G = C14.202- 1+4 order 448 = 26·7
20th non-split extension by C14 of 2- 1+4 acting via 2- 1+4/C2×Q8=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.202- 1+4, C14.542+ 1+4, C22⋊Q8⋊15D7, C4⋊C4.193D14, (C2×Q8).76D14, D28⋊C4⋊29C2, D14⋊3Q8⋊20C2, D14.5(C4○D4), D14⋊D4.1C2, Dic7.Q8⋊20C2, C22⋊C4.18D14, D14.5D4⋊20C2, D14.D4⋊26C2, (C2×C14).182C24, (C2×C28).627C23, (C22×C4).244D14, C2.56(D4⋊6D14), D14⋊C4.148C22, (C2×D28).151C22, C23.D14⋊22C2, Dic7⋊C4.80C22, C4⋊Dic7.218C22, (Q8×C14).112C22, C22.203(C23×D7), C23.121(C22×D7), C23.23D14⋊24C2, (C22×C14).210C23, (C22×C28).382C22, C7⋊4(C22.33C24), (C4×Dic7).110C22, (C2×Dic7).237C23, (C22×D7).203C23, C23.D7.122C22, C2.21(Q8.10D14), (D7×C4⋊C4)⋊29C2, (C4×C7⋊D4)⋊58C2, C2.53(D7×C4○D4), C4⋊C4⋊D7⋊18C2, (C7×C22⋊Q8)⋊18C2, C14.165(C2×C4○D4), (C2×C4×D7).210C22, (C2×C4).52(C22×D7), (C7×C4⋊C4).163C22, (C2×C7⋊D4).129C22, (C7×C22⋊C4).37C22, SmallGroup(448,1091)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.202- 1+4
G = < a,b,c,d,e | a14=b4=1, c2=e2=a7, d2=a7b2, bab-1=dad-1=eae-1=a-1, ac=ca, cbc-1=a7b-1, dbd-1=a7b, be=eb, dcd-1=a7c, ce=ec, ede-1=a7b2d >
Subgroups: 988 in 218 conjugacy classes, 93 normal (91 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, Dic7, C28, D14, D14, C2×C14, C2×C14, C2×C4⋊C4, C4×D4, C4⋊D4, C22⋊Q8, C22⋊Q8, C22.D4, C42.C2, C42⋊2C2, C4×D7, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×Q8, C22×D7, C22×C14, C22.33C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C2×C4×D7, C2×D28, C2×C7⋊D4, C22×C28, Q8×C14, C23.D14, D14.D4, D14⋊D4, Dic7.Q8, D7×C4⋊C4, D28⋊C4, D14.5D4, C4⋊C4⋊D7, C4×C7⋊D4, C23.23D14, D14⋊3Q8, C7×C22⋊Q8, C14.202- 1+4
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, 2- 1+4, C22×D7, C22.33C24, C23×D7, D4⋊6D14, Q8.10D14, D7×C4○D4, C14.202- 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)
(1 194 29 160)(2 193 30 159)(3 192 31 158)(4 191 32 157)(5 190 33 156)(6 189 34 155)(7 188 35 168)(8 187 36 167)(9 186 37 166)(10 185 38 165)(11 184 39 164)(12 183 40 163)(13 196 41 162)(14 195 42 161)(15 70 115 50)(16 69 116 49)(17 68 117 48)(18 67 118 47)(19 66 119 46)(20 65 120 45)(21 64 121 44)(22 63 122 43)(23 62 123 56)(24 61 124 55)(25 60 125 54)(26 59 126 53)(27 58 113 52)(28 57 114 51)(71 97 133 154)(72 96 134 153)(73 95 135 152)(74 94 136 151)(75 93 137 150)(76 92 138 149)(77 91 139 148)(78 90 140 147)(79 89 127 146)(80 88 128 145)(81 87 129 144)(82 86 130 143)(83 85 131 142)(84 98 132 141)(99 221 173 199)(100 220 174 198)(101 219 175 197)(102 218 176 210)(103 217 177 209)(104 216 178 208)(105 215 179 207)(106 214 180 206)(107 213 181 205)(108 212 182 204)(109 211 169 203)(110 224 170 202)(111 223 171 201)(112 222 172 200)
(1 167 8 160)(2 168 9 161)(3 155 10 162)(4 156 11 163)(5 157 12 164)(6 158 13 165)(7 159 14 166)(15 60 22 67)(16 61 23 68)(17 62 24 69)(18 63 25 70)(19 64 26 57)(20 65 27 58)(21 66 28 59)(29 187 36 194)(30 188 37 195)(31 189 38 196)(32 190 39 183)(33 191 40 184)(34 192 41 185)(35 193 42 186)(43 125 50 118)(44 126 51 119)(45 113 52 120)(46 114 53 121)(47 115 54 122)(48 116 55 123)(49 117 56 124)(71 97 78 90)(72 98 79 91)(73 85 80 92)(74 86 81 93)(75 87 82 94)(76 88 83 95)(77 89 84 96)(99 198 106 205)(100 199 107 206)(101 200 108 207)(102 201 109 208)(103 202 110 209)(104 203 111 210)(105 204 112 197)(127 148 134 141)(128 149 135 142)(129 150 136 143)(130 151 137 144)(131 152 138 145)(132 153 139 146)(133 154 140 147)(169 216 176 223)(170 217 177 224)(171 218 178 211)(172 219 179 212)(173 220 180 213)(174 221 181 214)(175 222 182 215)
(1 45 36 58)(2 44 37 57)(3 43 38 70)(4 56 39 69)(5 55 40 68)(6 54 41 67)(7 53 42 66)(8 52 29 65)(9 51 30 64)(10 50 31 63)(11 49 32 62)(12 48 33 61)(13 47 34 60)(14 46 35 59)(15 165 122 192)(16 164 123 191)(17 163 124 190)(18 162 125 189)(19 161 126 188)(20 160 113 187)(21 159 114 186)(22 158 115 185)(23 157 116 184)(24 156 117 183)(25 155 118 196)(26 168 119 195)(27 167 120 194)(28 166 121 193)(71 224 140 209)(72 223 127 208)(73 222 128 207)(74 221 129 206)(75 220 130 205)(76 219 131 204)(77 218 132 203)(78 217 133 202)(79 216 134 201)(80 215 135 200)(81 214 136 199)(82 213 137 198)(83 212 138 197)(84 211 139 210)(85 175 149 108)(86 174 150 107)(87 173 151 106)(88 172 152 105)(89 171 153 104)(90 170 154 103)(91 169 141 102)(92 182 142 101)(93 181 143 100)(94 180 144 99)(95 179 145 112)(96 178 146 111)(97 177 147 110)(98 176 148 109)
(1 90 8 97)(2 89 9 96)(3 88 10 95)(4 87 11 94)(5 86 12 93)(6 85 13 92)(7 98 14 91)(15 222 22 215)(16 221 23 214)(17 220 24 213)(18 219 25 212)(19 218 26 211)(20 217 27 224)(21 216 28 223)(29 147 36 154)(30 146 37 153)(31 145 38 152)(32 144 39 151)(33 143 40 150)(34 142 41 149)(35 141 42 148)(43 105 50 112)(44 104 51 111)(45 103 52 110)(46 102 53 109)(47 101 54 108)(48 100 55 107)(49 99 56 106)(57 171 64 178)(58 170 65 177)(59 169 66 176)(60 182 67 175)(61 181 68 174)(62 180 69 173)(63 179 70 172)(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)(113 202 120 209)(114 201 121 208)(115 200 122 207)(116 199 123 206)(117 198 124 205)(118 197 125 204)(119 210 126 203)(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)
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), (1,194,29,160)(2,193,30,159)(3,192,31,158)(4,191,32,157)(5,190,33,156)(6,189,34,155)(7,188,35,168)(8,187,36,167)(9,186,37,166)(10,185,38,165)(11,184,39,164)(12,183,40,163)(13,196,41,162)(14,195,42,161)(15,70,115,50)(16,69,116,49)(17,68,117,48)(18,67,118,47)(19,66,119,46)(20,65,120,45)(21,64,121,44)(22,63,122,43)(23,62,123,56)(24,61,124,55)(25,60,125,54)(26,59,126,53)(27,58,113,52)(28,57,114,51)(71,97,133,154)(72,96,134,153)(73,95,135,152)(74,94,136,151)(75,93,137,150)(76,92,138,149)(77,91,139,148)(78,90,140,147)(79,89,127,146)(80,88,128,145)(81,87,129,144)(82,86,130,143)(83,85,131,142)(84,98,132,141)(99,221,173,199)(100,220,174,198)(101,219,175,197)(102,218,176,210)(103,217,177,209)(104,216,178,208)(105,215,179,207)(106,214,180,206)(107,213,181,205)(108,212,182,204)(109,211,169,203)(110,224,170,202)(111,223,171,201)(112,222,172,200), (1,167,8,160)(2,168,9,161)(3,155,10,162)(4,156,11,163)(5,157,12,164)(6,158,13,165)(7,159,14,166)(15,60,22,67)(16,61,23,68)(17,62,24,69)(18,63,25,70)(19,64,26,57)(20,65,27,58)(21,66,28,59)(29,187,36,194)(30,188,37,195)(31,189,38,196)(32,190,39,183)(33,191,40,184)(34,192,41,185)(35,193,42,186)(43,125,50,118)(44,126,51,119)(45,113,52,120)(46,114,53,121)(47,115,54,122)(48,116,55,123)(49,117,56,124)(71,97,78,90)(72,98,79,91)(73,85,80,92)(74,86,81,93)(75,87,82,94)(76,88,83,95)(77,89,84,96)(99,198,106,205)(100,199,107,206)(101,200,108,207)(102,201,109,208)(103,202,110,209)(104,203,111,210)(105,204,112,197)(127,148,134,141)(128,149,135,142)(129,150,136,143)(130,151,137,144)(131,152,138,145)(132,153,139,146)(133,154,140,147)(169,216,176,223)(170,217,177,224)(171,218,178,211)(172,219,179,212)(173,220,180,213)(174,221,181,214)(175,222,182,215), (1,45,36,58)(2,44,37,57)(3,43,38,70)(4,56,39,69)(5,55,40,68)(6,54,41,67)(7,53,42,66)(8,52,29,65)(9,51,30,64)(10,50,31,63)(11,49,32,62)(12,48,33,61)(13,47,34,60)(14,46,35,59)(15,165,122,192)(16,164,123,191)(17,163,124,190)(18,162,125,189)(19,161,126,188)(20,160,113,187)(21,159,114,186)(22,158,115,185)(23,157,116,184)(24,156,117,183)(25,155,118,196)(26,168,119,195)(27,167,120,194)(28,166,121,193)(71,224,140,209)(72,223,127,208)(73,222,128,207)(74,221,129,206)(75,220,130,205)(76,219,131,204)(77,218,132,203)(78,217,133,202)(79,216,134,201)(80,215,135,200)(81,214,136,199)(82,213,137,198)(83,212,138,197)(84,211,139,210)(85,175,149,108)(86,174,150,107)(87,173,151,106)(88,172,152,105)(89,171,153,104)(90,170,154,103)(91,169,141,102)(92,182,142,101)(93,181,143,100)(94,180,144,99)(95,179,145,112)(96,178,146,111)(97,177,147,110)(98,176,148,109), (1,90,8,97)(2,89,9,96)(3,88,10,95)(4,87,11,94)(5,86,12,93)(6,85,13,92)(7,98,14,91)(15,222,22,215)(16,221,23,214)(17,220,24,213)(18,219,25,212)(19,218,26,211)(20,217,27,224)(21,216,28,223)(29,147,36,154)(30,146,37,153)(31,145,38,152)(32,144,39,151)(33,143,40,150)(34,142,41,149)(35,141,42,148)(43,105,50,112)(44,104,51,111)(45,103,52,110)(46,102,53,109)(47,101,54,108)(48,100,55,107)(49,99,56,106)(57,171,64,178)(58,170,65,177)(59,169,66,176)(60,182,67,175)(61,181,68,174)(62,180,69,173)(63,179,70,172)(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)(113,202,120,209)(114,201,121,208)(115,200,122,207)(116,199,123,206)(117,198,124,205)(118,197,125,204)(119,210,126,203)(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)>;
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), (1,194,29,160)(2,193,30,159)(3,192,31,158)(4,191,32,157)(5,190,33,156)(6,189,34,155)(7,188,35,168)(8,187,36,167)(9,186,37,166)(10,185,38,165)(11,184,39,164)(12,183,40,163)(13,196,41,162)(14,195,42,161)(15,70,115,50)(16,69,116,49)(17,68,117,48)(18,67,118,47)(19,66,119,46)(20,65,120,45)(21,64,121,44)(22,63,122,43)(23,62,123,56)(24,61,124,55)(25,60,125,54)(26,59,126,53)(27,58,113,52)(28,57,114,51)(71,97,133,154)(72,96,134,153)(73,95,135,152)(74,94,136,151)(75,93,137,150)(76,92,138,149)(77,91,139,148)(78,90,140,147)(79,89,127,146)(80,88,128,145)(81,87,129,144)(82,86,130,143)(83,85,131,142)(84,98,132,141)(99,221,173,199)(100,220,174,198)(101,219,175,197)(102,218,176,210)(103,217,177,209)(104,216,178,208)(105,215,179,207)(106,214,180,206)(107,213,181,205)(108,212,182,204)(109,211,169,203)(110,224,170,202)(111,223,171,201)(112,222,172,200), (1,167,8,160)(2,168,9,161)(3,155,10,162)(4,156,11,163)(5,157,12,164)(6,158,13,165)(7,159,14,166)(15,60,22,67)(16,61,23,68)(17,62,24,69)(18,63,25,70)(19,64,26,57)(20,65,27,58)(21,66,28,59)(29,187,36,194)(30,188,37,195)(31,189,38,196)(32,190,39,183)(33,191,40,184)(34,192,41,185)(35,193,42,186)(43,125,50,118)(44,126,51,119)(45,113,52,120)(46,114,53,121)(47,115,54,122)(48,116,55,123)(49,117,56,124)(71,97,78,90)(72,98,79,91)(73,85,80,92)(74,86,81,93)(75,87,82,94)(76,88,83,95)(77,89,84,96)(99,198,106,205)(100,199,107,206)(101,200,108,207)(102,201,109,208)(103,202,110,209)(104,203,111,210)(105,204,112,197)(127,148,134,141)(128,149,135,142)(129,150,136,143)(130,151,137,144)(131,152,138,145)(132,153,139,146)(133,154,140,147)(169,216,176,223)(170,217,177,224)(171,218,178,211)(172,219,179,212)(173,220,180,213)(174,221,181,214)(175,222,182,215), (1,45,36,58)(2,44,37,57)(3,43,38,70)(4,56,39,69)(5,55,40,68)(6,54,41,67)(7,53,42,66)(8,52,29,65)(9,51,30,64)(10,50,31,63)(11,49,32,62)(12,48,33,61)(13,47,34,60)(14,46,35,59)(15,165,122,192)(16,164,123,191)(17,163,124,190)(18,162,125,189)(19,161,126,188)(20,160,113,187)(21,159,114,186)(22,158,115,185)(23,157,116,184)(24,156,117,183)(25,155,118,196)(26,168,119,195)(27,167,120,194)(28,166,121,193)(71,224,140,209)(72,223,127,208)(73,222,128,207)(74,221,129,206)(75,220,130,205)(76,219,131,204)(77,218,132,203)(78,217,133,202)(79,216,134,201)(80,215,135,200)(81,214,136,199)(82,213,137,198)(83,212,138,197)(84,211,139,210)(85,175,149,108)(86,174,150,107)(87,173,151,106)(88,172,152,105)(89,171,153,104)(90,170,154,103)(91,169,141,102)(92,182,142,101)(93,181,143,100)(94,180,144,99)(95,179,145,112)(96,178,146,111)(97,177,147,110)(98,176,148,109), (1,90,8,97)(2,89,9,96)(3,88,10,95)(4,87,11,94)(5,86,12,93)(6,85,13,92)(7,98,14,91)(15,222,22,215)(16,221,23,214)(17,220,24,213)(18,219,25,212)(19,218,26,211)(20,217,27,224)(21,216,28,223)(29,147,36,154)(30,146,37,153)(31,145,38,152)(32,144,39,151)(33,143,40,150)(34,142,41,149)(35,141,42,148)(43,105,50,112)(44,104,51,111)(45,103,52,110)(46,102,53,109)(47,101,54,108)(48,100,55,107)(49,99,56,106)(57,171,64,178)(58,170,65,177)(59,169,66,176)(60,182,67,175)(61,181,68,174)(62,180,69,173)(63,179,70,172)(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)(113,202,120,209)(114,201,121,208)(115,200,122,207)(116,199,123,206)(117,198,124,205)(118,197,125,204)(119,210,126,203)(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) );
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)], [(1,194,29,160),(2,193,30,159),(3,192,31,158),(4,191,32,157),(5,190,33,156),(6,189,34,155),(7,188,35,168),(8,187,36,167),(9,186,37,166),(10,185,38,165),(11,184,39,164),(12,183,40,163),(13,196,41,162),(14,195,42,161),(15,70,115,50),(16,69,116,49),(17,68,117,48),(18,67,118,47),(19,66,119,46),(20,65,120,45),(21,64,121,44),(22,63,122,43),(23,62,123,56),(24,61,124,55),(25,60,125,54),(26,59,126,53),(27,58,113,52),(28,57,114,51),(71,97,133,154),(72,96,134,153),(73,95,135,152),(74,94,136,151),(75,93,137,150),(76,92,138,149),(77,91,139,148),(78,90,140,147),(79,89,127,146),(80,88,128,145),(81,87,129,144),(82,86,130,143),(83,85,131,142),(84,98,132,141),(99,221,173,199),(100,220,174,198),(101,219,175,197),(102,218,176,210),(103,217,177,209),(104,216,178,208),(105,215,179,207),(106,214,180,206),(107,213,181,205),(108,212,182,204),(109,211,169,203),(110,224,170,202),(111,223,171,201),(112,222,172,200)], [(1,167,8,160),(2,168,9,161),(3,155,10,162),(4,156,11,163),(5,157,12,164),(6,158,13,165),(7,159,14,166),(15,60,22,67),(16,61,23,68),(17,62,24,69),(18,63,25,70),(19,64,26,57),(20,65,27,58),(21,66,28,59),(29,187,36,194),(30,188,37,195),(31,189,38,196),(32,190,39,183),(33,191,40,184),(34,192,41,185),(35,193,42,186),(43,125,50,118),(44,126,51,119),(45,113,52,120),(46,114,53,121),(47,115,54,122),(48,116,55,123),(49,117,56,124),(71,97,78,90),(72,98,79,91),(73,85,80,92),(74,86,81,93),(75,87,82,94),(76,88,83,95),(77,89,84,96),(99,198,106,205),(100,199,107,206),(101,200,108,207),(102,201,109,208),(103,202,110,209),(104,203,111,210),(105,204,112,197),(127,148,134,141),(128,149,135,142),(129,150,136,143),(130,151,137,144),(131,152,138,145),(132,153,139,146),(133,154,140,147),(169,216,176,223),(170,217,177,224),(171,218,178,211),(172,219,179,212),(173,220,180,213),(174,221,181,214),(175,222,182,215)], [(1,45,36,58),(2,44,37,57),(3,43,38,70),(4,56,39,69),(5,55,40,68),(6,54,41,67),(7,53,42,66),(8,52,29,65),(9,51,30,64),(10,50,31,63),(11,49,32,62),(12,48,33,61),(13,47,34,60),(14,46,35,59),(15,165,122,192),(16,164,123,191),(17,163,124,190),(18,162,125,189),(19,161,126,188),(20,160,113,187),(21,159,114,186),(22,158,115,185),(23,157,116,184),(24,156,117,183),(25,155,118,196),(26,168,119,195),(27,167,120,194),(28,166,121,193),(71,224,140,209),(72,223,127,208),(73,222,128,207),(74,221,129,206),(75,220,130,205),(76,219,131,204),(77,218,132,203),(78,217,133,202),(79,216,134,201),(80,215,135,200),(81,214,136,199),(82,213,137,198),(83,212,138,197),(84,211,139,210),(85,175,149,108),(86,174,150,107),(87,173,151,106),(88,172,152,105),(89,171,153,104),(90,170,154,103),(91,169,141,102),(92,182,142,101),(93,181,143,100),(94,180,144,99),(95,179,145,112),(96,178,146,111),(97,177,147,110),(98,176,148,109)], [(1,90,8,97),(2,89,9,96),(3,88,10,95),(4,87,11,94),(5,86,12,93),(6,85,13,92),(7,98,14,91),(15,222,22,215),(16,221,23,214),(17,220,24,213),(18,219,25,212),(19,218,26,211),(20,217,27,224),(21,216,28,223),(29,147,36,154),(30,146,37,153),(31,145,38,152),(32,144,39,151),(33,143,40,150),(34,142,41,149),(35,141,42,148),(43,105,50,112),(44,104,51,111),(45,103,52,110),(46,102,53,109),(47,101,54,108),(48,100,55,107),(49,99,56,106),(57,171,64,178),(58,170,65,177),(59,169,66,176),(60,182,67,175),(61,181,68,174),(62,180,69,173),(63,179,70,172),(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),(113,202,120,209),(114,201,121,208),(115,200,122,207),(116,199,123,206),(117,198,124,205),(118,197,125,204),(119,210,126,203),(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)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | ··· | 4G | 4H | 4I | 4J | ··· | 4N | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 14 | 14 | 28 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 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 | 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 | C2 | D7 | C4○D4 | D14 | D14 | D14 | D14 | 2+ 1+4 | 2- 1+4 | D4⋊6D14 | Q8.10D14 | D7×C4○D4 |
| kernel | C14.202- 1+4 | C23.D14 | D14.D4 | D14⋊D4 | Dic7.Q8 | D7×C4⋊C4 | D28⋊C4 | D14.5D4 | C4⋊C4⋊D7 | C4×C7⋊D4 | C23.23D14 | D14⋊3Q8 | C7×C22⋊Q8 | C22⋊Q8 | D14 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×Q8 | C14 | C14 | C2 | C2 | C2 |
| # reps | 1 | 1 | 2 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 3 | 4 | 6 | 9 | 3 | 3 | 1 | 1 | 6 | 6 | 6 |
Matrix representation of C14.202- 1+4 ►in GL8(𝔽29)
| 10 | 17 | 0 | 0 | 0 | 0 | 0 | 0 |
| 21 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 21 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 26 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 21 | 21 |
| 0 | 0 | 0 | 0 | 0 | 0 | 8 | 26 |
| 9 | 0 | 9 | 16 | 0 | 0 | 0 | 0 |
| 14 | 20 | 21 | 19 | 0 | 0 | 0 | 0 |
| 17 | 4 | 7 | 19 | 0 | 0 | 0 | 0 |
| 27 | 5 | 20 | 22 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 25 | 22 | 16 | 0 |
| 0 | 0 | 0 | 0 | 10 | 4 | 19 | 13 |
| 0 | 0 | 0 | 0 | 16 | 0 | 25 | 22 |
| 0 | 0 | 0 | 0 | 19 | 13 | 10 | 4 |
| 9 | 0 | 9 | 16 | 0 | 0 | 0 | 0 |
| 0 | 9 | 22 | 22 | 0 | 0 | 0 | 0 |
| 20 | 25 | 20 | 0 | 0 | 0 | 0 | 0 |
| 9 | 24 | 0 | 20 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 25 | 22 | 16 | 0 |
| 0 | 0 | 0 | 0 | 7 | 4 | 0 | 16 |
| 0 | 0 | 0 | 0 | 13 | 0 | 4 | 7 |
| 0 | 0 | 0 | 0 | 0 | 13 | 22 | 25 |
| 20 | 0 | 20 | 13 | 0 | 0 | 0 | 0 |
| 15 | 9 | 8 | 10 | 0 | 0 | 0 | 0 |
| 11 | 6 | 22 | 10 | 0 | 0 | 0 | 0 |
| 26 | 22 | 9 | 7 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 16 | 0 | 25 | 22 |
| 0 | 0 | 0 | 0 | 19 | 13 | 10 | 4 |
| 0 | 0 | 0 | 0 | 25 | 22 | 16 | 0 |
| 0 | 0 | 0 | 0 | 10 | 4 | 19 | 13 |
| 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 9 | 17 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 23 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 5 | 16 |
| 0 | 0 | 0 | 0 | 0 | 0 | 2 | 24 |
| 0 | 0 | 0 | 0 | 24 | 13 | 0 | 0 |
| 0 | 0 | 0 | 0 | 27 | 5 | 0 | 0 |
G:=sub<GL(8,GF(29))| [10,21,0,0,0,0,0,0,17,1,0,0,0,0,0,0,0,0,11,21,0,0,0,0,0,0,11,0,0,0,0,0,0,0,0,0,21,8,0,0,0,0,0,0,21,26,0,0,0,0,0,0,0,0,21,8,0,0,0,0,0,0,21,26],[9,14,17,27,0,0,0,0,0,20,4,5,0,0,0,0,9,21,7,20,0,0,0,0,16,19,19,22,0,0,0,0,0,0,0,0,25,10,16,19,0,0,0,0,22,4,0,13,0,0,0,0,16,19,25,10,0,0,0,0,0,13,22,4],[9,0,20,9,0,0,0,0,0,9,25,24,0,0,0,0,9,22,20,0,0,0,0,0,16,22,0,20,0,0,0,0,0,0,0,0,25,7,13,0,0,0,0,0,22,4,0,13,0,0,0,0,16,0,4,22,0,0,0,0,0,16,7,25],[20,15,11,26,0,0,0,0,0,9,6,22,0,0,0,0,20,8,22,9,0,0,0,0,13,10,10,7,0,0,0,0,0,0,0,0,16,19,25,10,0,0,0,0,0,13,22,4,0,0,0,0,25,10,16,19,0,0,0,0,22,4,0,13],[12,9,0,0,0,0,0,0,0,17,0,0,0,0,0,0,0,0,10,12,0,0,0,0,0,0,23,19,0,0,0,0,0,0,0,0,0,0,24,27,0,0,0,0,0,0,13,5,0,0,0,0,5,2,0,0,0,0,0,0,16,24,0,0] >;
C14.202- 1+4 in GAP, Magma, Sage, TeX
C_{14}._{20}2_-^{1+4} % in TeX
G:=Group("C14.20ES-(2,2)"); // GroupNames label
G:=SmallGroup(448,1091);
// by ID
G=gap.SmallGroup(448,1091);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,219,268,675,570,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=1,c^2=e^2=a^7,d^2=a^7*b^2,b*a*b^-1=d*a*d^-1=e*a*e^-1=a^-1,a*c=c*a,c*b*c^-1=a^7*b^-1,d*b*d^-1=a^7*b,b*e=e*b,d*c*d^-1=a^7*c,c*e=e*c,e*d*e^-1=a^7*b^2*d>;
// generators/relations