G = C14.82+ 1+4 order 448 = 26·7
8th non-split extension by C14 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.82+ 1+4, C14.22- 1+4, C4○D28⋊9C4, D28⋊23(C2×C4), D28⋊C4⋊8C2, C4⋊C4.305D14, Dic14⋊22(C2×C4), Dic7⋊3Q8⋊8C2, (C2×C14).48C24, C14.14(C23×C4), C28.89(C22×C4), 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×C28).216C22, (C22×C14).397C23, 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 C14.82+ 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, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C14, C2×C4⋊C4, C2×C4⋊C4, C42⋊C2, C4×D4, C4×Q8, C2×C4○D4, Dic14, C4×D7, C4×D7, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C22×D7, C22×C14, C23.33C23, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C4○D28, C2×C7⋊D4, C22×C28, C22×C28, Dic7⋊3Q8, D7×C4⋊C4, C4⋊C4⋊7D7, D28⋊C4, C23.21D14, C4×C7⋊D4, C14×C4⋊C4, C2×C4○D28, C14.82+ 1+4
Quotients: C1, C2, C4, C22, C2×C4, C23, D7, C22×C4, C24, D14, C23×C4, 2+ 1+4, 2- 1+4, C4×D7, C22×D7, C23.33C23, C2×C4×D7, C23×D7, D7×C22×C4, D4⋊6D14, Q8.10D14, C14.82+ 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)
(1 100 98 121)(2 99 85 120)(3 112 86 119)(4 111 87 118)(5 110 88 117)(6 109 89 116)(7 108 90 115)(8 107 91 114)(9 106 92 113)(10 105 93 126)(11 104 94 125)(12 103 95 124)(13 102 96 123)(14 101 97 122)(15 217 47 64)(16 216 48 63)(17 215 49 62)(18 214 50 61)(19 213 51 60)(20 212 52 59)(21 211 53 58)(22 224 54 57)(23 223 55 70)(24 222 56 69)(25 221 43 68)(26 220 44 67)(27 219 45 66)(28 218 46 65)(29 135 143 158)(30 134 144 157)(31 133 145 156)(32 132 146 155)(33 131 147 168)(34 130 148 167)(35 129 149 166)(36 128 150 165)(37 127 151 164)(38 140 152 163)(39 139 153 162)(40 138 154 161)(41 137 141 160)(42 136 142 159)(71 176 183 207)(72 175 184 206)(73 174 185 205)(74 173 186 204)(75 172 187 203)(76 171 188 202)(77 170 189 201)(78 169 190 200)(79 182 191 199)(80 181 192 198)(81 180 193 197)(82 179 194 210)(83 178 195 209)(84 177 196 208)
(1 16 8 23)(2 15 9 22)(3 28 10 21)(4 27 11 20)(5 26 12 19)(6 25 13 18)(7 24 14 17)(29 205 36 198)(30 204 37 197)(31 203 38 210)(32 202 39 209)(33 201 40 208)(34 200 41 207)(35 199 42 206)(43 96 50 89)(44 95 51 88)(45 94 52 87)(46 93 53 86)(47 92 54 85)(48 91 55 98)(49 90 56 97)(57 106 64 99)(58 105 65 112)(59 104 66 111)(60 103 67 110)(61 102 68 109)(62 101 69 108)(63 100 70 107)(71 160 78 167)(72 159 79 166)(73 158 80 165)(74 157 81 164)(75 156 82 163)(76 155 83 162)(77 168 84 161)(113 217 120 224)(114 216 121 223)(115 215 122 222)(116 214 123 221)(117 213 124 220)(118 212 125 219)(119 211 126 218)(127 186 134 193)(128 185 135 192)(129 184 136 191)(130 183 137 190)(131 196 138 189)(132 195 139 188)(133 194 140 187)(141 176 148 169)(142 175 149 182)(143 174 150 181)(144 173 151 180)(145 172 152 179)(146 171 153 178)(147 170 154 177)
(1 107 98 114)(2 108 85 115)(3 109 86 116)(4 110 87 117)(5 111 88 118)(6 112 89 119)(7 99 90 120)(8 100 91 121)(9 101 92 122)(10 102 93 123)(11 103 94 124)(12 104 95 125)(13 105 96 126)(14 106 97 113)(15 62 47 215)(16 63 48 216)(17 64 49 217)(18 65 50 218)(19 66 51 219)(20 67 52 220)(21 68 53 221)(22 69 54 222)(23 70 55 223)(24 57 56 224)(25 58 43 211)(26 59 44 212)(27 60 45 213)(28 61 46 214)(29 136 143 159)(30 137 144 160)(31 138 145 161)(32 139 146 162)(33 140 147 163)(34 127 148 164)(35 128 149 165)(36 129 150 166)(37 130 151 167)(38 131 152 168)(39 132 153 155)(40 133 154 156)(41 134 141 157)(42 135 142 158)(71 197 183 180)(72 198 184 181)(73 199 185 182)(74 200 186 169)(75 201 187 170)(76 202 188 171)(77 203 189 172)(78 204 190 173)(79 205 191 174)(80 206 192 175)(81 207 193 176)(82 208 194 177)(83 209 195 178)(84 210 196 179)
(1 188 98 76)(2 189 85 77)(3 190 86 78)(4 191 87 79)(5 192 88 80)(6 193 89 81)(7 194 90 82)(8 195 91 83)(9 196 92 84)(10 183 93 71)(11 184 94 72)(12 185 95 73)(13 186 96 74)(14 187 97 75)(15 131 47 168)(16 132 48 155)(17 133 49 156)(18 134 50 157)(19 135 51 158)(20 136 52 159)(21 137 53 160)(22 138 54 161)(23 139 55 162)(24 140 56 163)(25 127 43 164)(26 128 44 165)(27 129 45 166)(28 130 46 167)(29 213 143 60)(30 214 144 61)(31 215 145 62)(32 216 146 63)(33 217 147 64)(34 218 148 65)(35 219 149 66)(36 220 150 67)(37 221 151 68)(38 222 152 69)(39 223 153 70)(40 224 154 57)(41 211 141 58)(42 212 142 59)(99 201 120 170)(100 202 121 171)(101 203 122 172)(102 204 123 173)(103 205 124 174)(104 206 125 175)(105 207 126 176)(106 208 113 177)(107 209 114 178)(108 210 115 179)(109 197 116 180)(110 198 117 181)(111 199 118 182)(112 200 119 169)
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), (1,100,98,121)(2,99,85,120)(3,112,86,119)(4,111,87,118)(5,110,88,117)(6,109,89,116)(7,108,90,115)(8,107,91,114)(9,106,92,113)(10,105,93,126)(11,104,94,125)(12,103,95,124)(13,102,96,123)(14,101,97,122)(15,217,47,64)(16,216,48,63)(17,215,49,62)(18,214,50,61)(19,213,51,60)(20,212,52,59)(21,211,53,58)(22,224,54,57)(23,223,55,70)(24,222,56,69)(25,221,43,68)(26,220,44,67)(27,219,45,66)(28,218,46,65)(29,135,143,158)(30,134,144,157)(31,133,145,156)(32,132,146,155)(33,131,147,168)(34,130,148,167)(35,129,149,166)(36,128,150,165)(37,127,151,164)(38,140,152,163)(39,139,153,162)(40,138,154,161)(41,137,141,160)(42,136,142,159)(71,176,183,207)(72,175,184,206)(73,174,185,205)(74,173,186,204)(75,172,187,203)(76,171,188,202)(77,170,189,201)(78,169,190,200)(79,182,191,199)(80,181,192,198)(81,180,193,197)(82,179,194,210)(83,178,195,209)(84,177,196,208), (1,16,8,23)(2,15,9,22)(3,28,10,21)(4,27,11,20)(5,26,12,19)(6,25,13,18)(7,24,14,17)(29,205,36,198)(30,204,37,197)(31,203,38,210)(32,202,39,209)(33,201,40,208)(34,200,41,207)(35,199,42,206)(43,96,50,89)(44,95,51,88)(45,94,52,87)(46,93,53,86)(47,92,54,85)(48,91,55,98)(49,90,56,97)(57,106,64,99)(58,105,65,112)(59,104,66,111)(60,103,67,110)(61,102,68,109)(62,101,69,108)(63,100,70,107)(71,160,78,167)(72,159,79,166)(73,158,80,165)(74,157,81,164)(75,156,82,163)(76,155,83,162)(77,168,84,161)(113,217,120,224)(114,216,121,223)(115,215,122,222)(116,214,123,221)(117,213,124,220)(118,212,125,219)(119,211,126,218)(127,186,134,193)(128,185,135,192)(129,184,136,191)(130,183,137,190)(131,196,138,189)(132,195,139,188)(133,194,140,187)(141,176,148,169)(142,175,149,182)(143,174,150,181)(144,173,151,180)(145,172,152,179)(146,171,153,178)(147,170,154,177), (1,107,98,114)(2,108,85,115)(3,109,86,116)(4,110,87,117)(5,111,88,118)(6,112,89,119)(7,99,90,120)(8,100,91,121)(9,101,92,122)(10,102,93,123)(11,103,94,124)(12,104,95,125)(13,105,96,126)(14,106,97,113)(15,62,47,215)(16,63,48,216)(17,64,49,217)(18,65,50,218)(19,66,51,219)(20,67,52,220)(21,68,53,221)(22,69,54,222)(23,70,55,223)(24,57,56,224)(25,58,43,211)(26,59,44,212)(27,60,45,213)(28,61,46,214)(29,136,143,159)(30,137,144,160)(31,138,145,161)(32,139,146,162)(33,140,147,163)(34,127,148,164)(35,128,149,165)(36,129,150,166)(37,130,151,167)(38,131,152,168)(39,132,153,155)(40,133,154,156)(41,134,141,157)(42,135,142,158)(71,197,183,180)(72,198,184,181)(73,199,185,182)(74,200,186,169)(75,201,187,170)(76,202,188,171)(77,203,189,172)(78,204,190,173)(79,205,191,174)(80,206,192,175)(81,207,193,176)(82,208,194,177)(83,209,195,178)(84,210,196,179), (1,188,98,76)(2,189,85,77)(3,190,86,78)(4,191,87,79)(5,192,88,80)(6,193,89,81)(7,194,90,82)(8,195,91,83)(9,196,92,84)(10,183,93,71)(11,184,94,72)(12,185,95,73)(13,186,96,74)(14,187,97,75)(15,131,47,168)(16,132,48,155)(17,133,49,156)(18,134,50,157)(19,135,51,158)(20,136,52,159)(21,137,53,160)(22,138,54,161)(23,139,55,162)(24,140,56,163)(25,127,43,164)(26,128,44,165)(27,129,45,166)(28,130,46,167)(29,213,143,60)(30,214,144,61)(31,215,145,62)(32,216,146,63)(33,217,147,64)(34,218,148,65)(35,219,149,66)(36,220,150,67)(37,221,151,68)(38,222,152,69)(39,223,153,70)(40,224,154,57)(41,211,141,58)(42,212,142,59)(99,201,120,170)(100,202,121,171)(101,203,122,172)(102,204,123,173)(103,205,124,174)(104,206,125,175)(105,207,126,176)(106,208,113,177)(107,209,114,178)(108,210,115,179)(109,197,116,180)(110,198,117,181)(111,199,118,182)(112,200,119,169)>;
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), (1,100,98,121)(2,99,85,120)(3,112,86,119)(4,111,87,118)(5,110,88,117)(6,109,89,116)(7,108,90,115)(8,107,91,114)(9,106,92,113)(10,105,93,126)(11,104,94,125)(12,103,95,124)(13,102,96,123)(14,101,97,122)(15,217,47,64)(16,216,48,63)(17,215,49,62)(18,214,50,61)(19,213,51,60)(20,212,52,59)(21,211,53,58)(22,224,54,57)(23,223,55,70)(24,222,56,69)(25,221,43,68)(26,220,44,67)(27,219,45,66)(28,218,46,65)(29,135,143,158)(30,134,144,157)(31,133,145,156)(32,132,146,155)(33,131,147,168)(34,130,148,167)(35,129,149,166)(36,128,150,165)(37,127,151,164)(38,140,152,163)(39,139,153,162)(40,138,154,161)(41,137,141,160)(42,136,142,159)(71,176,183,207)(72,175,184,206)(73,174,185,205)(74,173,186,204)(75,172,187,203)(76,171,188,202)(77,170,189,201)(78,169,190,200)(79,182,191,199)(80,181,192,198)(81,180,193,197)(82,179,194,210)(83,178,195,209)(84,177,196,208), (1,16,8,23)(2,15,9,22)(3,28,10,21)(4,27,11,20)(5,26,12,19)(6,25,13,18)(7,24,14,17)(29,205,36,198)(30,204,37,197)(31,203,38,210)(32,202,39,209)(33,201,40,208)(34,200,41,207)(35,199,42,206)(43,96,50,89)(44,95,51,88)(45,94,52,87)(46,93,53,86)(47,92,54,85)(48,91,55,98)(49,90,56,97)(57,106,64,99)(58,105,65,112)(59,104,66,111)(60,103,67,110)(61,102,68,109)(62,101,69,108)(63,100,70,107)(71,160,78,167)(72,159,79,166)(73,158,80,165)(74,157,81,164)(75,156,82,163)(76,155,83,162)(77,168,84,161)(113,217,120,224)(114,216,121,223)(115,215,122,222)(116,214,123,221)(117,213,124,220)(118,212,125,219)(119,211,126,218)(127,186,134,193)(128,185,135,192)(129,184,136,191)(130,183,137,190)(131,196,138,189)(132,195,139,188)(133,194,140,187)(141,176,148,169)(142,175,149,182)(143,174,150,181)(144,173,151,180)(145,172,152,179)(146,171,153,178)(147,170,154,177), (1,107,98,114)(2,108,85,115)(3,109,86,116)(4,110,87,117)(5,111,88,118)(6,112,89,119)(7,99,90,120)(8,100,91,121)(9,101,92,122)(10,102,93,123)(11,103,94,124)(12,104,95,125)(13,105,96,126)(14,106,97,113)(15,62,47,215)(16,63,48,216)(17,64,49,217)(18,65,50,218)(19,66,51,219)(20,67,52,220)(21,68,53,221)(22,69,54,222)(23,70,55,223)(24,57,56,224)(25,58,43,211)(26,59,44,212)(27,60,45,213)(28,61,46,214)(29,136,143,159)(30,137,144,160)(31,138,145,161)(32,139,146,162)(33,140,147,163)(34,127,148,164)(35,128,149,165)(36,129,150,166)(37,130,151,167)(38,131,152,168)(39,132,153,155)(40,133,154,156)(41,134,141,157)(42,135,142,158)(71,197,183,180)(72,198,184,181)(73,199,185,182)(74,200,186,169)(75,201,187,170)(76,202,188,171)(77,203,189,172)(78,204,190,173)(79,205,191,174)(80,206,192,175)(81,207,193,176)(82,208,194,177)(83,209,195,178)(84,210,196,179), (1,188,98,76)(2,189,85,77)(3,190,86,78)(4,191,87,79)(5,192,88,80)(6,193,89,81)(7,194,90,82)(8,195,91,83)(9,196,92,84)(10,183,93,71)(11,184,94,72)(12,185,95,73)(13,186,96,74)(14,187,97,75)(15,131,47,168)(16,132,48,155)(17,133,49,156)(18,134,50,157)(19,135,51,158)(20,136,52,159)(21,137,53,160)(22,138,54,161)(23,139,55,162)(24,140,56,163)(25,127,43,164)(26,128,44,165)(27,129,45,166)(28,130,46,167)(29,213,143,60)(30,214,144,61)(31,215,145,62)(32,216,146,63)(33,217,147,64)(34,218,148,65)(35,219,149,66)(36,220,150,67)(37,221,151,68)(38,222,152,69)(39,223,153,70)(40,224,154,57)(41,211,141,58)(42,212,142,59)(99,201,120,170)(100,202,121,171)(101,203,122,172)(102,204,123,173)(103,205,124,174)(104,206,125,175)(105,207,126,176)(106,208,113,177)(107,209,114,178)(108,210,115,179)(109,197,116,180)(110,198,117,181)(111,199,118,182)(112,200,119,169) );
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)], [(1,100,98,121),(2,99,85,120),(3,112,86,119),(4,111,87,118),(5,110,88,117),(6,109,89,116),(7,108,90,115),(8,107,91,114),(9,106,92,113),(10,105,93,126),(11,104,94,125),(12,103,95,124),(13,102,96,123),(14,101,97,122),(15,217,47,64),(16,216,48,63),(17,215,49,62),(18,214,50,61),(19,213,51,60),(20,212,52,59),(21,211,53,58),(22,224,54,57),(23,223,55,70),(24,222,56,69),(25,221,43,68),(26,220,44,67),(27,219,45,66),(28,218,46,65),(29,135,143,158),(30,134,144,157),(31,133,145,156),(32,132,146,155),(33,131,147,168),(34,130,148,167),(35,129,149,166),(36,128,150,165),(37,127,151,164),(38,140,152,163),(39,139,153,162),(40,138,154,161),(41,137,141,160),(42,136,142,159),(71,176,183,207),(72,175,184,206),(73,174,185,205),(74,173,186,204),(75,172,187,203),(76,171,188,202),(77,170,189,201),(78,169,190,200),(79,182,191,199),(80,181,192,198),(81,180,193,197),(82,179,194,210),(83,178,195,209),(84,177,196,208)], [(1,16,8,23),(2,15,9,22),(3,28,10,21),(4,27,11,20),(5,26,12,19),(6,25,13,18),(7,24,14,17),(29,205,36,198),(30,204,37,197),(31,203,38,210),(32,202,39,209),(33,201,40,208),(34,200,41,207),(35,199,42,206),(43,96,50,89),(44,95,51,88),(45,94,52,87),(46,93,53,86),(47,92,54,85),(48,91,55,98),(49,90,56,97),(57,106,64,99),(58,105,65,112),(59,104,66,111),(60,103,67,110),(61,102,68,109),(62,101,69,108),(63,100,70,107),(71,160,78,167),(72,159,79,166),(73,158,80,165),(74,157,81,164),(75,156,82,163),(76,155,83,162),(77,168,84,161),(113,217,120,224),(114,216,121,223),(115,215,122,222),(116,214,123,221),(117,213,124,220),(118,212,125,219),(119,211,126,218),(127,186,134,193),(128,185,135,192),(129,184,136,191),(130,183,137,190),(131,196,138,189),(132,195,139,188),(133,194,140,187),(141,176,148,169),(142,175,149,182),(143,174,150,181),(144,173,151,180),(145,172,152,179),(146,171,153,178),(147,170,154,177)], [(1,107,98,114),(2,108,85,115),(3,109,86,116),(4,110,87,117),(5,111,88,118),(6,112,89,119),(7,99,90,120),(8,100,91,121),(9,101,92,122),(10,102,93,123),(11,103,94,124),(12,104,95,125),(13,105,96,126),(14,106,97,113),(15,62,47,215),(16,63,48,216),(17,64,49,217),(18,65,50,218),(19,66,51,219),(20,67,52,220),(21,68,53,221),(22,69,54,222),(23,70,55,223),(24,57,56,224),(25,58,43,211),(26,59,44,212),(27,60,45,213),(28,61,46,214),(29,136,143,159),(30,137,144,160),(31,138,145,161),(32,139,146,162),(33,140,147,163),(34,127,148,164),(35,128,149,165),(36,129,150,166),(37,130,151,167),(38,131,152,168),(39,132,153,155),(40,133,154,156),(41,134,141,157),(42,135,142,158),(71,197,183,180),(72,198,184,181),(73,199,185,182),(74,200,186,169),(75,201,187,170),(76,202,188,171),(77,203,189,172),(78,204,190,173),(79,205,191,174),(80,206,192,175),(81,207,193,176),(82,208,194,177),(83,209,195,178),(84,210,196,179)], [(1,188,98,76),(2,189,85,77),(3,190,86,78),(4,191,87,79),(5,192,88,80),(6,193,89,81),(7,194,90,82),(8,195,91,83),(9,196,92,84),(10,183,93,71),(11,184,94,72),(12,185,95,73),(13,186,96,74),(14,187,97,75),(15,131,47,168),(16,132,48,155),(17,133,49,156),(18,134,50,157),(19,135,51,158),(20,136,52,159),(21,137,53,160),(22,138,54,161),(23,139,55,162),(24,140,56,163),(25,127,43,164),(26,128,44,165),(27,129,45,166),(28,130,46,167),(29,213,143,60),(30,214,144,61),(31,215,145,62),(32,216,146,63),(33,217,147,64),(34,218,148,65),(35,219,149,66),(36,220,150,67),(37,221,151,68),(38,222,152,69),(39,223,153,70),(40,224,154,57),(41,211,141,58),(42,212,142,59),(99,201,120,170),(100,202,121,171),(101,203,122,172),(102,204,123,173),(103,205,124,174),(104,206,125,175),(105,207,126,176),(106,208,113,177),(107,209,114,178),(108,210,115,179),(109,197,116,180),(110,198,117,181),(111,199,118,182),(112,200,119,169)]])
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 | C14.82+ 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 C14.82+ 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] >;
C14.82+ 1+4 in GAP, Magma, Sage, TeX
C_{14}._82_+^{1+4} % in TeX
G:=Group("C14.8ES+(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