G = C14.262- 1+4 order 448 = 26·7
26th non-split extension by C14 of 2- 1+4 acting via 2- 1+4/C2×Q8=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.262- 1+4, C14.592+ 1+4, C22⋊Q8⋊24D7, C28⋊7D4⋊47C2, C4⋊D28⋊28C2, C4⋊C4.102D14, (C2×Q8).80D14, D14⋊D4⋊27C2, D14⋊3Q8⋊26C2, D14⋊2Q8⋊30C2, D14⋊Q8⋊25C2, Dic7.Q8⋊23C2, C22⋊C4.24D14, D14.5D4⋊24C2, D14.D4⋊28C2, C28.23D4⋊18C2, (C2×C28).177C23, (C2×C14).191C24, D14⋊C4.29C22, (C22×C4).253D14, C4⋊Dic7.48C22, C2.39(D4⋊8D14), C2.61(D4⋊6D14), Dic7.D4⋊28C2, (C2×D28).154C22, Dic7⋊C4.36C22, (Q8×C14).120C22, (C2×Dic7).97C23, (C22×D7).82C23, C23.127(C22×D7), C22.212(C23×D7), C23.D7.37C22, C23.23D14⋊14C2, (C22×C14).219C23, (C22×C28).319C22, C7⋊2(C22.56C24), (C4×Dic7).118C22, C2.27(Q8.10D14), (C2×Dic14).165C22, (C7×C22⋊Q8)⋊27C2, (C2×C4×D7).107C22, (C2×C4).57(C22×D7), (C7×C4⋊C4).171C22, (C2×C7⋊D4).43C22, (C7×C22⋊C4).46C22, SmallGroup(448,1100)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.262- 1+4
G = < a,b,c,d,e | a14=b4=c2=1, d2=b2, e2=a7b2, ab=ba, cac=dad-1=a-1, ae=ea, cbc=b-1, dbd-1=ebe-1=a7b, cd=dc, ece-1=a7c, ede-1=a7b2d >
Subgroups: 1148 in 220 conjugacy classes, 91 normal (all 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, C2×Q8, Dic7, C28, D14, C2×C14, C2×C14, C4⋊D4, C22⋊Q8, C22⋊Q8, C22.D4, C4.4D4, C42.C2, Dic14, C4×D7, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×Q8, C22×D7, C22×C14, C22.56C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C2×C7⋊D4, C22×C28, Q8×C14, D14.D4, D14⋊D4, Dic7.D4, Dic7.Q8, D14.5D4, C4⋊D28, D14⋊Q8, D14⋊2Q8, C23.23D14, C28⋊7D4, D14⋊3Q8, C28.23D4, C7×C22⋊Q8, C14.262- 1+4
Quotients: C1, C2, C22, C23, D7, C24, D14, 2+ 1+4, 2- 1+4, C22×D7, C22.56C24, C23×D7, D4⋊6D14, Q8.10D14, D4⋊8D14, C14.262- 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 84 26 60)(2 71 27 61)(3 72 28 62)(4 73 15 63)(5 74 16 64)(6 75 17 65)(7 76 18 66)(8 77 19 67)(9 78 20 68)(10 79 21 69)(11 80 22 70)(12 81 23 57)(13 82 24 58)(14 83 25 59)(29 103 47 87)(30 104 48 88)(31 105 49 89)(32 106 50 90)(33 107 51 91)(34 108 52 92)(35 109 53 93)(36 110 54 94)(37 111 55 95)(38 112 56 96)(39 99 43 97)(40 100 44 98)(41 101 45 85)(42 102 46 86)(113 182 135 192)(114 169 136 193)(115 170 137 194)(116 171 138 195)(117 172 139 196)(118 173 140 183)(119 174 127 184)(120 175 128 185)(121 176 129 186)(122 177 130 187)(123 178 131 188)(124 179 132 189)(125 180 133 190)(126 181 134 191)(141 198 162 220)(142 199 163 221)(143 200 164 222)(144 201 165 223)(145 202 166 224)(146 203 167 211)(147 204 168 212)(148 205 155 213)(149 206 156 214)(150 207 157 215)(151 208 158 216)(152 209 159 217)(153 210 160 218)(154 197 161 219)
(1 194)(2 193)(3 192)(4 191)(5 190)(6 189)(7 188)(8 187)(9 186)(10 185)(11 184)(12 183)(13 196)(14 195)(15 181)(16 180)(17 179)(18 178)(19 177)(20 176)(21 175)(22 174)(23 173)(24 172)(25 171)(26 170)(27 169)(28 182)(29 222)(30 221)(31 220)(32 219)(33 218)(34 217)(35 216)(36 215)(37 214)(38 213)(39 212)(40 211)(41 224)(42 223)(43 204)(44 203)(45 202)(46 201)(47 200)(48 199)(49 198)(50 197)(51 210)(52 209)(53 208)(54 207)(55 206)(56 205)(57 118)(58 117)(59 116)(60 115)(61 114)(62 113)(63 126)(64 125)(65 124)(66 123)(67 122)(68 121)(69 120)(70 119)(71 136)(72 135)(73 134)(74 133)(75 132)(76 131)(77 130)(78 129)(79 128)(80 127)(81 140)(82 139)(83 138)(84 137)(85 145)(86 144)(87 143)(88 142)(89 141)(90 154)(91 153)(92 152)(93 151)(94 150)(95 149)(96 148)(97 147)(98 146)(99 168)(100 167)(101 166)(102 165)(103 164)(104 163)(105 162)(106 161)(107 160)(108 159)(109 158)(110 157)(111 156)(112 155)
(1 152 26 159)(2 151 27 158)(3 150 28 157)(4 149 15 156)(5 148 16 155)(6 147 17 168)(7 146 18 167)(8 145 19 166)(9 144 20 165)(10 143 21 164)(11 142 22 163)(12 141 23 162)(13 154 24 161)(14 153 25 160)(29 135 47 113)(30 134 48 126)(31 133 49 125)(32 132 50 124)(33 131 51 123)(34 130 52 122)(35 129 53 121)(36 128 54 120)(37 127 55 119)(38 140 56 118)(39 139 43 117)(40 138 44 116)(41 137 45 115)(42 136 46 114)(57 213 81 205)(58 212 82 204)(59 211 83 203)(60 224 84 202)(61 223 71 201)(62 222 72 200)(63 221 73 199)(64 220 74 198)(65 219 75 197)(66 218 76 210)(67 217 77 209)(68 216 78 208)(69 215 79 207)(70 214 80 206)(85 177 101 187)(86 176 102 186)(87 175 103 185)(88 174 104 184)(89 173 105 183)(90 172 106 196)(91 171 107 195)(92 170 108 194)(93 169 109 193)(94 182 110 192)(95 181 111 191)(96 180 112 190)(97 179 99 189)(98 178 100 188)
(1 77 19 60)(2 78 20 61)(3 79 21 62)(4 80 22 63)(5 81 23 64)(6 82 24 65)(7 83 25 66)(8 84 26 67)(9 71 27 68)(10 72 28 69)(11 73 15 70)(12 74 16 57)(13 75 17 58)(14 76 18 59)(29 110 54 87)(30 111 55 88)(31 112 56 89)(32 99 43 90)(33 100 44 91)(34 101 45 92)(35 102 46 93)(36 103 47 94)(37 104 48 95)(38 105 49 96)(39 106 50 97)(40 107 51 98)(41 108 52 85)(42 109 53 86)(113 185 128 182)(114 186 129 169)(115 187 130 170)(116 188 131 171)(117 189 132 172)(118 190 133 173)(119 191 134 174)(120 192 135 175)(121 193 136 176)(122 194 137 177)(123 195 138 178)(124 196 139 179)(125 183 140 180)(126 184 127 181)(141 213 155 198)(142 214 156 199)(143 215 157 200)(144 216 158 201)(145 217 159 202)(146 218 160 203)(147 219 161 204)(148 220 162 205)(149 221 163 206)(150 222 164 207)(151 223 165 208)(152 224 166 209)(153 211 167 210)(154 212 168 197)
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), (1,84,26,60)(2,71,27,61)(3,72,28,62)(4,73,15,63)(5,74,16,64)(6,75,17,65)(7,76,18,66)(8,77,19,67)(9,78,20,68)(10,79,21,69)(11,80,22,70)(12,81,23,57)(13,82,24,58)(14,83,25,59)(29,103,47,87)(30,104,48,88)(31,105,49,89)(32,106,50,90)(33,107,51,91)(34,108,52,92)(35,109,53,93)(36,110,54,94)(37,111,55,95)(38,112,56,96)(39,99,43,97)(40,100,44,98)(41,101,45,85)(42,102,46,86)(113,182,135,192)(114,169,136,193)(115,170,137,194)(116,171,138,195)(117,172,139,196)(118,173,140,183)(119,174,127,184)(120,175,128,185)(121,176,129,186)(122,177,130,187)(123,178,131,188)(124,179,132,189)(125,180,133,190)(126,181,134,191)(141,198,162,220)(142,199,163,221)(143,200,164,222)(144,201,165,223)(145,202,166,224)(146,203,167,211)(147,204,168,212)(148,205,155,213)(149,206,156,214)(150,207,157,215)(151,208,158,216)(152,209,159,217)(153,210,160,218)(154,197,161,219), (1,194)(2,193)(3,192)(4,191)(5,190)(6,189)(7,188)(8,187)(9,186)(10,185)(11,184)(12,183)(13,196)(14,195)(15,181)(16,180)(17,179)(18,178)(19,177)(20,176)(21,175)(22,174)(23,173)(24,172)(25,171)(26,170)(27,169)(28,182)(29,222)(30,221)(31,220)(32,219)(33,218)(34,217)(35,216)(36,215)(37,214)(38,213)(39,212)(40,211)(41,224)(42,223)(43,204)(44,203)(45,202)(46,201)(47,200)(48,199)(49,198)(50,197)(51,210)(52,209)(53,208)(54,207)(55,206)(56,205)(57,118)(58,117)(59,116)(60,115)(61,114)(62,113)(63,126)(64,125)(65,124)(66,123)(67,122)(68,121)(69,120)(70,119)(71,136)(72,135)(73,134)(74,133)(75,132)(76,131)(77,130)(78,129)(79,128)(80,127)(81,140)(82,139)(83,138)(84,137)(85,145)(86,144)(87,143)(88,142)(89,141)(90,154)(91,153)(92,152)(93,151)(94,150)(95,149)(96,148)(97,147)(98,146)(99,168)(100,167)(101,166)(102,165)(103,164)(104,163)(105,162)(106,161)(107,160)(108,159)(109,158)(110,157)(111,156)(112,155), (1,152,26,159)(2,151,27,158)(3,150,28,157)(4,149,15,156)(5,148,16,155)(6,147,17,168)(7,146,18,167)(8,145,19,166)(9,144,20,165)(10,143,21,164)(11,142,22,163)(12,141,23,162)(13,154,24,161)(14,153,25,160)(29,135,47,113)(30,134,48,126)(31,133,49,125)(32,132,50,124)(33,131,51,123)(34,130,52,122)(35,129,53,121)(36,128,54,120)(37,127,55,119)(38,140,56,118)(39,139,43,117)(40,138,44,116)(41,137,45,115)(42,136,46,114)(57,213,81,205)(58,212,82,204)(59,211,83,203)(60,224,84,202)(61,223,71,201)(62,222,72,200)(63,221,73,199)(64,220,74,198)(65,219,75,197)(66,218,76,210)(67,217,77,209)(68,216,78,208)(69,215,79,207)(70,214,80,206)(85,177,101,187)(86,176,102,186)(87,175,103,185)(88,174,104,184)(89,173,105,183)(90,172,106,196)(91,171,107,195)(92,170,108,194)(93,169,109,193)(94,182,110,192)(95,181,111,191)(96,180,112,190)(97,179,99,189)(98,178,100,188), (1,77,19,60)(2,78,20,61)(3,79,21,62)(4,80,22,63)(5,81,23,64)(6,82,24,65)(7,83,25,66)(8,84,26,67)(9,71,27,68)(10,72,28,69)(11,73,15,70)(12,74,16,57)(13,75,17,58)(14,76,18,59)(29,110,54,87)(30,111,55,88)(31,112,56,89)(32,99,43,90)(33,100,44,91)(34,101,45,92)(35,102,46,93)(36,103,47,94)(37,104,48,95)(38,105,49,96)(39,106,50,97)(40,107,51,98)(41,108,52,85)(42,109,53,86)(113,185,128,182)(114,186,129,169)(115,187,130,170)(116,188,131,171)(117,189,132,172)(118,190,133,173)(119,191,134,174)(120,192,135,175)(121,193,136,176)(122,194,137,177)(123,195,138,178)(124,196,139,179)(125,183,140,180)(126,184,127,181)(141,213,155,198)(142,214,156,199)(143,215,157,200)(144,216,158,201)(145,217,159,202)(146,218,160,203)(147,219,161,204)(148,220,162,205)(149,221,163,206)(150,222,164,207)(151,223,165,208)(152,224,166,209)(153,211,167,210)(154,212,168,197)>;
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), (1,84,26,60)(2,71,27,61)(3,72,28,62)(4,73,15,63)(5,74,16,64)(6,75,17,65)(7,76,18,66)(8,77,19,67)(9,78,20,68)(10,79,21,69)(11,80,22,70)(12,81,23,57)(13,82,24,58)(14,83,25,59)(29,103,47,87)(30,104,48,88)(31,105,49,89)(32,106,50,90)(33,107,51,91)(34,108,52,92)(35,109,53,93)(36,110,54,94)(37,111,55,95)(38,112,56,96)(39,99,43,97)(40,100,44,98)(41,101,45,85)(42,102,46,86)(113,182,135,192)(114,169,136,193)(115,170,137,194)(116,171,138,195)(117,172,139,196)(118,173,140,183)(119,174,127,184)(120,175,128,185)(121,176,129,186)(122,177,130,187)(123,178,131,188)(124,179,132,189)(125,180,133,190)(126,181,134,191)(141,198,162,220)(142,199,163,221)(143,200,164,222)(144,201,165,223)(145,202,166,224)(146,203,167,211)(147,204,168,212)(148,205,155,213)(149,206,156,214)(150,207,157,215)(151,208,158,216)(152,209,159,217)(153,210,160,218)(154,197,161,219), (1,194)(2,193)(3,192)(4,191)(5,190)(6,189)(7,188)(8,187)(9,186)(10,185)(11,184)(12,183)(13,196)(14,195)(15,181)(16,180)(17,179)(18,178)(19,177)(20,176)(21,175)(22,174)(23,173)(24,172)(25,171)(26,170)(27,169)(28,182)(29,222)(30,221)(31,220)(32,219)(33,218)(34,217)(35,216)(36,215)(37,214)(38,213)(39,212)(40,211)(41,224)(42,223)(43,204)(44,203)(45,202)(46,201)(47,200)(48,199)(49,198)(50,197)(51,210)(52,209)(53,208)(54,207)(55,206)(56,205)(57,118)(58,117)(59,116)(60,115)(61,114)(62,113)(63,126)(64,125)(65,124)(66,123)(67,122)(68,121)(69,120)(70,119)(71,136)(72,135)(73,134)(74,133)(75,132)(76,131)(77,130)(78,129)(79,128)(80,127)(81,140)(82,139)(83,138)(84,137)(85,145)(86,144)(87,143)(88,142)(89,141)(90,154)(91,153)(92,152)(93,151)(94,150)(95,149)(96,148)(97,147)(98,146)(99,168)(100,167)(101,166)(102,165)(103,164)(104,163)(105,162)(106,161)(107,160)(108,159)(109,158)(110,157)(111,156)(112,155), (1,152,26,159)(2,151,27,158)(3,150,28,157)(4,149,15,156)(5,148,16,155)(6,147,17,168)(7,146,18,167)(8,145,19,166)(9,144,20,165)(10,143,21,164)(11,142,22,163)(12,141,23,162)(13,154,24,161)(14,153,25,160)(29,135,47,113)(30,134,48,126)(31,133,49,125)(32,132,50,124)(33,131,51,123)(34,130,52,122)(35,129,53,121)(36,128,54,120)(37,127,55,119)(38,140,56,118)(39,139,43,117)(40,138,44,116)(41,137,45,115)(42,136,46,114)(57,213,81,205)(58,212,82,204)(59,211,83,203)(60,224,84,202)(61,223,71,201)(62,222,72,200)(63,221,73,199)(64,220,74,198)(65,219,75,197)(66,218,76,210)(67,217,77,209)(68,216,78,208)(69,215,79,207)(70,214,80,206)(85,177,101,187)(86,176,102,186)(87,175,103,185)(88,174,104,184)(89,173,105,183)(90,172,106,196)(91,171,107,195)(92,170,108,194)(93,169,109,193)(94,182,110,192)(95,181,111,191)(96,180,112,190)(97,179,99,189)(98,178,100,188), (1,77,19,60)(2,78,20,61)(3,79,21,62)(4,80,22,63)(5,81,23,64)(6,82,24,65)(7,83,25,66)(8,84,26,67)(9,71,27,68)(10,72,28,69)(11,73,15,70)(12,74,16,57)(13,75,17,58)(14,76,18,59)(29,110,54,87)(30,111,55,88)(31,112,56,89)(32,99,43,90)(33,100,44,91)(34,101,45,92)(35,102,46,93)(36,103,47,94)(37,104,48,95)(38,105,49,96)(39,106,50,97)(40,107,51,98)(41,108,52,85)(42,109,53,86)(113,185,128,182)(114,186,129,169)(115,187,130,170)(116,188,131,171)(117,189,132,172)(118,190,133,173)(119,191,134,174)(120,192,135,175)(121,193,136,176)(122,194,137,177)(123,195,138,178)(124,196,139,179)(125,183,140,180)(126,184,127,181)(141,213,155,198)(142,214,156,199)(143,215,157,200)(144,216,158,201)(145,217,159,202)(146,218,160,203)(147,219,161,204)(148,220,162,205)(149,221,163,206)(150,222,164,207)(151,223,165,208)(152,224,166,209)(153,211,167,210)(154,212,168,197) );
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)], [(1,84,26,60),(2,71,27,61),(3,72,28,62),(4,73,15,63),(5,74,16,64),(6,75,17,65),(7,76,18,66),(8,77,19,67),(9,78,20,68),(10,79,21,69),(11,80,22,70),(12,81,23,57),(13,82,24,58),(14,83,25,59),(29,103,47,87),(30,104,48,88),(31,105,49,89),(32,106,50,90),(33,107,51,91),(34,108,52,92),(35,109,53,93),(36,110,54,94),(37,111,55,95),(38,112,56,96),(39,99,43,97),(40,100,44,98),(41,101,45,85),(42,102,46,86),(113,182,135,192),(114,169,136,193),(115,170,137,194),(116,171,138,195),(117,172,139,196),(118,173,140,183),(119,174,127,184),(120,175,128,185),(121,176,129,186),(122,177,130,187),(123,178,131,188),(124,179,132,189),(125,180,133,190),(126,181,134,191),(141,198,162,220),(142,199,163,221),(143,200,164,222),(144,201,165,223),(145,202,166,224),(146,203,167,211),(147,204,168,212),(148,205,155,213),(149,206,156,214),(150,207,157,215),(151,208,158,216),(152,209,159,217),(153,210,160,218),(154,197,161,219)], [(1,194),(2,193),(3,192),(4,191),(5,190),(6,189),(7,188),(8,187),(9,186),(10,185),(11,184),(12,183),(13,196),(14,195),(15,181),(16,180),(17,179),(18,178),(19,177),(20,176),(21,175),(22,174),(23,173),(24,172),(25,171),(26,170),(27,169),(28,182),(29,222),(30,221),(31,220),(32,219),(33,218),(34,217),(35,216),(36,215),(37,214),(38,213),(39,212),(40,211),(41,224),(42,223),(43,204),(44,203),(45,202),(46,201),(47,200),(48,199),(49,198),(50,197),(51,210),(52,209),(53,208),(54,207),(55,206),(56,205),(57,118),(58,117),(59,116),(60,115),(61,114),(62,113),(63,126),(64,125),(65,124),(66,123),(67,122),(68,121),(69,120),(70,119),(71,136),(72,135),(73,134),(74,133),(75,132),(76,131),(77,130),(78,129),(79,128),(80,127),(81,140),(82,139),(83,138),(84,137),(85,145),(86,144),(87,143),(88,142),(89,141),(90,154),(91,153),(92,152),(93,151),(94,150),(95,149),(96,148),(97,147),(98,146),(99,168),(100,167),(101,166),(102,165),(103,164),(104,163),(105,162),(106,161),(107,160),(108,159),(109,158),(110,157),(111,156),(112,155)], [(1,152,26,159),(2,151,27,158),(3,150,28,157),(4,149,15,156),(5,148,16,155),(6,147,17,168),(7,146,18,167),(8,145,19,166),(9,144,20,165),(10,143,21,164),(11,142,22,163),(12,141,23,162),(13,154,24,161),(14,153,25,160),(29,135,47,113),(30,134,48,126),(31,133,49,125),(32,132,50,124),(33,131,51,123),(34,130,52,122),(35,129,53,121),(36,128,54,120),(37,127,55,119),(38,140,56,118),(39,139,43,117),(40,138,44,116),(41,137,45,115),(42,136,46,114),(57,213,81,205),(58,212,82,204),(59,211,83,203),(60,224,84,202),(61,223,71,201),(62,222,72,200),(63,221,73,199),(64,220,74,198),(65,219,75,197),(66,218,76,210),(67,217,77,209),(68,216,78,208),(69,215,79,207),(70,214,80,206),(85,177,101,187),(86,176,102,186),(87,175,103,185),(88,174,104,184),(89,173,105,183),(90,172,106,196),(91,171,107,195),(92,170,108,194),(93,169,109,193),(94,182,110,192),(95,181,111,191),(96,180,112,190),(97,179,99,189),(98,178,100,188)], [(1,77,19,60),(2,78,20,61),(3,79,21,62),(4,80,22,63),(5,81,23,64),(6,82,24,65),(7,83,25,66),(8,84,26,67),(9,71,27,68),(10,72,28,69),(11,73,15,70),(12,74,16,57),(13,75,17,58),(14,76,18,59),(29,110,54,87),(30,111,55,88),(31,112,56,89),(32,99,43,90),(33,100,44,91),(34,101,45,92),(35,102,46,93),(36,103,47,94),(37,104,48,95),(38,105,49,96),(39,106,50,97),(40,107,51,98),(41,108,52,85),(42,109,53,86),(113,185,128,182),(114,186,129,169),(115,187,130,170),(116,188,131,171),(117,189,132,172),(118,190,133,173),(119,191,134,174),(120,192,135,175),(121,193,136,176),(122,194,137,177),(123,195,138,178),(124,196,139,179),(125,183,140,180),(126,184,127,181),(141,213,155,198),(142,214,156,199),(143,215,157,200),(144,216,158,201),(145,217,159,202),(146,218,160,203),(147,219,161,204),(148,220,162,205),(149,221,163,206),(150,222,164,207),(151,223,165,208),(152,224,166,209),(153,211,167,210),(154,212,168,197)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | ··· | 4F | 4G | ··· | 4K | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28X |
| order | 1 | 2 | 2 | 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 | 4 | 28 | 28 | 28 | 4 | ··· | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 8 | ··· | 8 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 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 | C2 | D7 | D14 | D14 | D14 | D14 | 2+ 1+4 | 2- 1+4 | D4⋊6D14 | Q8.10D14 | D4⋊8D14 |
| kernel | C14.262- 1+4 | D14.D4 | D14⋊D4 | Dic7.D4 | Dic7.Q8 | D14.5D4 | C4⋊D28 | D14⋊Q8 | D14⋊2Q8 | C23.23D14 | C28⋊7D4 | D14⋊3Q8 | C28.23D4 | C7×C22⋊Q8 | C22⋊Q8 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×Q8 | C14 | C14 | C2 | C2 | C2 |
| # reps | 1 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 6 | 9 | 3 | 3 | 2 | 1 | 6 | 6 | 6 |
Matrix representation of C14.262- 1+4 ►in GL8(𝔽29)
| 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 20 | 0 | 0 | 0 | 0 | 0 | 0 |
| 14 | 8 | 16 | 0 | 0 | 0 | 0 | 0 |
| 15 | 25 | 0 | 16 | 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 | 19 | 19 |
| 0 | 0 | 0 | 0 | 0 | 0 | 10 | 7 |
| 2 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 24 | 27 | 0 | 0 | 0 | 0 | 0 | 0 |
| 4 | 7 | 9 | 11 | 0 | 0 | 0 | 0 |
| 15 | 11 | 11 | 20 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 | 27 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 | 0 | 27 |
| 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 |
| 13 | 16 | 25 | 8 | 0 | 0 | 0 | 0 |
| 11 | 14 | 14 | 13 | 0 | 0 | 0 | 0 |
| 5 | 2 | 14 | 25 | 0 | 0 | 0 | 0 |
| 3 | 5 | 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 7 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 22 | 1 | 22 | 1 |
| 8 | 23 | 0 | 23 | 0 | 0 | 0 | 0 |
| 27 | 24 | 21 | 8 | 0 | 0 | 0 | 0 |
| 0 | 9 | 13 | 24 | 0 | 0 | 0 | 0 |
| 8 | 26 | 8 | 13 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 15 | 11 | 1 |
| 0 | 0 | 0 | 0 | 10 | 9 | 20 | 18 |
| 0 | 0 | 0 | 0 | 0 | 0 | 9 | 14 |
| 0 | 0 | 0 | 0 | 0 | 0 | 19 | 20 |
| 2 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 24 | 27 | 0 | 0 | 0 | 0 | 0 | 0 |
| 19 | 21 | 20 | 18 | 0 | 0 | 0 | 0 |
| 10 | 15 | 18 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 | 27 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 | 0 | 27 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(8,GF(29))| [20,0,14,15,0,0,0,0,0,20,8,25,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,19,10,0,0,0,0,0,0,19,7,0,0,0,0,0,0,0,0,19,10,0,0,0,0,0,0,19,7],[2,24,4,15,0,0,0,0,1,27,7,11,0,0,0,0,0,0,9,11,0,0,0,0,0,0,11,20,0,0,0,0,0,0,0,0,28,0,1,0,0,0,0,0,0,28,0,1,0,0,0,0,27,0,1,0,0,0,0,0,0,27,0,1],[13,11,5,3,0,0,0,0,16,14,2,5,0,0,0,0,25,14,14,0,0,0,0,0,8,13,25,17,0,0,0,0,0,0,0,0,1,7,28,22,0,0,0,0,0,28,0,1,0,0,0,0,0,0,28,22,0,0,0,0,0,0,0,1],[8,27,0,8,0,0,0,0,23,24,9,26,0,0,0,0,0,21,13,8,0,0,0,0,23,8,24,13,0,0,0,0,0,0,0,0,20,10,0,0,0,0,0,0,15,9,0,0,0,0,0,0,11,20,9,19,0,0,0,0,1,18,14,20],[2,24,19,10,0,0,0,0,1,27,21,15,0,0,0,0,0,0,20,18,0,0,0,0,0,0,18,9,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,27,0,1,0,0,0,0,0,0,27,0,1] >;
C14.262- 1+4 in GAP, Magma, Sage, TeX
C_{14}._{26}2_-^{1+4} % in TeX
G:=Group("C14.26ES-(2,2)"); // GroupNames label
G:=SmallGroup(448,1100);
// by ID
G=gap.SmallGroup(448,1100);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,758,219,100,1571,570,18822]);
// 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,a*b=b*a,c*a*c=d*a*d^-1=a^-1,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=a^7*b^2*d>;
// generators/relations