G = C14.242- 1+4 order 448 = 26·7
24th non-split extension by C14 of 2- 1+4 acting via 2- 1+4/C2×Q8=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.242- 1+4, C14.1192+ 1+4, C28⋊Q8⋊28C2, C4⋊C4.99D14, C22⋊Q8⋊20D7, (Q8×Dic7)⋊17C2, D28⋊C4⋊30C2, D14⋊2Q8⋊29C2, C28⋊7D4.16C2, (C2×Q8).133D14, C22⋊C4.22D14, D14.D4⋊27C2, C28.214(C4○D4), C28.23D4⋊16C2, C4.73(D4⋊2D7), (C2×C14).187C24, (C2×C28).175C23, D14⋊C4.28C22, (C22×C4).249D14, C2.37(D4⋊8D14), Dic7.D4⋊27C2, (C2×D28).153C22, Dic7⋊C4.35C22, C4⋊Dic7.312C22, (Q8×C14).117C22, (C2×Dic7).94C23, (C22×D7).78C23, C22.208(C23×D7), C23.125(C22×D7), C23.21D14⋊31C2, (C22×C14).215C23, (C22×C28).262C22, C7⋊6(C22.36C24), (C4×Dic7).115C22, C23.D7.126C22, C2.25(Q8.10D14), (C2×Dic14).164C22, C4⋊C4⋊D7⋊22C2, C14.91(C2×C4○D4), (C7×C22⋊Q8)⋊23C2, C2.50(C2×D4⋊2D7), (C2×C4×D7).104C22, (C7×C4⋊C4).168C22, (C2×C4).593(C22×D7), (C2×C7⋊D4).39C22, (C7×C22⋊C4).42C22, SmallGroup(448,1096)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.242- 1+4
G = < a,b,c,d,e | a14=b4=c2=1, d2=b2, e2=a7b2, bab-1=cac=a-1, ad=da, ae=ea, cbc=b-1, dbd-1=ebe-1=a7b, cd=dc, ece-1=a7c, ede-1=b2d >
Subgroups: 988 in 216 conjugacy classes, 95 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, C2×Q8, Dic7, C28, C28, D14, C2×C14, C2×C14, C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22⋊Q8, C22.D4, C4.4D4, C42⋊2C2, C4⋊Q8, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×Q8, C22×D7, C22×C14, C22.36C24, C4×Dic7, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C2×C7⋊D4, C22×C28, Q8×C14, D14.D4, Dic7.D4, C28⋊Q8, D28⋊C4, D14⋊2Q8, C4⋊C4⋊D7, C23.21D14, C28⋊7D4, Q8×Dic7, C28.23D4, C7×C22⋊Q8, C14.242- 1+4
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, 2- 1+4, C22×D7, C22.36C24, D4⋊2D7, C23×D7, C2×D4⋊2D7, Q8.10D14, D4⋊8D14, C14.242- 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 75 205 176)(2 74 206 175)(3 73 207 174)(4 72 208 173)(5 71 209 172)(6 84 210 171)(7 83 197 170)(8 82 198 169)(9 81 199 182)(10 80 200 181)(11 79 201 180)(12 78 202 179)(13 77 203 178)(14 76 204 177)(15 111 212 190)(16 110 213 189)(17 109 214 188)(18 108 215 187)(19 107 216 186)(20 106 217 185)(21 105 218 184)(22 104 219 183)(23 103 220 196)(24 102 221 195)(25 101 222 194)(26 100 223 193)(27 99 224 192)(28 112 211 191)(29 95 60 148)(30 94 61 147)(31 93 62 146)(32 92 63 145)(33 91 64 144)(34 90 65 143)(35 89 66 142)(36 88 67 141)(37 87 68 154)(38 86 69 153)(39 85 70 152)(40 98 57 151)(41 97 58 150)(42 96 59 149)(43 124 132 158)(44 123 133 157)(45 122 134 156)(46 121 135 155)(47 120 136 168)(48 119 137 167)(49 118 138 166)(50 117 139 165)(51 116 140 164)(52 115 127 163)(53 114 128 162)(54 113 129 161)(55 126 130 160)(56 125 131 159)
(1 198)(2 197)(3 210)(4 209)(5 208)(6 207)(7 206)(8 205)(9 204)(10 203)(11 202)(12 201)(13 200)(14 199)(15 218)(16 217)(17 216)(18 215)(19 214)(20 213)(21 212)(22 211)(23 224)(24 223)(25 222)(26 221)(27 220)(28 219)(29 66)(30 65)(31 64)(32 63)(33 62)(34 61)(35 60)(36 59)(37 58)(38 57)(39 70)(40 69)(41 68)(42 67)(43 48)(44 47)(45 46)(49 56)(50 55)(51 54)(52 53)(71 72)(73 84)(74 83)(75 82)(76 81)(77 80)(78 79)(86 98)(87 97)(88 96)(89 95)(90 94)(91 93)(99 103)(100 102)(104 112)(105 111)(106 110)(107 109)(113 164)(114 163)(115 162)(116 161)(117 160)(118 159)(119 158)(120 157)(121 156)(122 155)(123 168)(124 167)(125 166)(126 165)(127 128)(129 140)(130 139)(131 138)(132 137)(133 136)(134 135)(141 149)(142 148)(143 147)(144 146)(150 154)(151 153)(169 176)(170 175)(171 174)(172 173)(177 182)(178 181)(179 180)(183 191)(184 190)(185 189)(186 188)(192 196)(193 195)
(1 118 205 166)(2 119 206 167)(3 120 207 168)(4 121 208 155)(5 122 209 156)(6 123 210 157)(7 124 197 158)(8 125 198 159)(9 126 199 160)(10 113 200 161)(11 114 201 162)(12 115 202 163)(13 116 203 164)(14 117 204 165)(15 36 212 67)(16 37 213 68)(17 38 214 69)(18 39 215 70)(19 40 216 57)(20 41 217 58)(21 42 218 59)(22 29 219 60)(23 30 220 61)(24 31 221 62)(25 32 222 63)(26 33 223 64)(27 34 224 65)(28 35 211 66)(43 76 132 177)(44 77 133 178)(45 78 134 179)(46 79 135 180)(47 80 136 181)(48 81 137 182)(49 82 138 169)(50 83 139 170)(51 84 140 171)(52 71 127 172)(53 72 128 173)(54 73 129 174)(55 74 130 175)(56 75 131 176)(85 194 152 101)(86 195 153 102)(87 196 154 103)(88 183 141 104)(89 184 142 105)(90 185 143 106)(91 186 144 107)(92 187 145 108)(93 188 146 109)(94 189 147 110)(95 190 148 111)(96 191 149 112)(97 192 150 99)(98 193 151 100)
(1 63 198 39)(2 64 199 40)(3 65 200 41)(4 66 201 42)(5 67 202 29)(6 68 203 30)(7 69 204 31)(8 70 205 32)(9 57 206 33)(10 58 207 34)(11 59 208 35)(12 60 209 36)(13 61 210 37)(14 62 197 38)(15 115 219 156)(16 116 220 157)(17 117 221 158)(18 118 222 159)(19 119 223 160)(20 120 224 161)(21 121 211 162)(22 122 212 163)(23 123 213 164)(24 124 214 165)(25 125 215 166)(26 126 216 167)(27 113 217 168)(28 114 218 155)(43 102 139 188)(44 103 140 189)(45 104 127 190)(46 105 128 191)(47 106 129 192)(48 107 130 193)(49 108 131 194)(50 109 132 195)(51 110 133 196)(52 111 134 183)(53 112 135 184)(54 99 136 185)(55 100 137 186)(56 101 138 187)(71 148 179 88)(72 149 180 89)(73 150 181 90)(74 151 182 91)(75 152 169 92)(76 153 170 93)(77 154 171 94)(78 141 172 95)(79 142 173 96)(80 143 174 97)(81 144 175 98)(82 145 176 85)(83 146 177 86)(84 147 178 87)
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), (1,75,205,176)(2,74,206,175)(3,73,207,174)(4,72,208,173)(5,71,209,172)(6,84,210,171)(7,83,197,170)(8,82,198,169)(9,81,199,182)(10,80,200,181)(11,79,201,180)(12,78,202,179)(13,77,203,178)(14,76,204,177)(15,111,212,190)(16,110,213,189)(17,109,214,188)(18,108,215,187)(19,107,216,186)(20,106,217,185)(21,105,218,184)(22,104,219,183)(23,103,220,196)(24,102,221,195)(25,101,222,194)(26,100,223,193)(27,99,224,192)(28,112,211,191)(29,95,60,148)(30,94,61,147)(31,93,62,146)(32,92,63,145)(33,91,64,144)(34,90,65,143)(35,89,66,142)(36,88,67,141)(37,87,68,154)(38,86,69,153)(39,85,70,152)(40,98,57,151)(41,97,58,150)(42,96,59,149)(43,124,132,158)(44,123,133,157)(45,122,134,156)(46,121,135,155)(47,120,136,168)(48,119,137,167)(49,118,138,166)(50,117,139,165)(51,116,140,164)(52,115,127,163)(53,114,128,162)(54,113,129,161)(55,126,130,160)(56,125,131,159), (1,198)(2,197)(3,210)(4,209)(5,208)(6,207)(7,206)(8,205)(9,204)(10,203)(11,202)(12,201)(13,200)(14,199)(15,218)(16,217)(17,216)(18,215)(19,214)(20,213)(21,212)(22,211)(23,224)(24,223)(25,222)(26,221)(27,220)(28,219)(29,66)(30,65)(31,64)(32,63)(33,62)(34,61)(35,60)(36,59)(37,58)(38,57)(39,70)(40,69)(41,68)(42,67)(43,48)(44,47)(45,46)(49,56)(50,55)(51,54)(52,53)(71,72)(73,84)(74,83)(75,82)(76,81)(77,80)(78,79)(86,98)(87,97)(88,96)(89,95)(90,94)(91,93)(99,103)(100,102)(104,112)(105,111)(106,110)(107,109)(113,164)(114,163)(115,162)(116,161)(117,160)(118,159)(119,158)(120,157)(121,156)(122,155)(123,168)(124,167)(125,166)(126,165)(127,128)(129,140)(130,139)(131,138)(132,137)(133,136)(134,135)(141,149)(142,148)(143,147)(144,146)(150,154)(151,153)(169,176)(170,175)(171,174)(172,173)(177,182)(178,181)(179,180)(183,191)(184,190)(185,189)(186,188)(192,196)(193,195), (1,118,205,166)(2,119,206,167)(3,120,207,168)(4,121,208,155)(5,122,209,156)(6,123,210,157)(7,124,197,158)(8,125,198,159)(9,126,199,160)(10,113,200,161)(11,114,201,162)(12,115,202,163)(13,116,203,164)(14,117,204,165)(15,36,212,67)(16,37,213,68)(17,38,214,69)(18,39,215,70)(19,40,216,57)(20,41,217,58)(21,42,218,59)(22,29,219,60)(23,30,220,61)(24,31,221,62)(25,32,222,63)(26,33,223,64)(27,34,224,65)(28,35,211,66)(43,76,132,177)(44,77,133,178)(45,78,134,179)(46,79,135,180)(47,80,136,181)(48,81,137,182)(49,82,138,169)(50,83,139,170)(51,84,140,171)(52,71,127,172)(53,72,128,173)(54,73,129,174)(55,74,130,175)(56,75,131,176)(85,194,152,101)(86,195,153,102)(87,196,154,103)(88,183,141,104)(89,184,142,105)(90,185,143,106)(91,186,144,107)(92,187,145,108)(93,188,146,109)(94,189,147,110)(95,190,148,111)(96,191,149,112)(97,192,150,99)(98,193,151,100), (1,63,198,39)(2,64,199,40)(3,65,200,41)(4,66,201,42)(5,67,202,29)(6,68,203,30)(7,69,204,31)(8,70,205,32)(9,57,206,33)(10,58,207,34)(11,59,208,35)(12,60,209,36)(13,61,210,37)(14,62,197,38)(15,115,219,156)(16,116,220,157)(17,117,221,158)(18,118,222,159)(19,119,223,160)(20,120,224,161)(21,121,211,162)(22,122,212,163)(23,123,213,164)(24,124,214,165)(25,125,215,166)(26,126,216,167)(27,113,217,168)(28,114,218,155)(43,102,139,188)(44,103,140,189)(45,104,127,190)(46,105,128,191)(47,106,129,192)(48,107,130,193)(49,108,131,194)(50,109,132,195)(51,110,133,196)(52,111,134,183)(53,112,135,184)(54,99,136,185)(55,100,137,186)(56,101,138,187)(71,148,179,88)(72,149,180,89)(73,150,181,90)(74,151,182,91)(75,152,169,92)(76,153,170,93)(77,154,171,94)(78,141,172,95)(79,142,173,96)(80,143,174,97)(81,144,175,98)(82,145,176,85)(83,146,177,86)(84,147,178,87)>;
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), (1,75,205,176)(2,74,206,175)(3,73,207,174)(4,72,208,173)(5,71,209,172)(6,84,210,171)(7,83,197,170)(8,82,198,169)(9,81,199,182)(10,80,200,181)(11,79,201,180)(12,78,202,179)(13,77,203,178)(14,76,204,177)(15,111,212,190)(16,110,213,189)(17,109,214,188)(18,108,215,187)(19,107,216,186)(20,106,217,185)(21,105,218,184)(22,104,219,183)(23,103,220,196)(24,102,221,195)(25,101,222,194)(26,100,223,193)(27,99,224,192)(28,112,211,191)(29,95,60,148)(30,94,61,147)(31,93,62,146)(32,92,63,145)(33,91,64,144)(34,90,65,143)(35,89,66,142)(36,88,67,141)(37,87,68,154)(38,86,69,153)(39,85,70,152)(40,98,57,151)(41,97,58,150)(42,96,59,149)(43,124,132,158)(44,123,133,157)(45,122,134,156)(46,121,135,155)(47,120,136,168)(48,119,137,167)(49,118,138,166)(50,117,139,165)(51,116,140,164)(52,115,127,163)(53,114,128,162)(54,113,129,161)(55,126,130,160)(56,125,131,159), (1,198)(2,197)(3,210)(4,209)(5,208)(6,207)(7,206)(8,205)(9,204)(10,203)(11,202)(12,201)(13,200)(14,199)(15,218)(16,217)(17,216)(18,215)(19,214)(20,213)(21,212)(22,211)(23,224)(24,223)(25,222)(26,221)(27,220)(28,219)(29,66)(30,65)(31,64)(32,63)(33,62)(34,61)(35,60)(36,59)(37,58)(38,57)(39,70)(40,69)(41,68)(42,67)(43,48)(44,47)(45,46)(49,56)(50,55)(51,54)(52,53)(71,72)(73,84)(74,83)(75,82)(76,81)(77,80)(78,79)(86,98)(87,97)(88,96)(89,95)(90,94)(91,93)(99,103)(100,102)(104,112)(105,111)(106,110)(107,109)(113,164)(114,163)(115,162)(116,161)(117,160)(118,159)(119,158)(120,157)(121,156)(122,155)(123,168)(124,167)(125,166)(126,165)(127,128)(129,140)(130,139)(131,138)(132,137)(133,136)(134,135)(141,149)(142,148)(143,147)(144,146)(150,154)(151,153)(169,176)(170,175)(171,174)(172,173)(177,182)(178,181)(179,180)(183,191)(184,190)(185,189)(186,188)(192,196)(193,195), (1,118,205,166)(2,119,206,167)(3,120,207,168)(4,121,208,155)(5,122,209,156)(6,123,210,157)(7,124,197,158)(8,125,198,159)(9,126,199,160)(10,113,200,161)(11,114,201,162)(12,115,202,163)(13,116,203,164)(14,117,204,165)(15,36,212,67)(16,37,213,68)(17,38,214,69)(18,39,215,70)(19,40,216,57)(20,41,217,58)(21,42,218,59)(22,29,219,60)(23,30,220,61)(24,31,221,62)(25,32,222,63)(26,33,223,64)(27,34,224,65)(28,35,211,66)(43,76,132,177)(44,77,133,178)(45,78,134,179)(46,79,135,180)(47,80,136,181)(48,81,137,182)(49,82,138,169)(50,83,139,170)(51,84,140,171)(52,71,127,172)(53,72,128,173)(54,73,129,174)(55,74,130,175)(56,75,131,176)(85,194,152,101)(86,195,153,102)(87,196,154,103)(88,183,141,104)(89,184,142,105)(90,185,143,106)(91,186,144,107)(92,187,145,108)(93,188,146,109)(94,189,147,110)(95,190,148,111)(96,191,149,112)(97,192,150,99)(98,193,151,100), (1,63,198,39)(2,64,199,40)(3,65,200,41)(4,66,201,42)(5,67,202,29)(6,68,203,30)(7,69,204,31)(8,70,205,32)(9,57,206,33)(10,58,207,34)(11,59,208,35)(12,60,209,36)(13,61,210,37)(14,62,197,38)(15,115,219,156)(16,116,220,157)(17,117,221,158)(18,118,222,159)(19,119,223,160)(20,120,224,161)(21,121,211,162)(22,122,212,163)(23,123,213,164)(24,124,214,165)(25,125,215,166)(26,126,216,167)(27,113,217,168)(28,114,218,155)(43,102,139,188)(44,103,140,189)(45,104,127,190)(46,105,128,191)(47,106,129,192)(48,107,130,193)(49,108,131,194)(50,109,132,195)(51,110,133,196)(52,111,134,183)(53,112,135,184)(54,99,136,185)(55,100,137,186)(56,101,138,187)(71,148,179,88)(72,149,180,89)(73,150,181,90)(74,151,182,91)(75,152,169,92)(76,153,170,93)(77,154,171,94)(78,141,172,95)(79,142,173,96)(80,143,174,97)(81,144,175,98)(82,145,176,85)(83,146,177,86)(84,147,178,87) );
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)], [(1,75,205,176),(2,74,206,175),(3,73,207,174),(4,72,208,173),(5,71,209,172),(6,84,210,171),(7,83,197,170),(8,82,198,169),(9,81,199,182),(10,80,200,181),(11,79,201,180),(12,78,202,179),(13,77,203,178),(14,76,204,177),(15,111,212,190),(16,110,213,189),(17,109,214,188),(18,108,215,187),(19,107,216,186),(20,106,217,185),(21,105,218,184),(22,104,219,183),(23,103,220,196),(24,102,221,195),(25,101,222,194),(26,100,223,193),(27,99,224,192),(28,112,211,191),(29,95,60,148),(30,94,61,147),(31,93,62,146),(32,92,63,145),(33,91,64,144),(34,90,65,143),(35,89,66,142),(36,88,67,141),(37,87,68,154),(38,86,69,153),(39,85,70,152),(40,98,57,151),(41,97,58,150),(42,96,59,149),(43,124,132,158),(44,123,133,157),(45,122,134,156),(46,121,135,155),(47,120,136,168),(48,119,137,167),(49,118,138,166),(50,117,139,165),(51,116,140,164),(52,115,127,163),(53,114,128,162),(54,113,129,161),(55,126,130,160),(56,125,131,159)], [(1,198),(2,197),(3,210),(4,209),(5,208),(6,207),(7,206),(8,205),(9,204),(10,203),(11,202),(12,201),(13,200),(14,199),(15,218),(16,217),(17,216),(18,215),(19,214),(20,213),(21,212),(22,211),(23,224),(24,223),(25,222),(26,221),(27,220),(28,219),(29,66),(30,65),(31,64),(32,63),(33,62),(34,61),(35,60),(36,59),(37,58),(38,57),(39,70),(40,69),(41,68),(42,67),(43,48),(44,47),(45,46),(49,56),(50,55),(51,54),(52,53),(71,72),(73,84),(74,83),(75,82),(76,81),(77,80),(78,79),(86,98),(87,97),(88,96),(89,95),(90,94),(91,93),(99,103),(100,102),(104,112),(105,111),(106,110),(107,109),(113,164),(114,163),(115,162),(116,161),(117,160),(118,159),(119,158),(120,157),(121,156),(122,155),(123,168),(124,167),(125,166),(126,165),(127,128),(129,140),(130,139),(131,138),(132,137),(133,136),(134,135),(141,149),(142,148),(143,147),(144,146),(150,154),(151,153),(169,176),(170,175),(171,174),(172,173),(177,182),(178,181),(179,180),(183,191),(184,190),(185,189),(186,188),(192,196),(193,195)], [(1,118,205,166),(2,119,206,167),(3,120,207,168),(4,121,208,155),(5,122,209,156),(6,123,210,157),(7,124,197,158),(8,125,198,159),(9,126,199,160),(10,113,200,161),(11,114,201,162),(12,115,202,163),(13,116,203,164),(14,117,204,165),(15,36,212,67),(16,37,213,68),(17,38,214,69),(18,39,215,70),(19,40,216,57),(20,41,217,58),(21,42,218,59),(22,29,219,60),(23,30,220,61),(24,31,221,62),(25,32,222,63),(26,33,223,64),(27,34,224,65),(28,35,211,66),(43,76,132,177),(44,77,133,178),(45,78,134,179),(46,79,135,180),(47,80,136,181),(48,81,137,182),(49,82,138,169),(50,83,139,170),(51,84,140,171),(52,71,127,172),(53,72,128,173),(54,73,129,174),(55,74,130,175),(56,75,131,176),(85,194,152,101),(86,195,153,102),(87,196,154,103),(88,183,141,104),(89,184,142,105),(90,185,143,106),(91,186,144,107),(92,187,145,108),(93,188,146,109),(94,189,147,110),(95,190,148,111),(96,191,149,112),(97,192,150,99),(98,193,151,100)], [(1,63,198,39),(2,64,199,40),(3,65,200,41),(4,66,201,42),(5,67,202,29),(6,68,203,30),(7,69,204,31),(8,70,205,32),(9,57,206,33),(10,58,207,34),(11,59,208,35),(12,60,209,36),(13,61,210,37),(14,62,197,38),(15,115,219,156),(16,116,220,157),(17,117,221,158),(18,118,222,159),(19,119,223,160),(20,120,224,161),(21,121,211,162),(22,122,212,163),(23,123,213,164),(24,124,214,165),(25,125,215,166),(26,126,216,167),(27,113,217,168),(28,114,218,155),(43,102,139,188),(44,103,140,189),(45,104,127,190),(46,105,128,191),(47,106,129,192),(48,107,130,193),(49,108,131,194),(50,109,132,195),(51,110,133,196),(52,111,134,183),(53,112,135,184),(54,99,136,185),(55,100,137,186),(56,101,138,187),(71,148,179,88),(72,149,180,89),(73,150,181,90),(74,151,182,91),(75,152,169,92),(76,153,170,93),(77,154,171,94),(78,141,172,95),(79,142,173,96),(80,143,174,97),(81,144,175,98),(82,145,176,85),(83,146,177,86),(84,147,178,87)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | ··· | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 28 | 28 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | D14 | 2+ 1+4 | 2- 1+4 | D4⋊2D7 | Q8.10D14 | D4⋊8D14 |
| kernel | C14.242- 1+4 | D14.D4 | Dic7.D4 | C28⋊Q8 | D28⋊C4 | D14⋊2Q8 | C4⋊C4⋊D7 | C23.21D14 | C28⋊7D4 | Q8×Dic7 | C28.23D4 | C7×C22⋊Q8 | C22⋊Q8 | C28 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×Q8 | C14 | C14 | C4 | C2 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 6 | 9 | 3 | 3 | 1 | 1 | 6 | 6 | 6 |
Matrix representation of C14.242- 1+4 ►in GL8(𝔽29)
| 20 | 19 | 0 | 0 | 0 | 0 | 0 | 0 |
| 20 | 6 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 7 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 22 | 10 | 0 | 0 |
| 0 | 0 | 0 | 0 | 19 | 10 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 22 | 10 |
| 0 | 0 | 0 | 0 | 0 | 0 | 19 | 10 |
| 16 | 3 | 28 | 25 | 0 | 0 | 0 | 0 |
| 11 | 13 | 15 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 10 | 0 | 0 |
| 0 | 0 | 0 | 0 | 15 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 20 | 10 |
| 0 | 0 | 0 | 0 | 0 | 0 | 15 | 9 |
| 11 | 22 | 0 | 0 | 0 | 0 | 0 | 0 |
| 13 | 18 | 0 | 0 | 0 | 0 | 0 | 0 |
| 27 | 6 | 28 | 0 | 0 | 0 | 0 | 0 |
| 21 | 13 | 22 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 22 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 28 | 22 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 25 | 19 | 13 | 27 | 0 | 0 | 0 | 0 |
| 20 | 11 | 12 | 22 | 0 | 0 | 0 | 0 |
| 22 | 21 | 5 | 10 | 0 | 0 | 0 | 0 |
| 8 | 0 | 19 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 15 | 0 | 21 | 0 |
| 0 | 0 | 0 | 0 | 0 | 15 | 0 | 21 |
| 0 | 0 | 0 | 0 | 21 | 0 | 14 | 0 |
| 0 | 0 | 0 | 0 | 0 | 21 | 0 | 14 |
| 17 | 0 | 0 | 25 | 0 | 0 | 0 | 0 |
| 0 | 17 | 4 | 18 | 0 | 0 | 0 | 0 |
| 24 | 15 | 12 | 0 | 0 | 0 | 0 | 0 |
| 14 | 0 | 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 | 0 | 0 |
G:=sub<GL(8,GF(29))| [20,20,0,0,0,0,0,0,19,6,0,0,0,0,0,0,0,0,19,10,0,0,0,0,0,0,19,7,0,0,0,0,0,0,0,0,22,19,0,0,0,0,0,0,10,10,0,0,0,0,0,0,0,0,22,19,0,0,0,0,0,0,10,10],[16,11,0,0,0,0,0,0,3,13,0,0,0,0,0,0,28,15,17,3,0,0,0,0,25,18,0,12,0,0,0,0,0,0,0,0,20,15,0,0,0,0,0,0,10,9,0,0,0,0,0,0,0,0,20,15,0,0,0,0,0,0,10,9],[11,13,27,21,0,0,0,0,22,18,6,13,0,0,0,0,0,0,28,22,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,22,1,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,22,1],[25,20,22,8,0,0,0,0,19,11,21,0,0,0,0,0,13,12,5,19,0,0,0,0,27,22,10,17,0,0,0,0,0,0,0,0,15,0,21,0,0,0,0,0,0,15,0,21,0,0,0,0,21,0,14,0,0,0,0,0,0,21,0,14],[17,0,24,14,0,0,0,0,0,17,15,0,0,0,0,0,0,4,12,0,0,0,0,0,25,18,0,12,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0] >;
C14.242- 1+4 in GAP, Magma, Sage, TeX
C_{14}._{24}2_-^{1+4} % in TeX
G:=Group("C14.24ES-(2,2)"); // GroupNames label
G:=SmallGroup(448,1096);
// by ID
G=gap.SmallGroup(448,1096);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,219,675,570,192,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=c^2=1,d^2=b^2,e^2=a^7*b^2,b*a*b^-1=c*a*c=a^-1,a*d=d*a,a*e=e*a,c*b*c=b^-1,d*b*d^-1=e*b*e^-1=a^7*b,c*d=d*c,e*c*e^-1=a^7*c,e*d*e^-1=b^2*d>;
// generators/relations