G = C14.832- 1+4 order 448 = 26·7
38th non-split extension by C14 of 2- 1+4 acting via 2- 1+4/C4○D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.832- 1+4, C14.632+ 1+4, C4⋊C4.107D14, D14⋊Q8⋊31C2, D14.7(C4○D4), (C2×D4).100D14, C28⋊2D4.11C2, Dic7.Q8⋊27C2, C22⋊C4.28D14, C28.3Q8⋊29C2, C22.D4⋊9D7, Dic7⋊4D4⋊22C2, D14.D4⋊33C2, C28.48D4⋊22C2, (C2×C28).180C23, (C2×C14).204C24, (C22×C4).259D14, C2.65(D4⋊6D14), C23.28(C22×D7), D14⋊C4.108C22, C22⋊Dic14⋊33C2, (D4×C14).142C22, C23.D14⋊32C2, Dic7⋊C4.42C22, C4⋊Dic7.228C22, (C22×C14).36C23, C22.225(C23×D7), C23.D7.44C22, C23.18D14⋊15C2, (C22×C28).115C22, C7⋊6(C22.33C24), (C2×Dic14).37C22, (C4×Dic7).124C22, (C2×Dic7).106C23, (C22×D7).210C23, C2.44(D4.10D14), (C22×Dic7).130C22, (D7×C4⋊C4)⋊33C2, (C4×C7⋊D4)⋊7C2, C2.66(D7×C4○D4), C14.178(C2×C4○D4), (C2×C4×D7).113C22, (C2×C4).66(C22×D7), (C7×C4⋊C4).177C22, (C2×C7⋊D4).48C22, (C7×C22.D4)⋊12C2, (C7×C22⋊C4).52C22, SmallGroup(448,1113)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.832- 1+4
G = < a,b,c,d,e | a14=b4=e2=1, c2=a7, d2=b2, ab=ba, ac=ca, dad-1=a-1, ae=ea, cbc-1=b-1, dbd-1=ebe=a7b, cd=dc, ce=ec, ede=b2d >
Subgroups: 940 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×D4, C2×Q8, Dic7, C28, D14, D14, C2×C14, C2×C14, C2×C4⋊C4, C4×D4, C4⋊D4, C22⋊Q8, C22.D4, C22.D4, C42.C2, C42⋊2C2, Dic14, C4×D7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C22.33C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C22×Dic7, C2×C7⋊D4, C22×C28, D4×C14, C22⋊Dic14, C23.D14, Dic7⋊4D4, D14.D4, Dic7.Q8, C28.3Q8, D7×C4⋊C4, D14⋊Q8, C28.48D4, C4×C7⋊D4, C23.18D14, C28⋊2D4, C7×C22.D4, C14.832- 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, D7×C4○D4, D4.10D14, C14.832- 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)
(1 189 27 170)(2 190 28 171)(3 191 15 172)(4 192 16 173)(5 193 17 174)(6 194 18 175)(7 195 19 176)(8 196 20 177)(9 183 21 178)(10 184 22 179)(11 185 23 180)(12 186 24 181)(13 187 25 182)(14 188 26 169)(29 216 45 208)(30 217 46 209)(31 218 47 210)(32 219 48 197)(33 220 49 198)(34 221 50 199)(35 222 51 200)(36 223 52 201)(37 224 53 202)(38 211 54 203)(39 212 55 204)(40 213 56 205)(41 214 43 206)(42 215 44 207)(57 134 71 123)(58 135 72 124)(59 136 73 125)(60 137 74 126)(61 138 75 113)(62 139 76 114)(63 140 77 115)(64 127 78 116)(65 128 79 117)(66 129 80 118)(67 130 81 119)(68 131 82 120)(69 132 83 121)(70 133 84 122)(85 165 102 145)(86 166 103 146)(87 167 104 147)(88 168 105 148)(89 155 106 149)(90 156 107 150)(91 157 108 151)(92 158 109 152)(93 159 110 153)(94 160 111 154)(95 161 112 141)(96 162 99 142)(97 163 100 143)(98 164 101 144)
(1 124 8 117)(2 125 9 118)(3 126 10 119)(4 113 11 120)(5 114 12 121)(6 115 13 122)(7 116 14 123)(15 137 22 130)(16 138 23 131)(17 139 24 132)(18 140 25 133)(19 127 26 134)(20 128 27 135)(21 129 28 136)(29 150 36 143)(30 151 37 144)(31 152 38 145)(32 153 39 146)(33 154 40 147)(34 141 41 148)(35 142 42 149)(43 168 50 161)(44 155 51 162)(45 156 52 163)(46 157 53 164)(47 158 54 165)(48 159 55 166)(49 160 56 167)(57 176 64 169)(58 177 65 170)(59 178 66 171)(60 179 67 172)(61 180 68 173)(62 181 69 174)(63 182 70 175)(71 195 78 188)(72 196 79 189)(73 183 80 190)(74 184 81 191)(75 185 82 192)(76 186 83 193)(77 187 84 194)(85 210 92 203)(86 197 93 204)(87 198 94 205)(88 199 95 206)(89 200 96 207)(90 201 97 208)(91 202 98 209)(99 215 106 222)(100 216 107 223)(101 217 108 224)(102 218 109 211)(103 219 110 212)(104 220 111 213)(105 221 112 214)
(1 43 27 41)(2 56 28 40)(3 55 15 39)(4 54 16 38)(5 53 17 37)(6 52 18 36)(7 51 19 35)(8 50 20 34)(9 49 21 33)(10 48 22 32)(11 47 23 31)(12 46 24 30)(13 45 25 29)(14 44 26 42)(57 99 71 96)(58 112 72 95)(59 111 73 94)(60 110 74 93)(61 109 75 92)(62 108 76 91)(63 107 77 90)(64 106 78 89)(65 105 79 88)(66 104 80 87)(67 103 81 86)(68 102 82 85)(69 101 83 98)(70 100 84 97)(113 165 138 145)(114 164 139 144)(115 163 140 143)(116 162 127 142)(117 161 128 141)(118 160 129 154)(119 159 130 153)(120 158 131 152)(121 157 132 151)(122 156 133 150)(123 155 134 149)(124 168 135 148)(125 167 136 147)(126 166 137 146)(169 222 188 200)(170 221 189 199)(171 220 190 198)(172 219 191 197)(173 218 192 210)(174 217 193 209)(175 216 194 208)(176 215 195 207)(177 214 196 206)(178 213 183 205)(179 212 184 204)(180 211 185 203)(181 224 186 202)(182 223 187 201)
(1 41)(2 42)(3 29)(4 30)(5 31)(6 32)(7 33)(8 34)(9 35)(10 36)(11 37)(12 38)(13 39)(14 40)(15 45)(16 46)(17 47)(18 48)(19 49)(20 50)(21 51)(22 52)(23 53)(24 54)(25 55)(26 56)(27 43)(28 44)(57 94)(58 95)(59 96)(60 97)(61 98)(62 85)(63 86)(64 87)(65 88)(66 89)(67 90)(68 91)(69 92)(70 93)(71 111)(72 112)(73 99)(74 100)(75 101)(76 102)(77 103)(78 104)(79 105)(80 106)(81 107)(82 108)(83 109)(84 110)(113 151)(114 152)(115 153)(116 154)(117 141)(118 142)(119 143)(120 144)(121 145)(122 146)(123 147)(124 148)(125 149)(126 150)(127 160)(128 161)(129 162)(130 163)(131 164)(132 165)(133 166)(134 167)(135 168)(136 155)(137 156)(138 157)(139 158)(140 159)(169 198)(170 199)(171 200)(172 201)(173 202)(174 203)(175 204)(176 205)(177 206)(178 207)(179 208)(180 209)(181 210)(182 197)(183 215)(184 216)(185 217)(186 218)(187 219)(188 220)(189 221)(190 222)(191 223)(192 224)(193 211)(194 212)(195 213)(196 214)
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), (1,189,27,170)(2,190,28,171)(3,191,15,172)(4,192,16,173)(5,193,17,174)(6,194,18,175)(7,195,19,176)(8,196,20,177)(9,183,21,178)(10,184,22,179)(11,185,23,180)(12,186,24,181)(13,187,25,182)(14,188,26,169)(29,216,45,208)(30,217,46,209)(31,218,47,210)(32,219,48,197)(33,220,49,198)(34,221,50,199)(35,222,51,200)(36,223,52,201)(37,224,53,202)(38,211,54,203)(39,212,55,204)(40,213,56,205)(41,214,43,206)(42,215,44,207)(57,134,71,123)(58,135,72,124)(59,136,73,125)(60,137,74,126)(61,138,75,113)(62,139,76,114)(63,140,77,115)(64,127,78,116)(65,128,79,117)(66,129,80,118)(67,130,81,119)(68,131,82,120)(69,132,83,121)(70,133,84,122)(85,165,102,145)(86,166,103,146)(87,167,104,147)(88,168,105,148)(89,155,106,149)(90,156,107,150)(91,157,108,151)(92,158,109,152)(93,159,110,153)(94,160,111,154)(95,161,112,141)(96,162,99,142)(97,163,100,143)(98,164,101,144), (1,124,8,117)(2,125,9,118)(3,126,10,119)(4,113,11,120)(5,114,12,121)(6,115,13,122)(7,116,14,123)(15,137,22,130)(16,138,23,131)(17,139,24,132)(18,140,25,133)(19,127,26,134)(20,128,27,135)(21,129,28,136)(29,150,36,143)(30,151,37,144)(31,152,38,145)(32,153,39,146)(33,154,40,147)(34,141,41,148)(35,142,42,149)(43,168,50,161)(44,155,51,162)(45,156,52,163)(46,157,53,164)(47,158,54,165)(48,159,55,166)(49,160,56,167)(57,176,64,169)(58,177,65,170)(59,178,66,171)(60,179,67,172)(61,180,68,173)(62,181,69,174)(63,182,70,175)(71,195,78,188)(72,196,79,189)(73,183,80,190)(74,184,81,191)(75,185,82,192)(76,186,83,193)(77,187,84,194)(85,210,92,203)(86,197,93,204)(87,198,94,205)(88,199,95,206)(89,200,96,207)(90,201,97,208)(91,202,98,209)(99,215,106,222)(100,216,107,223)(101,217,108,224)(102,218,109,211)(103,219,110,212)(104,220,111,213)(105,221,112,214), (1,43,27,41)(2,56,28,40)(3,55,15,39)(4,54,16,38)(5,53,17,37)(6,52,18,36)(7,51,19,35)(8,50,20,34)(9,49,21,33)(10,48,22,32)(11,47,23,31)(12,46,24,30)(13,45,25,29)(14,44,26,42)(57,99,71,96)(58,112,72,95)(59,111,73,94)(60,110,74,93)(61,109,75,92)(62,108,76,91)(63,107,77,90)(64,106,78,89)(65,105,79,88)(66,104,80,87)(67,103,81,86)(68,102,82,85)(69,101,83,98)(70,100,84,97)(113,165,138,145)(114,164,139,144)(115,163,140,143)(116,162,127,142)(117,161,128,141)(118,160,129,154)(119,159,130,153)(120,158,131,152)(121,157,132,151)(122,156,133,150)(123,155,134,149)(124,168,135,148)(125,167,136,147)(126,166,137,146)(169,222,188,200)(170,221,189,199)(171,220,190,198)(172,219,191,197)(173,218,192,210)(174,217,193,209)(175,216,194,208)(176,215,195,207)(177,214,196,206)(178,213,183,205)(179,212,184,204)(180,211,185,203)(181,224,186,202)(182,223,187,201), (1,41)(2,42)(3,29)(4,30)(5,31)(6,32)(7,33)(8,34)(9,35)(10,36)(11,37)(12,38)(13,39)(14,40)(15,45)(16,46)(17,47)(18,48)(19,49)(20,50)(21,51)(22,52)(23,53)(24,54)(25,55)(26,56)(27,43)(28,44)(57,94)(58,95)(59,96)(60,97)(61,98)(62,85)(63,86)(64,87)(65,88)(66,89)(67,90)(68,91)(69,92)(70,93)(71,111)(72,112)(73,99)(74,100)(75,101)(76,102)(77,103)(78,104)(79,105)(80,106)(81,107)(82,108)(83,109)(84,110)(113,151)(114,152)(115,153)(116,154)(117,141)(118,142)(119,143)(120,144)(121,145)(122,146)(123,147)(124,148)(125,149)(126,150)(127,160)(128,161)(129,162)(130,163)(131,164)(132,165)(133,166)(134,167)(135,168)(136,155)(137,156)(138,157)(139,158)(140,159)(169,198)(170,199)(171,200)(172,201)(173,202)(174,203)(175,204)(176,205)(177,206)(178,207)(179,208)(180,209)(181,210)(182,197)(183,215)(184,216)(185,217)(186,218)(187,219)(188,220)(189,221)(190,222)(191,223)(192,224)(193,211)(194,212)(195,213)(196,214)>;
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), (1,189,27,170)(2,190,28,171)(3,191,15,172)(4,192,16,173)(5,193,17,174)(6,194,18,175)(7,195,19,176)(8,196,20,177)(9,183,21,178)(10,184,22,179)(11,185,23,180)(12,186,24,181)(13,187,25,182)(14,188,26,169)(29,216,45,208)(30,217,46,209)(31,218,47,210)(32,219,48,197)(33,220,49,198)(34,221,50,199)(35,222,51,200)(36,223,52,201)(37,224,53,202)(38,211,54,203)(39,212,55,204)(40,213,56,205)(41,214,43,206)(42,215,44,207)(57,134,71,123)(58,135,72,124)(59,136,73,125)(60,137,74,126)(61,138,75,113)(62,139,76,114)(63,140,77,115)(64,127,78,116)(65,128,79,117)(66,129,80,118)(67,130,81,119)(68,131,82,120)(69,132,83,121)(70,133,84,122)(85,165,102,145)(86,166,103,146)(87,167,104,147)(88,168,105,148)(89,155,106,149)(90,156,107,150)(91,157,108,151)(92,158,109,152)(93,159,110,153)(94,160,111,154)(95,161,112,141)(96,162,99,142)(97,163,100,143)(98,164,101,144), (1,124,8,117)(2,125,9,118)(3,126,10,119)(4,113,11,120)(5,114,12,121)(6,115,13,122)(7,116,14,123)(15,137,22,130)(16,138,23,131)(17,139,24,132)(18,140,25,133)(19,127,26,134)(20,128,27,135)(21,129,28,136)(29,150,36,143)(30,151,37,144)(31,152,38,145)(32,153,39,146)(33,154,40,147)(34,141,41,148)(35,142,42,149)(43,168,50,161)(44,155,51,162)(45,156,52,163)(46,157,53,164)(47,158,54,165)(48,159,55,166)(49,160,56,167)(57,176,64,169)(58,177,65,170)(59,178,66,171)(60,179,67,172)(61,180,68,173)(62,181,69,174)(63,182,70,175)(71,195,78,188)(72,196,79,189)(73,183,80,190)(74,184,81,191)(75,185,82,192)(76,186,83,193)(77,187,84,194)(85,210,92,203)(86,197,93,204)(87,198,94,205)(88,199,95,206)(89,200,96,207)(90,201,97,208)(91,202,98,209)(99,215,106,222)(100,216,107,223)(101,217,108,224)(102,218,109,211)(103,219,110,212)(104,220,111,213)(105,221,112,214), (1,43,27,41)(2,56,28,40)(3,55,15,39)(4,54,16,38)(5,53,17,37)(6,52,18,36)(7,51,19,35)(8,50,20,34)(9,49,21,33)(10,48,22,32)(11,47,23,31)(12,46,24,30)(13,45,25,29)(14,44,26,42)(57,99,71,96)(58,112,72,95)(59,111,73,94)(60,110,74,93)(61,109,75,92)(62,108,76,91)(63,107,77,90)(64,106,78,89)(65,105,79,88)(66,104,80,87)(67,103,81,86)(68,102,82,85)(69,101,83,98)(70,100,84,97)(113,165,138,145)(114,164,139,144)(115,163,140,143)(116,162,127,142)(117,161,128,141)(118,160,129,154)(119,159,130,153)(120,158,131,152)(121,157,132,151)(122,156,133,150)(123,155,134,149)(124,168,135,148)(125,167,136,147)(126,166,137,146)(169,222,188,200)(170,221,189,199)(171,220,190,198)(172,219,191,197)(173,218,192,210)(174,217,193,209)(175,216,194,208)(176,215,195,207)(177,214,196,206)(178,213,183,205)(179,212,184,204)(180,211,185,203)(181,224,186,202)(182,223,187,201), (1,41)(2,42)(3,29)(4,30)(5,31)(6,32)(7,33)(8,34)(9,35)(10,36)(11,37)(12,38)(13,39)(14,40)(15,45)(16,46)(17,47)(18,48)(19,49)(20,50)(21,51)(22,52)(23,53)(24,54)(25,55)(26,56)(27,43)(28,44)(57,94)(58,95)(59,96)(60,97)(61,98)(62,85)(63,86)(64,87)(65,88)(66,89)(67,90)(68,91)(69,92)(70,93)(71,111)(72,112)(73,99)(74,100)(75,101)(76,102)(77,103)(78,104)(79,105)(80,106)(81,107)(82,108)(83,109)(84,110)(113,151)(114,152)(115,153)(116,154)(117,141)(118,142)(119,143)(120,144)(121,145)(122,146)(123,147)(124,148)(125,149)(126,150)(127,160)(128,161)(129,162)(130,163)(131,164)(132,165)(133,166)(134,167)(135,168)(136,155)(137,156)(138,157)(139,158)(140,159)(169,198)(170,199)(171,200)(172,201)(173,202)(174,203)(175,204)(176,205)(177,206)(178,207)(179,208)(180,209)(181,210)(182,197)(183,215)(184,216)(185,217)(186,218)(187,219)(188,220)(189,221)(190,222)(191,223)(192,224)(193,211)(194,212)(195,213)(196,214) );
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)], [(1,189,27,170),(2,190,28,171),(3,191,15,172),(4,192,16,173),(5,193,17,174),(6,194,18,175),(7,195,19,176),(8,196,20,177),(9,183,21,178),(10,184,22,179),(11,185,23,180),(12,186,24,181),(13,187,25,182),(14,188,26,169),(29,216,45,208),(30,217,46,209),(31,218,47,210),(32,219,48,197),(33,220,49,198),(34,221,50,199),(35,222,51,200),(36,223,52,201),(37,224,53,202),(38,211,54,203),(39,212,55,204),(40,213,56,205),(41,214,43,206),(42,215,44,207),(57,134,71,123),(58,135,72,124),(59,136,73,125),(60,137,74,126),(61,138,75,113),(62,139,76,114),(63,140,77,115),(64,127,78,116),(65,128,79,117),(66,129,80,118),(67,130,81,119),(68,131,82,120),(69,132,83,121),(70,133,84,122),(85,165,102,145),(86,166,103,146),(87,167,104,147),(88,168,105,148),(89,155,106,149),(90,156,107,150),(91,157,108,151),(92,158,109,152),(93,159,110,153),(94,160,111,154),(95,161,112,141),(96,162,99,142),(97,163,100,143),(98,164,101,144)], [(1,124,8,117),(2,125,9,118),(3,126,10,119),(4,113,11,120),(5,114,12,121),(6,115,13,122),(7,116,14,123),(15,137,22,130),(16,138,23,131),(17,139,24,132),(18,140,25,133),(19,127,26,134),(20,128,27,135),(21,129,28,136),(29,150,36,143),(30,151,37,144),(31,152,38,145),(32,153,39,146),(33,154,40,147),(34,141,41,148),(35,142,42,149),(43,168,50,161),(44,155,51,162),(45,156,52,163),(46,157,53,164),(47,158,54,165),(48,159,55,166),(49,160,56,167),(57,176,64,169),(58,177,65,170),(59,178,66,171),(60,179,67,172),(61,180,68,173),(62,181,69,174),(63,182,70,175),(71,195,78,188),(72,196,79,189),(73,183,80,190),(74,184,81,191),(75,185,82,192),(76,186,83,193),(77,187,84,194),(85,210,92,203),(86,197,93,204),(87,198,94,205),(88,199,95,206),(89,200,96,207),(90,201,97,208),(91,202,98,209),(99,215,106,222),(100,216,107,223),(101,217,108,224),(102,218,109,211),(103,219,110,212),(104,220,111,213),(105,221,112,214)], [(1,43,27,41),(2,56,28,40),(3,55,15,39),(4,54,16,38),(5,53,17,37),(6,52,18,36),(7,51,19,35),(8,50,20,34),(9,49,21,33),(10,48,22,32),(11,47,23,31),(12,46,24,30),(13,45,25,29),(14,44,26,42),(57,99,71,96),(58,112,72,95),(59,111,73,94),(60,110,74,93),(61,109,75,92),(62,108,76,91),(63,107,77,90),(64,106,78,89),(65,105,79,88),(66,104,80,87),(67,103,81,86),(68,102,82,85),(69,101,83,98),(70,100,84,97),(113,165,138,145),(114,164,139,144),(115,163,140,143),(116,162,127,142),(117,161,128,141),(118,160,129,154),(119,159,130,153),(120,158,131,152),(121,157,132,151),(122,156,133,150),(123,155,134,149),(124,168,135,148),(125,167,136,147),(126,166,137,146),(169,222,188,200),(170,221,189,199),(171,220,190,198),(172,219,191,197),(173,218,192,210),(174,217,193,209),(175,216,194,208),(176,215,195,207),(177,214,196,206),(178,213,183,205),(179,212,184,204),(180,211,185,203),(181,224,186,202),(182,223,187,201)], [(1,41),(2,42),(3,29),(4,30),(5,31),(6,32),(7,33),(8,34),(9,35),(10,36),(11,37),(12,38),(13,39),(14,40),(15,45),(16,46),(17,47),(18,48),(19,49),(20,50),(21,51),(22,52),(23,53),(24,54),(25,55),(26,56),(27,43),(28,44),(57,94),(58,95),(59,96),(60,97),(61,98),(62,85),(63,86),(64,87),(65,88),(66,89),(67,90),(68,91),(69,92),(70,93),(71,111),(72,112),(73,99),(74,100),(75,101),(76,102),(77,103),(78,104),(79,105),(80,106),(81,107),(82,108),(83,109),(84,110),(113,151),(114,152),(115,153),(116,154),(117,141),(118,142),(119,143),(120,144),(121,145),(122,146),(123,147),(124,148),(125,149),(126,150),(127,160),(128,161),(129,162),(130,163),(131,164),(132,165),(133,166),(134,167),(135,168),(136,155),(137,156),(138,157),(139,158),(140,159),(169,198),(170,199),(171,200),(172,201),(173,202),(174,203),(175,204),(176,205),(177,206),(178,207),(179,208),(180,209),(181,210),(182,197),(183,215),(184,216),(185,217),(186,218),(187,219),(188,220),(189,221),(190,222),(191,223),(192,224),(193,211),(194,212),(195,213),(196,214)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4N | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 14P | 14Q | 14R | 28A | ··· | 28L | 28M | ··· | 28U |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 14 | 14 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 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 | C2 | D7 | C4○D4 | D14 | D14 | D14 | D14 | 2+ 1+4 | 2- 1+4 | D4⋊6D14 | D7×C4○D4 | D4.10D14 |
| kernel | C14.832- 1+4 | C22⋊Dic14 | C23.D14 | Dic7⋊4D4 | D14.D4 | Dic7.Q8 | C28.3Q8 | D7×C4⋊C4 | D14⋊Q8 | C28.48D4 | C4×C7⋊D4 | C23.18D14 | C28⋊2D4 | C7×C22.D4 | C22.D4 | D14 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C14 | C14 | C2 | C2 | C2 |
| # reps | 1 | 1 | 2 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 9 | 6 | 3 | 3 | 1 | 1 | 6 | 6 | 6 |
Matrix representation of C14.832- 1+4 ►in GL8(𝔽29)
| 21 | 21 | 0 | 0 | 0 | 0 | 0 | 0 |
| 8 | 26 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 28 |
| 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 23 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 1 | 7 | 8 | 17 |
| 0 | 0 | 0 | 0 | 20 | 0 | 6 | 0 |
| 0 | 0 | 0 | 0 | 11 | 9 | 27 | 22 |
| 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 7 | 0 | 18 | 0 |
| 0 | 0 | 0 | 0 | 17 | 23 | 14 | 11 |
| 0 | 0 | 0 | 0 | 23 | 0 | 22 | 0 |
| 0 | 0 | 0 | 0 | 14 | 23 | 23 | 6 |
| 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 26 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 21 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 7 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 12 | 17 | 1 |
| 0 | 0 | 0 | 0 | 26 | 10 | 0 | 12 |
| 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 21 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 5 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 12 | 17 | 1 |
| 0 | 0 | 0 | 0 | 21 | 10 | 2 | 12 |
G:=sub<GL(8,GF(29))| [21,8,0,0,0,0,0,0,21,26,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,17,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,23,1,20,11,0,0,0,0,0,7,0,9,0,0,0,0,17,8,6,27,0,0,0,0,0,17,0,22],[28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,7,17,23,14,0,0,0,0,0,23,0,23,0,0,0,0,18,14,22,23,0,0,0,0,0,11,0,6],[28,26,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,21,7,20,26,0,0,0,0,28,8,12,10,0,0,0,0,0,0,17,0,0,0,0,0,0,0,1,12],[28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,21,5,20,21,0,0,0,0,28,8,12,10,0,0,0,0,0,0,17,2,0,0,0,0,0,0,1,12] >;
C14.832- 1+4 in GAP, Magma, Sage, TeX
C_{14}._{83}2_-^{1+4} % in TeX
G:=Group("C14.83ES-(2,2)"); // GroupNames label
G:=SmallGroup(448,1113);
// by ID
G=gap.SmallGroup(448,1113);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,219,184,675,297,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=e^2=1,c^2=a^7,d^2=b^2,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,a*e=e*a,c*b*c^-1=b^-1,d*b*d^-1=e*b*e=a^7*b,c*d=d*c,c*e=e*c,e*d*e=b^2*d>;
// generators/relations