G = C14.442+ 1+4 order 448 = 26·7
44th non-split extension by C14 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.442+ 1+4, C4⋊D4⋊18D7, C4⋊C4.92D14, C28⋊2D4⋊24C2, C28⋊D4⋊18C2, (C2×D4).93D14, D14⋊D4⋊22C2, Dic7.Q8⋊13C2, C22⋊C4.50D14, Dic7⋊D4⋊31C2, Dic7⋊4D4⋊12C2, D14.D4⋊21C2, D14.5D4⋊13C2, (C2×C28).597C23, (C2×C14).159C24, D14⋊C4.71C22, Dic7.5(C4○D4), (C22×C4).226D14, C2.46(D4⋊6D14), C23.19(C22×D7), (D4×C14).125C22, (C2×D28).144C22, C23.11D14⋊6C2, C4⋊Dic7.208C22, (C22×C14).26C23, (C2×Dic7).78C23, (C22×D7).66C23, C22.180(C23×D7), C23.D7.27C22, C23.18D14⋊12C2, C23.23D14⋊23C2, Dic7⋊C4.160C22, (C22×C28).379C22, C7⋊3(C22.34C24), (C4×Dic7).211C22, (C22×Dic7).112C22, (C4×C7⋊D4)⋊56C2, C2.43(D7×C4○D4), (C7×C4⋊D4)⋊21C2, C14.156(C2×C4○D4), (C2×C4×D7).209C22, (C7×C4⋊C4).147C22, (C2×C4).179(C22×D7), (C2×C7⋊D4).32C22, (C7×C22⋊C4).16C22, SmallGroup(448,1068)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.442+ 1+4
G = < a,b,c,d,e | a14=b4=1, c2=e2=a7, d2=b2, ab=ba, ac=ca, dad-1=a-1, ae=ea, cbc-1=a7b-1, bd=db, ebe-1=a7b, cd=dc, ce=ec, ede-1=a7b2d >
Subgroups: 1164 in 240 conjugacy classes, 93 normal (91 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, Dic7, Dic7, C28, D14, C2×C14, C2×C14, C42⋊C2, C4×D4, C4⋊D4, C4⋊D4, C22.D4, C42.C2, C4⋊1D4, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C22.34C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C2×C4×D7, C2×D28, C22×Dic7, C2×C7⋊D4, C22×C28, D4×C14, C23.11D14, Dic7⋊4D4, D14.D4, D14⋊D4, Dic7.Q8, D14.5D4, C4×C7⋊D4, C23.23D14, C23.18D14, C28⋊2D4, Dic7⋊D4, C28⋊D4, C7×C4⋊D4, C14.442+ 1+4
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.34C24, C23×D7, D4⋊6D14, D7×C4○D4, C14.442+ 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)
(1 193 25 169)(2 194 26 170)(3 195 27 171)(4 196 28 172)(5 183 15 173)(6 184 16 174)(7 185 17 175)(8 186 18 176)(9 187 19 177)(10 188 20 178)(11 189 21 179)(12 190 22 180)(13 191 23 181)(14 192 24 182)(29 218 52 205)(30 219 53 206)(31 220 54 207)(32 221 55 208)(33 222 56 209)(34 223 43 210)(35 224 44 197)(36 211 45 198)(37 212 46 199)(38 213 47 200)(39 214 48 201)(40 215 49 202)(41 216 50 203)(42 217 51 204)(57 128 74 118)(58 129 75 119)(59 130 76 120)(60 131 77 121)(61 132 78 122)(62 133 79 123)(63 134 80 124)(64 135 81 125)(65 136 82 126)(66 137 83 113)(67 138 84 114)(68 139 71 115)(69 140 72 116)(70 127 73 117)(85 162 101 149)(86 163 102 150)(87 164 103 151)(88 165 104 152)(89 166 105 153)(90 167 106 154)(91 168 107 141)(92 155 108 142)(93 156 109 143)(94 157 110 144)(95 158 111 145)(96 159 112 146)(97 160 99 147)(98 161 100 148)
(1 115 8 122)(2 116 9 123)(3 117 10 124)(4 118 11 125)(5 119 12 126)(6 120 13 113)(7 121 14 114)(15 129 22 136)(16 130 23 137)(17 131 24 138)(18 132 25 139)(19 133 26 140)(20 134 27 127)(21 135 28 128)(29 147 36 154)(30 148 37 141)(31 149 38 142)(32 150 39 143)(33 151 40 144)(34 152 41 145)(35 153 42 146)(43 165 50 158)(44 166 51 159)(45 167 52 160)(46 168 53 161)(47 155 54 162)(48 156 55 163)(49 157 56 164)(57 172 64 179)(58 173 65 180)(59 174 66 181)(60 175 67 182)(61 176 68 169)(62 177 69 170)(63 178 70 171)(71 193 78 186)(72 194 79 187)(73 195 80 188)(74 196 81 189)(75 183 82 190)(76 184 83 191)(77 185 84 192)(85 207 92 200)(86 208 93 201)(87 209 94 202)(88 210 95 203)(89 197 96 204)(90 198 97 205)(91 199 98 206)(99 218 106 211)(100 219 107 212)(101 220 108 213)(102 221 109 214)(103 222 110 215)(104 223 111 216)(105 224 112 217)
(1 56 25 33)(2 55 26 32)(3 54 27 31)(4 53 28 30)(5 52 15 29)(6 51 16 42)(7 50 17 41)(8 49 18 40)(9 48 19 39)(10 47 20 38)(11 46 21 37)(12 45 22 36)(13 44 23 35)(14 43 24 34)(57 100 74 98)(58 99 75 97)(59 112 76 96)(60 111 77 95)(61 110 78 94)(62 109 79 93)(63 108 80 92)(64 107 81 91)(65 106 82 90)(66 105 83 89)(67 104 84 88)(68 103 71 87)(69 102 72 86)(70 101 73 85)(113 166 137 153)(114 165 138 152)(115 164 139 151)(116 163 140 150)(117 162 127 149)(118 161 128 148)(119 160 129 147)(120 159 130 146)(121 158 131 145)(122 157 132 144)(123 156 133 143)(124 155 134 142)(125 168 135 141)(126 167 136 154)(169 222 193 209)(170 221 194 208)(171 220 195 207)(172 219 196 206)(173 218 183 205)(174 217 184 204)(175 216 185 203)(176 215 186 202)(177 214 187 201)(178 213 188 200)(179 212 189 199)(180 211 190 198)(181 224 191 197)(182 223 192 210)
(1 40 8 33)(2 41 9 34)(3 42 10 35)(4 29 11 36)(5 30 12 37)(6 31 13 38)(7 32 14 39)(15 53 22 46)(16 54 23 47)(17 55 24 48)(18 56 25 49)(19 43 26 50)(20 44 27 51)(21 45 28 52)(57 90 64 97)(58 91 65 98)(59 92 66 85)(60 93 67 86)(61 94 68 87)(62 95 69 88)(63 96 70 89)(71 103 78 110)(72 104 79 111)(73 105 80 112)(74 106 81 99)(75 107 82 100)(76 108 83 101)(77 109 84 102)(113 142 120 149)(114 143 121 150)(115 144 122 151)(116 145 123 152)(117 146 124 153)(118 147 125 154)(119 148 126 141)(127 159 134 166)(128 160 135 167)(129 161 136 168)(130 162 137 155)(131 163 138 156)(132 164 139 157)(133 165 140 158)(169 209 176 202)(170 210 177 203)(171 197 178 204)(172 198 179 205)(173 199 180 206)(174 200 181 207)(175 201 182 208)(183 212 190 219)(184 213 191 220)(185 214 192 221)(186 215 193 222)(187 216 194 223)(188 217 195 224)(189 218 196 211)
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), (1,193,25,169)(2,194,26,170)(3,195,27,171)(4,196,28,172)(5,183,15,173)(6,184,16,174)(7,185,17,175)(8,186,18,176)(9,187,19,177)(10,188,20,178)(11,189,21,179)(12,190,22,180)(13,191,23,181)(14,192,24,182)(29,218,52,205)(30,219,53,206)(31,220,54,207)(32,221,55,208)(33,222,56,209)(34,223,43,210)(35,224,44,197)(36,211,45,198)(37,212,46,199)(38,213,47,200)(39,214,48,201)(40,215,49,202)(41,216,50,203)(42,217,51,204)(57,128,74,118)(58,129,75,119)(59,130,76,120)(60,131,77,121)(61,132,78,122)(62,133,79,123)(63,134,80,124)(64,135,81,125)(65,136,82,126)(66,137,83,113)(67,138,84,114)(68,139,71,115)(69,140,72,116)(70,127,73,117)(85,162,101,149)(86,163,102,150)(87,164,103,151)(88,165,104,152)(89,166,105,153)(90,167,106,154)(91,168,107,141)(92,155,108,142)(93,156,109,143)(94,157,110,144)(95,158,111,145)(96,159,112,146)(97,160,99,147)(98,161,100,148), (1,115,8,122)(2,116,9,123)(3,117,10,124)(4,118,11,125)(5,119,12,126)(6,120,13,113)(7,121,14,114)(15,129,22,136)(16,130,23,137)(17,131,24,138)(18,132,25,139)(19,133,26,140)(20,134,27,127)(21,135,28,128)(29,147,36,154)(30,148,37,141)(31,149,38,142)(32,150,39,143)(33,151,40,144)(34,152,41,145)(35,153,42,146)(43,165,50,158)(44,166,51,159)(45,167,52,160)(46,168,53,161)(47,155,54,162)(48,156,55,163)(49,157,56,164)(57,172,64,179)(58,173,65,180)(59,174,66,181)(60,175,67,182)(61,176,68,169)(62,177,69,170)(63,178,70,171)(71,193,78,186)(72,194,79,187)(73,195,80,188)(74,196,81,189)(75,183,82,190)(76,184,83,191)(77,185,84,192)(85,207,92,200)(86,208,93,201)(87,209,94,202)(88,210,95,203)(89,197,96,204)(90,198,97,205)(91,199,98,206)(99,218,106,211)(100,219,107,212)(101,220,108,213)(102,221,109,214)(103,222,110,215)(104,223,111,216)(105,224,112,217), (1,56,25,33)(2,55,26,32)(3,54,27,31)(4,53,28,30)(5,52,15,29)(6,51,16,42)(7,50,17,41)(8,49,18,40)(9,48,19,39)(10,47,20,38)(11,46,21,37)(12,45,22,36)(13,44,23,35)(14,43,24,34)(57,100,74,98)(58,99,75,97)(59,112,76,96)(60,111,77,95)(61,110,78,94)(62,109,79,93)(63,108,80,92)(64,107,81,91)(65,106,82,90)(66,105,83,89)(67,104,84,88)(68,103,71,87)(69,102,72,86)(70,101,73,85)(113,166,137,153)(114,165,138,152)(115,164,139,151)(116,163,140,150)(117,162,127,149)(118,161,128,148)(119,160,129,147)(120,159,130,146)(121,158,131,145)(122,157,132,144)(123,156,133,143)(124,155,134,142)(125,168,135,141)(126,167,136,154)(169,222,193,209)(170,221,194,208)(171,220,195,207)(172,219,196,206)(173,218,183,205)(174,217,184,204)(175,216,185,203)(176,215,186,202)(177,214,187,201)(178,213,188,200)(179,212,189,199)(180,211,190,198)(181,224,191,197)(182,223,192,210), (1,40,8,33)(2,41,9,34)(3,42,10,35)(4,29,11,36)(5,30,12,37)(6,31,13,38)(7,32,14,39)(15,53,22,46)(16,54,23,47)(17,55,24,48)(18,56,25,49)(19,43,26,50)(20,44,27,51)(21,45,28,52)(57,90,64,97)(58,91,65,98)(59,92,66,85)(60,93,67,86)(61,94,68,87)(62,95,69,88)(63,96,70,89)(71,103,78,110)(72,104,79,111)(73,105,80,112)(74,106,81,99)(75,107,82,100)(76,108,83,101)(77,109,84,102)(113,142,120,149)(114,143,121,150)(115,144,122,151)(116,145,123,152)(117,146,124,153)(118,147,125,154)(119,148,126,141)(127,159,134,166)(128,160,135,167)(129,161,136,168)(130,162,137,155)(131,163,138,156)(132,164,139,157)(133,165,140,158)(169,209,176,202)(170,210,177,203)(171,197,178,204)(172,198,179,205)(173,199,180,206)(174,200,181,207)(175,201,182,208)(183,212,190,219)(184,213,191,220)(185,214,192,221)(186,215,193,222)(187,216,194,223)(188,217,195,224)(189,218,196,211)>;
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), (1,193,25,169)(2,194,26,170)(3,195,27,171)(4,196,28,172)(5,183,15,173)(6,184,16,174)(7,185,17,175)(8,186,18,176)(9,187,19,177)(10,188,20,178)(11,189,21,179)(12,190,22,180)(13,191,23,181)(14,192,24,182)(29,218,52,205)(30,219,53,206)(31,220,54,207)(32,221,55,208)(33,222,56,209)(34,223,43,210)(35,224,44,197)(36,211,45,198)(37,212,46,199)(38,213,47,200)(39,214,48,201)(40,215,49,202)(41,216,50,203)(42,217,51,204)(57,128,74,118)(58,129,75,119)(59,130,76,120)(60,131,77,121)(61,132,78,122)(62,133,79,123)(63,134,80,124)(64,135,81,125)(65,136,82,126)(66,137,83,113)(67,138,84,114)(68,139,71,115)(69,140,72,116)(70,127,73,117)(85,162,101,149)(86,163,102,150)(87,164,103,151)(88,165,104,152)(89,166,105,153)(90,167,106,154)(91,168,107,141)(92,155,108,142)(93,156,109,143)(94,157,110,144)(95,158,111,145)(96,159,112,146)(97,160,99,147)(98,161,100,148), (1,115,8,122)(2,116,9,123)(3,117,10,124)(4,118,11,125)(5,119,12,126)(6,120,13,113)(7,121,14,114)(15,129,22,136)(16,130,23,137)(17,131,24,138)(18,132,25,139)(19,133,26,140)(20,134,27,127)(21,135,28,128)(29,147,36,154)(30,148,37,141)(31,149,38,142)(32,150,39,143)(33,151,40,144)(34,152,41,145)(35,153,42,146)(43,165,50,158)(44,166,51,159)(45,167,52,160)(46,168,53,161)(47,155,54,162)(48,156,55,163)(49,157,56,164)(57,172,64,179)(58,173,65,180)(59,174,66,181)(60,175,67,182)(61,176,68,169)(62,177,69,170)(63,178,70,171)(71,193,78,186)(72,194,79,187)(73,195,80,188)(74,196,81,189)(75,183,82,190)(76,184,83,191)(77,185,84,192)(85,207,92,200)(86,208,93,201)(87,209,94,202)(88,210,95,203)(89,197,96,204)(90,198,97,205)(91,199,98,206)(99,218,106,211)(100,219,107,212)(101,220,108,213)(102,221,109,214)(103,222,110,215)(104,223,111,216)(105,224,112,217), (1,56,25,33)(2,55,26,32)(3,54,27,31)(4,53,28,30)(5,52,15,29)(6,51,16,42)(7,50,17,41)(8,49,18,40)(9,48,19,39)(10,47,20,38)(11,46,21,37)(12,45,22,36)(13,44,23,35)(14,43,24,34)(57,100,74,98)(58,99,75,97)(59,112,76,96)(60,111,77,95)(61,110,78,94)(62,109,79,93)(63,108,80,92)(64,107,81,91)(65,106,82,90)(66,105,83,89)(67,104,84,88)(68,103,71,87)(69,102,72,86)(70,101,73,85)(113,166,137,153)(114,165,138,152)(115,164,139,151)(116,163,140,150)(117,162,127,149)(118,161,128,148)(119,160,129,147)(120,159,130,146)(121,158,131,145)(122,157,132,144)(123,156,133,143)(124,155,134,142)(125,168,135,141)(126,167,136,154)(169,222,193,209)(170,221,194,208)(171,220,195,207)(172,219,196,206)(173,218,183,205)(174,217,184,204)(175,216,185,203)(176,215,186,202)(177,214,187,201)(178,213,188,200)(179,212,189,199)(180,211,190,198)(181,224,191,197)(182,223,192,210), (1,40,8,33)(2,41,9,34)(3,42,10,35)(4,29,11,36)(5,30,12,37)(6,31,13,38)(7,32,14,39)(15,53,22,46)(16,54,23,47)(17,55,24,48)(18,56,25,49)(19,43,26,50)(20,44,27,51)(21,45,28,52)(57,90,64,97)(58,91,65,98)(59,92,66,85)(60,93,67,86)(61,94,68,87)(62,95,69,88)(63,96,70,89)(71,103,78,110)(72,104,79,111)(73,105,80,112)(74,106,81,99)(75,107,82,100)(76,108,83,101)(77,109,84,102)(113,142,120,149)(114,143,121,150)(115,144,122,151)(116,145,123,152)(117,146,124,153)(118,147,125,154)(119,148,126,141)(127,159,134,166)(128,160,135,167)(129,161,136,168)(130,162,137,155)(131,163,138,156)(132,164,139,157)(133,165,140,158)(169,209,176,202)(170,210,177,203)(171,197,178,204)(172,198,179,205)(173,199,180,206)(174,200,181,207)(175,201,182,208)(183,212,190,219)(184,213,191,220)(185,214,192,221)(186,215,193,222)(187,216,194,223)(188,217,195,224)(189,218,196,211) );
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)], [(1,193,25,169),(2,194,26,170),(3,195,27,171),(4,196,28,172),(5,183,15,173),(6,184,16,174),(7,185,17,175),(8,186,18,176),(9,187,19,177),(10,188,20,178),(11,189,21,179),(12,190,22,180),(13,191,23,181),(14,192,24,182),(29,218,52,205),(30,219,53,206),(31,220,54,207),(32,221,55,208),(33,222,56,209),(34,223,43,210),(35,224,44,197),(36,211,45,198),(37,212,46,199),(38,213,47,200),(39,214,48,201),(40,215,49,202),(41,216,50,203),(42,217,51,204),(57,128,74,118),(58,129,75,119),(59,130,76,120),(60,131,77,121),(61,132,78,122),(62,133,79,123),(63,134,80,124),(64,135,81,125),(65,136,82,126),(66,137,83,113),(67,138,84,114),(68,139,71,115),(69,140,72,116),(70,127,73,117),(85,162,101,149),(86,163,102,150),(87,164,103,151),(88,165,104,152),(89,166,105,153),(90,167,106,154),(91,168,107,141),(92,155,108,142),(93,156,109,143),(94,157,110,144),(95,158,111,145),(96,159,112,146),(97,160,99,147),(98,161,100,148)], [(1,115,8,122),(2,116,9,123),(3,117,10,124),(4,118,11,125),(5,119,12,126),(6,120,13,113),(7,121,14,114),(15,129,22,136),(16,130,23,137),(17,131,24,138),(18,132,25,139),(19,133,26,140),(20,134,27,127),(21,135,28,128),(29,147,36,154),(30,148,37,141),(31,149,38,142),(32,150,39,143),(33,151,40,144),(34,152,41,145),(35,153,42,146),(43,165,50,158),(44,166,51,159),(45,167,52,160),(46,168,53,161),(47,155,54,162),(48,156,55,163),(49,157,56,164),(57,172,64,179),(58,173,65,180),(59,174,66,181),(60,175,67,182),(61,176,68,169),(62,177,69,170),(63,178,70,171),(71,193,78,186),(72,194,79,187),(73,195,80,188),(74,196,81,189),(75,183,82,190),(76,184,83,191),(77,185,84,192),(85,207,92,200),(86,208,93,201),(87,209,94,202),(88,210,95,203),(89,197,96,204),(90,198,97,205),(91,199,98,206),(99,218,106,211),(100,219,107,212),(101,220,108,213),(102,221,109,214),(103,222,110,215),(104,223,111,216),(105,224,112,217)], [(1,56,25,33),(2,55,26,32),(3,54,27,31),(4,53,28,30),(5,52,15,29),(6,51,16,42),(7,50,17,41),(8,49,18,40),(9,48,19,39),(10,47,20,38),(11,46,21,37),(12,45,22,36),(13,44,23,35),(14,43,24,34),(57,100,74,98),(58,99,75,97),(59,112,76,96),(60,111,77,95),(61,110,78,94),(62,109,79,93),(63,108,80,92),(64,107,81,91),(65,106,82,90),(66,105,83,89),(67,104,84,88),(68,103,71,87),(69,102,72,86),(70,101,73,85),(113,166,137,153),(114,165,138,152),(115,164,139,151),(116,163,140,150),(117,162,127,149),(118,161,128,148),(119,160,129,147),(120,159,130,146),(121,158,131,145),(122,157,132,144),(123,156,133,143),(124,155,134,142),(125,168,135,141),(126,167,136,154),(169,222,193,209),(170,221,194,208),(171,220,195,207),(172,219,196,206),(173,218,183,205),(174,217,184,204),(175,216,185,203),(176,215,186,202),(177,214,187,201),(178,213,188,200),(179,212,189,199),(180,211,190,198),(181,224,191,197),(182,223,192,210)], [(1,40,8,33),(2,41,9,34),(3,42,10,35),(4,29,11,36),(5,30,12,37),(6,31,13,38),(7,32,14,39),(15,53,22,46),(16,54,23,47),(17,55,24,48),(18,56,25,49),(19,43,26,50),(20,44,27,51),(21,45,28,52),(57,90,64,97),(58,91,65,98),(59,92,66,85),(60,93,67,86),(61,94,68,87),(62,95,69,88),(63,96,70,89),(71,103,78,110),(72,104,79,111),(73,105,80,112),(74,106,81,99),(75,107,82,100),(76,108,83,101),(77,109,84,102),(113,142,120,149),(114,143,121,150),(115,144,122,151),(116,145,123,152),(117,146,124,153),(118,147,125,154),(119,148,126,141),(127,159,134,166),(128,160,135,167),(129,161,136,168),(130,162,137,155),(131,163,138,156),(132,164,139,157),(133,165,140,158),(169,209,176,202),(170,210,177,203),(171,197,178,204),(172,198,179,205),(173,199,180,206),(174,200,181,207),(175,201,182,208),(183,212,190,219),(184,213,191,220),(185,214,192,221),(186,215,193,222),(187,216,194,223),(188,217,195,224),(189,218,196,211)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 14P | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28R |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 28 | 28 | 2 | 2 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 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 |
| 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 | D4⋊6D14 | D7×C4○D4 |
| kernel | C14.442+ 1+4 | C23.11D14 | Dic7⋊4D4 | D14.D4 | D14⋊D4 | Dic7.Q8 | D14.5D4 | C4×C7⋊D4 | C23.23D14 | C23.18D14 | C28⋊2D4 | Dic7⋊D4 | C28⋊D4 | C7×C4⋊D4 | C4⋊D4 | Dic7 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C14 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 1 | 1 | 3 | 4 | 6 | 3 | 3 | 9 | 2 | 12 | 6 |
Matrix representation of C14.442+ 1+4 ►in GL8(𝔽29)
| 28 | 10 | 0 | 0 | 0 | 0 | 0 | 0 |
| 14 | 4 | 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 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 5 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 19 | 12 | 27 |
| 0 | 0 | 0 | 0 | 4 | 25 | 28 | 17 |
| 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 19 | 12 | 27 |
| 0 | 0 | 0 | 0 | 0 | 19 | 24 | 27 |
| 0 | 0 | 0 | 0 | 17 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 6 | 25 | 10 |
| 1 | 19 | 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 | 12 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 24 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 19 | 12 | 27 |
| 0 | 0 | 0 | 0 | 25 | 0 | 28 | 17 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 24 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 10 | 17 | 2 |
| 0 | 0 | 0 | 0 | 0 | 4 | 0 | 12 |
G:=sub<GL(8,GF(29))| [28,14,0,0,0,0,0,0,10,4,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,17,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,17,5,0,4,0,0,0,0,12,12,19,25,0,0,0,0,0,0,12,28,0,0,0,0,0,0,27,17],[28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,17,0,0,0,0,0,0,0,0,17,0,0,0,0,0,0,0,0,0,0,17,1,0,0,0,0,19,19,12,6,0,0,0,0,12,24,0,25,0,0,0,0,27,27,0,10],[1,0,0,0,0,0,0,0,19,28,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,24,0,25,0,0,0,0,17,17,19,0,0,0,0,0,0,0,12,28,0,0,0,0,0,0,27,17],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,12,24,0,0,0,0,0,0,0,17,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,17,17,10,4,0,0,0,0,0,0,17,0,0,0,0,0,0,0,2,12] >;
C14.442+ 1+4 in GAP, Magma, Sage, TeX
C_{14}._{44}2_+^{1+4} % in TeX
G:=Group("C14.44ES+(2,2)"); // GroupNames label
G:=SmallGroup(448,1068);
// by ID
G=gap.SmallGroup(448,1068);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,219,675,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=1,c^2=e^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=a^7*b^-1,b*d=d*b,e*b*e^-1=a^7*b,c*d=d*c,c*e=e*c,e*d*e^-1=a^7*b^2*d>;
// generators/relations