9,189,52,162),(10,188,53,161),(11,187,54,160),(12,186,55,159),(13,185,56,158),(14,184,43,157),(15,38,205,103),(16,37,206,102),(17,36,207,101),(18,35,208,100),(19,34,209,99),(20,33,210,112),(21,32,197,111),(22,31,198,110),(23,30,199,109),(24,29,200,108),(25,42,201,107),(26,41,202,106),(27,40,203,105),(28,39,204,104),(57,147,94,113),(58,146,95,126),(59,145,96,125),(60,144,97,124),(61,143,98,123),(62,142,85,122),(63,141,86,121),(64,154,87,120),(65,153,88,119),(66,152,89,118),(67,151,90,117),(68,150,91,116),(69,149,92,115),(70,148,93,114),(71,170,213,135),(72,169,214,134),(73,182,215,133),(74,181,216,132),(75,180,217,131),(76,179,218,130),(77,178,219,129),(78,177,220,128),(79,176,221,127),(80,175,222,140),(81,174,223,139),(82,173,224,138),(83,172,211,137),(84,171,212,136)], [(1,125,8,118),(2,124,9,117),(3,123,10,116),(4,122,11,115),(5,121,12,114),(6,120,13,113),(7,119,14,126),(15,177,22,170),(16,176,23,169),(17,175,24,182),(18,174,25,181),(19,173,26,180),(20,172,27,179),(21,171,28,178),(29,80,36,73),(30,79,37,72),(31,78,38,71),(32,77,39,84),(33,76,40,83),(34,75,41,82),(35,74,42,81),(43,146,50,153),(44,145,51,152),(45,144,52,151),(46,143,53,150),(47,142,54,149),(48,141,55,148),(49,154,56,147),(57,158,64,165),(58,157,65,164),(59,156,66,163),(60,155,67,162),(61,168,68,161),(62,167,69,160),(63,166,70,159),(85,194,92,187),(86,193,93,186),(87,192,94,185),(88,191,95,184),(89,190,96,183),(90,189,97,196),(91,188,98,195),(99,217,106,224),(100,216,107,223),(101,215,108,222),(102,214,109,221),(103,213,110,220),(104,212,111,219),(105,211,112,218),(127,199,134,206),(128,198,135,205),(129,197,136,204),(130,210,137,203),(131,209,138,202),(132,208,139,201),(133,207,140,200)], [(1,190,44,163),(2,191,45,164),(3,192,46,165),(4,193,47,166),(5,194,48,167),(6,195,49,168),(7,196,50,155),(8,183,51,156),(9,184,52,157),(10,185,53,158),(11,186,54,159),(12,187,55,160),(13,188,56,161),(14,189,43,162),(15,107,205,42),(16,108,206,29),(17,109,207,30),(18,110,208,31),(19,111,209,32),(20,112,210,33),(21,99,197,34),(22,100,198,35),(23,101,199,36),(24,102,200,37),(25,103,201,38),(26,104,202,39),(27,105,203,40),(28,106,204,41),(57,123,94,143),(58,124,95,144),(59,125,96,145),(60,126,97,146),(61,113,98,147),(62,114,85,148),(63,115,86,149),(64,116,87,150),(65,117,88,151),(66,118,89,152),(67,119,90,153),(68,120,91,154),(69,121,92,141),(70,122,93,142),(71,181,213,132),(72,182,214,133),(73,169,215,134),(74,170,216,135),(75,171,217,136),(76,172,218,137),(77,173,219,138),(78,174,220,139),(79,175,221,140),(80,176,222,127),(81,177,223,128),(82,178,224,129),(83,179,211,130),(84,180,212,131)], [(1,20,44,210),(2,21,45,197),(3,22,46,198),(4,23,47,199),(5,24,48,200),(6,25,49,201),(7,26,50,202),(8,27,51,203),(9,28,52,204),(10,15,53,205),(11,16,54,206),(12,17,55,207),(13,18,56,208),(14,19,43,209),(29,166,108,193),(30,167,109,194),(31,168,110,195),(32,155,111,196),(33,156,112,183),(34,157,99,184),(35,158,100,185),(36,159,101,186),(37,160,102,187),(38,161,103,188),(39,162,104,189),(40,163,105,190),(41,164,106,191),(42,165,107,192),(57,223,94,81),(58,224,95,82),(59,211,96,83),(60,212,97,84),(61,213,98,71),(62,214,85,72),(63,215,86,73),(64,216,87,74),(65,217,88,75),(66,218,89,76),(67,219,90,77),(68,220,91,78),(69,221,92,79),(70,222,93,80),(113,174,147,139),(114,175,148,140),(115,176,149,127),(116,177,150,128),(117,178,151,129),(118,179,152,130),(119,180,153,131),(120,181,154,132),(121,182,141,133),(122,169,142,134),(123,170,143,135),(124,171,144,136),(125,172,145,137),(126,173,146,138)])
94 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | ··· | 4L | 4M | ··· | 4X | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 14 | 14 | 14 | 14 | 2 | ··· | 2 | 14 | ··· | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
94 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | D7 | D14 | D14 | C4×D7 | 2+ 1+4 | 2- 1+4 | D4⋊6D14 | Q8.10D14 |
| kernel | C14.22- 1+4 | Dic7⋊3Q8 | D7×C4⋊C4 | C4⋊C4⋊7D7 | D28⋊C4 | C23.21D14 | C4×C7⋊D4 | C14×C4⋊C4 | C2×C4○D28 | C4○D28 | C2×C4⋊C4 | C4⋊C4 | C22×C4 | C2×C4 | C14 | C14 | C2 | C2 |
| # reps | 1 | 2 | 2 | 2 | 2 | 1 | 4 | 1 | 1 | 16 | 3 | 12 | 9 | 24 | 1 | 1 | 6 | 6 |
Matrix representation of C14.22- 1+4 ►in GL6(𝔽29)
| 19 | 19 | 0 | 0 | 0 | 0 |
| 10 | 7 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 8 | 0 | 0 |
| 0 | 0 | 21 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 8 |
| 0 | 0 | 0 | 0 | 21 | 3 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 3 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 0 | 19 | 26 |
| 0 | 0 | 25 | 11 | 25 | 10 |
| 0 | 0 | 19 | 26 | 18 | 0 |
| 0 | 0 | 25 | 10 | 25 | 11 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 26 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 26 | 2 | 2 | 0 |
| 0 | 0 | 22 | 3 | 6 | 27 |
| 0 | 0 | 2 | 0 | 26 | 2 |
| 0 | 0 | 6 | 27 | 22 | 3 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 0 | 10 | 3 |
| 0 | 0 | 0 | 11 | 26 | 19 |
| 0 | 0 | 19 | 26 | 18 | 0 |
| 0 | 0 | 3 | 10 | 0 | 18 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
G:=sub<GL(6,GF(29))| [19,10,0,0,0,0,19,7,0,0,0,0,0,0,8,21,0,0,0,0,8,3,0,0,0,0,0,0,8,21,0,0,0,0,8,3],[17,3,0,0,0,0,0,12,0,0,0,0,0,0,18,25,19,25,0,0,0,11,26,10,0,0,19,25,18,25,0,0,26,10,0,11],[12,26,0,0,0,0,0,17,0,0,0,0,0,0,26,22,2,6,0,0,2,3,0,27,0,0,2,6,26,22,0,0,0,27,2,3],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,11,0,19,3,0,0,0,11,26,10,0,0,10,26,18,0,0,0,3,19,0,18],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,1,0,0] >;
C14.22- 1+4 in GAP, Magma, Sage, TeX
C_{14}._22_-^{1+4} % in TeX
G:=Group("C14.2ES-(2,2)"); // GroupNames label
G:=SmallGroup(448,957);
// by ID
G=gap.SmallGroup(448,957);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,570,80,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=1,c^2=a^7,d^2=e^2=b^2,b*a*b^-1=c*a*c^-1=a^-1,a*d=d*a,a*e=e*a,c*b*c^-1=a^7*b^-1,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=a^7*b^2*d>;
// generators/relations