G = C14.542+ 1+4 order 448 = 26·7
54th non-split extension by C14 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.542+ 1+4, C14.202- 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.D4⋊26C2, D14.5D4⋊20C2, (C2×C28).627C23, (C2×C14).182C24, (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, C23.121(C22×D7), C22.203(C23×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 C14.542+ 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 [×3], C2 [×4], C4 [×12], C22, C22 [×10], C7, C2×C4 [×6], C2×C4 [×12], D4 [×5], Q8, C23, C23 [×2], D7 [×3], C14 [×3], C14, C42 [×2], C22⋊C4 [×2], C22⋊C4 [×8], C4⋊C4 [×3], C4⋊C4 [×11], C22×C4, C22×C4 [×4], C2×D4 [×3], C2×Q8, Dic7 [×6], C28 [×6], D14 [×2], D14 [×5], C2×C14, C2×C14 [×3], C2×C4⋊C4, C4×D4 [×2], C4⋊D4, C22⋊Q8, C22⋊Q8 [×2], C22.D4 [×4], C42.C2 [×2], C42⋊2C2 [×2], C4×D7 [×5], D28 [×2], C2×Dic7 [×6], C7⋊D4 [×3], C2×C28 [×6], C2×C28, C7×Q8, C22×D7 [×2], C22×C14, C22.33C24, C4×Dic7 [×2], Dic7⋊C4 [×8], C4⋊Dic7 [×3], D14⋊C4 [×6], C23.D7 [×2], C7×C22⋊C4 [×2], C7×C4⋊C4 [×3], C2×C4×D7 [×4], C2×D28, C2×C7⋊D4 [×2], C22×C28, Q8×C14, C23.D14, D14.D4 [×2], D14⋊D4, Dic7.Q8 [×2], D7×C4⋊C4, D28⋊C4, D14.5D4, C4⋊C4⋊D7, C4×C7⋊D4, C23.23D14, D14⋊3Q8 [×2], C7×C22⋊Q8, C14.542+ 1+4
Quotients: C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×2], C24, D14 [×7], C2×C4○D4, 2+ 1+4, 2- 1+4, C22×D7 [×7], C22.33C24, C23×D7, D4⋊6D14, Q8.10D14, D7×C4○D4, C14.542+ 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 62 197 20)(2 61 198 19)(3 60 199 18)(4 59 200 17)(5 58 201 16)(6 57 202 15)(7 70 203 28)(8 69 204 27)(9 68 205 26)(10 67 206 25)(11 66 207 24)(12 65 208 23)(13 64 209 22)(14 63 210 21)(29 54 105 148)(30 53 106 147)(31 52 107 146)(32 51 108 145)(33 50 109 144)(34 49 110 143)(35 48 111 142)(36 47 112 141)(37 46 99 154)(38 45 100 153)(39 44 101 152)(40 43 102 151)(41 56 103 150)(42 55 104 149)(71 90 166 173)(72 89 167 172)(73 88 168 171)(74 87 155 170)(75 86 156 169)(76 85 157 182)(77 98 158 181)(78 97 159 180)(79 96 160 179)(80 95 161 178)(81 94 162 177)(82 93 163 176)(83 92 164 175)(84 91 165 174)(113 132 220 183)(114 131 221 196)(115 130 222 195)(116 129 223 194)(117 128 224 193)(118 127 211 192)(119 140 212 191)(120 139 213 190)(121 138 214 189)(122 137 215 188)(123 136 216 187)(124 135 217 186)(125 134 218 185)(126 133 219 184)
(1 27 8 20)(2 28 9 21)(3 15 10 22)(4 16 11 23)(5 17 12 24)(6 18 13 25)(7 19 14 26)(29 141 36 148)(30 142 37 149)(31 143 38 150)(32 144 39 151)(33 145 40 152)(34 146 41 153)(35 147 42 154)(43 108 50 101)(44 109 51 102)(45 110 52 103)(46 111 53 104)(47 112 54 105)(48 99 55 106)(49 100 56 107)(57 206 64 199)(58 207 65 200)(59 208 66 201)(60 209 67 202)(61 210 68 203)(62 197 69 204)(63 198 70 205)(71 176 78 169)(72 177 79 170)(73 178 80 171)(74 179 81 172)(75 180 82 173)(76 181 83 174)(77 182 84 175)(85 165 92 158)(86 166 93 159)(87 167 94 160)(88 168 95 161)(89 155 96 162)(90 156 97 163)(91 157 98 164)(113 140 120 133)(114 127 121 134)(115 128 122 135)(116 129 123 136)(117 130 124 137)(118 131 125 138)(119 132 126 139)(183 219 190 212)(184 220 191 213)(185 221 192 214)(186 222 193 215)(187 223 194 216)(188 224 195 217)(189 211 196 218)
(1 194 204 136)(2 193 205 135)(3 192 206 134)(4 191 207 133)(5 190 208 132)(6 189 209 131)(7 188 210 130)(8 187 197 129)(9 186 198 128)(10 185 199 127)(11 184 200 140)(12 183 201 139)(13 196 202 138)(14 195 203 137)(15 221 64 121)(16 220 65 120)(17 219 66 119)(18 218 67 118)(19 217 68 117)(20 216 69 116)(21 215 70 115)(22 214 57 114)(23 213 58 113)(24 212 59 126)(25 211 60 125)(26 224 61 124)(27 223 62 123)(28 222 63 122)(29 161 112 73)(30 160 99 72)(31 159 100 71)(32 158 101 84)(33 157 102 83)(34 156 103 82)(35 155 104 81)(36 168 105 80)(37 167 106 79)(38 166 107 78)(39 165 108 77)(40 164 109 76)(41 163 110 75)(42 162 111 74)(43 182 144 92)(44 181 145 91)(45 180 146 90)(46 179 147 89)(47 178 148 88)(48 177 149 87)(49 176 150 86)(50 175 151 85)(51 174 152 98)(52 173 153 97)(53 172 154 96)(54 171 141 95)(55 170 142 94)(56 169 143 93)
(1 105 8 112)(2 104 9 111)(3 103 10 110)(4 102 11 109)(5 101 12 108)(6 100 13 107)(7 99 14 106)(15 45 22 52)(16 44 23 51)(17 43 24 50)(18 56 25 49)(19 55 26 48)(20 54 27 47)(21 53 28 46)(29 204 36 197)(30 203 37 210)(31 202 38 209)(32 201 39 208)(33 200 40 207)(34 199 41 206)(35 198 42 205)(57 153 64 146)(58 152 65 145)(59 151 66 144)(60 150 67 143)(61 149 68 142)(62 148 69 141)(63 147 70 154)(71 138 78 131)(72 137 79 130)(73 136 80 129)(74 135 81 128)(75 134 82 127)(76 133 83 140)(77 132 84 139)(85 219 92 212)(86 218 93 211)(87 217 94 224)(88 216 95 223)(89 215 96 222)(90 214 97 221)(91 213 98 220)(113 174 120 181)(114 173 121 180)(115 172 122 179)(116 171 123 178)(117 170 124 177)(118 169 125 176)(119 182 126 175)(155 186 162 193)(156 185 163 192)(157 184 164 191)(158 183 165 190)(159 196 166 189)(160 195 167 188)(161 194 168 187)
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), (1,62,197,20)(2,61,198,19)(3,60,199,18)(4,59,200,17)(5,58,201,16)(6,57,202,15)(7,70,203,28)(8,69,204,27)(9,68,205,26)(10,67,206,25)(11,66,207,24)(12,65,208,23)(13,64,209,22)(14,63,210,21)(29,54,105,148)(30,53,106,147)(31,52,107,146)(32,51,108,145)(33,50,109,144)(34,49,110,143)(35,48,111,142)(36,47,112,141)(37,46,99,154)(38,45,100,153)(39,44,101,152)(40,43,102,151)(41,56,103,150)(42,55,104,149)(71,90,166,173)(72,89,167,172)(73,88,168,171)(74,87,155,170)(75,86,156,169)(76,85,157,182)(77,98,158,181)(78,97,159,180)(79,96,160,179)(80,95,161,178)(81,94,162,177)(82,93,163,176)(83,92,164,175)(84,91,165,174)(113,132,220,183)(114,131,221,196)(115,130,222,195)(116,129,223,194)(117,128,224,193)(118,127,211,192)(119,140,212,191)(120,139,213,190)(121,138,214,189)(122,137,215,188)(123,136,216,187)(124,135,217,186)(125,134,218,185)(126,133,219,184), (1,27,8,20)(2,28,9,21)(3,15,10,22)(4,16,11,23)(5,17,12,24)(6,18,13,25)(7,19,14,26)(29,141,36,148)(30,142,37,149)(31,143,38,150)(32,144,39,151)(33,145,40,152)(34,146,41,153)(35,147,42,154)(43,108,50,101)(44,109,51,102)(45,110,52,103)(46,111,53,104)(47,112,54,105)(48,99,55,106)(49,100,56,107)(57,206,64,199)(58,207,65,200)(59,208,66,201)(60,209,67,202)(61,210,68,203)(62,197,69,204)(63,198,70,205)(71,176,78,169)(72,177,79,170)(73,178,80,171)(74,179,81,172)(75,180,82,173)(76,181,83,174)(77,182,84,175)(85,165,92,158)(86,166,93,159)(87,167,94,160)(88,168,95,161)(89,155,96,162)(90,156,97,163)(91,157,98,164)(113,140,120,133)(114,127,121,134)(115,128,122,135)(116,129,123,136)(117,130,124,137)(118,131,125,138)(119,132,126,139)(183,219,190,212)(184,220,191,213)(185,221,192,214)(186,222,193,215)(187,223,194,216)(188,224,195,217)(189,211,196,218), (1,194,204,136)(2,193,205,135)(3,192,206,134)(4,191,207,133)(5,190,208,132)(6,189,209,131)(7,188,210,130)(8,187,197,129)(9,186,198,128)(10,185,199,127)(11,184,200,140)(12,183,201,139)(13,196,202,138)(14,195,203,137)(15,221,64,121)(16,220,65,120)(17,219,66,119)(18,218,67,118)(19,217,68,117)(20,216,69,116)(21,215,70,115)(22,214,57,114)(23,213,58,113)(24,212,59,126)(25,211,60,125)(26,224,61,124)(27,223,62,123)(28,222,63,122)(29,161,112,73)(30,160,99,72)(31,159,100,71)(32,158,101,84)(33,157,102,83)(34,156,103,82)(35,155,104,81)(36,168,105,80)(37,167,106,79)(38,166,107,78)(39,165,108,77)(40,164,109,76)(41,163,110,75)(42,162,111,74)(43,182,144,92)(44,181,145,91)(45,180,146,90)(46,179,147,89)(47,178,148,88)(48,177,149,87)(49,176,150,86)(50,175,151,85)(51,174,152,98)(52,173,153,97)(53,172,154,96)(54,171,141,95)(55,170,142,94)(56,169,143,93), (1,105,8,112)(2,104,9,111)(3,103,10,110)(4,102,11,109)(5,101,12,108)(6,100,13,107)(7,99,14,106)(15,45,22,52)(16,44,23,51)(17,43,24,50)(18,56,25,49)(19,55,26,48)(20,54,27,47)(21,53,28,46)(29,204,36,197)(30,203,37,210)(31,202,38,209)(32,201,39,208)(33,200,40,207)(34,199,41,206)(35,198,42,205)(57,153,64,146)(58,152,65,145)(59,151,66,144)(60,150,67,143)(61,149,68,142)(62,148,69,141)(63,147,70,154)(71,138,78,131)(72,137,79,130)(73,136,80,129)(74,135,81,128)(75,134,82,127)(76,133,83,140)(77,132,84,139)(85,219,92,212)(86,218,93,211)(87,217,94,224)(88,216,95,223)(89,215,96,222)(90,214,97,221)(91,213,98,220)(113,174,120,181)(114,173,121,180)(115,172,122,179)(116,171,123,178)(117,170,124,177)(118,169,125,176)(119,182,126,175)(155,186,162,193)(156,185,163,192)(157,184,164,191)(158,183,165,190)(159,196,166,189)(160,195,167,188)(161,194,168,187)>;
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), (1,62,197,20)(2,61,198,19)(3,60,199,18)(4,59,200,17)(5,58,201,16)(6,57,202,15)(7,70,203,28)(8,69,204,27)(9,68,205,26)(10,67,206,25)(11,66,207,24)(12,65,208,23)(13,64,209,22)(14,63,210,21)(29,54,105,148)(30,53,106,147)(31,52,107,146)(32,51,108,145)(33,50,109,144)(34,49,110,143)(35,48,111,142)(36,47,112,141)(37,46,99,154)(38,45,100,153)(39,44,101,152)(40,43,102,151)(41,56,103,150)(42,55,104,149)(71,90,166,173)(72,89,167,172)(73,88,168,171)(74,87,155,170)(75,86,156,169)(76,85,157,182)(77,98,158,181)(78,97,159,180)(79,96,160,179)(80,95,161,178)(81,94,162,177)(82,93,163,176)(83,92,164,175)(84,91,165,174)(113,132,220,183)(114,131,221,196)(115,130,222,195)(116,129,223,194)(117,128,224,193)(118,127,211,192)(119,140,212,191)(120,139,213,190)(121,138,214,189)(122,137,215,188)(123,136,216,187)(124,135,217,186)(125,134,218,185)(126,133,219,184), (1,27,8,20)(2,28,9,21)(3,15,10,22)(4,16,11,23)(5,17,12,24)(6,18,13,25)(7,19,14,26)(29,141,36,148)(30,142,37,149)(31,143,38,150)(32,144,39,151)(33,145,40,152)(34,146,41,153)(35,147,42,154)(43,108,50,101)(44,109,51,102)(45,110,52,103)(46,111,53,104)(47,112,54,105)(48,99,55,106)(49,100,56,107)(57,206,64,199)(58,207,65,200)(59,208,66,201)(60,209,67,202)(61,210,68,203)(62,197,69,204)(63,198,70,205)(71,176,78,169)(72,177,79,170)(73,178,80,171)(74,179,81,172)(75,180,82,173)(76,181,83,174)(77,182,84,175)(85,165,92,158)(86,166,93,159)(87,167,94,160)(88,168,95,161)(89,155,96,162)(90,156,97,163)(91,157,98,164)(113,140,120,133)(114,127,121,134)(115,128,122,135)(116,129,123,136)(117,130,124,137)(118,131,125,138)(119,132,126,139)(183,219,190,212)(184,220,191,213)(185,221,192,214)(186,222,193,215)(187,223,194,216)(188,224,195,217)(189,211,196,218), (1,194,204,136)(2,193,205,135)(3,192,206,134)(4,191,207,133)(5,190,208,132)(6,189,209,131)(7,188,210,130)(8,187,197,129)(9,186,198,128)(10,185,199,127)(11,184,200,140)(12,183,201,139)(13,196,202,138)(14,195,203,137)(15,221,64,121)(16,220,65,120)(17,219,66,119)(18,218,67,118)(19,217,68,117)(20,216,69,116)(21,215,70,115)(22,214,57,114)(23,213,58,113)(24,212,59,126)(25,211,60,125)(26,224,61,124)(27,223,62,123)(28,222,63,122)(29,161,112,73)(30,160,99,72)(31,159,100,71)(32,158,101,84)(33,157,102,83)(34,156,103,82)(35,155,104,81)(36,168,105,80)(37,167,106,79)(38,166,107,78)(39,165,108,77)(40,164,109,76)(41,163,110,75)(42,162,111,74)(43,182,144,92)(44,181,145,91)(45,180,146,90)(46,179,147,89)(47,178,148,88)(48,177,149,87)(49,176,150,86)(50,175,151,85)(51,174,152,98)(52,173,153,97)(53,172,154,96)(54,171,141,95)(55,170,142,94)(56,169,143,93), (1,105,8,112)(2,104,9,111)(3,103,10,110)(4,102,11,109)(5,101,12,108)(6,100,13,107)(7,99,14,106)(15,45,22,52)(16,44,23,51)(17,43,24,50)(18,56,25,49)(19,55,26,48)(20,54,27,47)(21,53,28,46)(29,204,36,197)(30,203,37,210)(31,202,38,209)(32,201,39,208)(33,200,40,207)(34,199,41,206)(35,198,42,205)(57,153,64,146)(58,152,65,145)(59,151,66,144)(60,150,67,143)(61,149,68,142)(62,148,69,141)(63,147,70,154)(71,138,78,131)(72,137,79,130)(73,136,80,129)(74,135,81,128)(75,134,82,127)(76,133,83,140)(77,132,84,139)(85,219,92,212)(86,218,93,211)(87,217,94,224)(88,216,95,223)(89,215,96,222)(90,214,97,221)(91,213,98,220)(113,174,120,181)(114,173,121,180)(115,172,122,179)(116,171,123,178)(117,170,124,177)(118,169,125,176)(119,182,126,175)(155,186,162,193)(156,185,163,192)(157,184,164,191)(158,183,165,190)(159,196,166,189)(160,195,167,188)(161,194,168,187) );
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)], [(1,62,197,20),(2,61,198,19),(3,60,199,18),(4,59,200,17),(5,58,201,16),(6,57,202,15),(7,70,203,28),(8,69,204,27),(9,68,205,26),(10,67,206,25),(11,66,207,24),(12,65,208,23),(13,64,209,22),(14,63,210,21),(29,54,105,148),(30,53,106,147),(31,52,107,146),(32,51,108,145),(33,50,109,144),(34,49,110,143),(35,48,111,142),(36,47,112,141),(37,46,99,154),(38,45,100,153),(39,44,101,152),(40,43,102,151),(41,56,103,150),(42,55,104,149),(71,90,166,173),(72,89,167,172),(73,88,168,171),(74,87,155,170),(75,86,156,169),(76,85,157,182),(77,98,158,181),(78,97,159,180),(79,96,160,179),(80,95,161,178),(81,94,162,177),(82,93,163,176),(83,92,164,175),(84,91,165,174),(113,132,220,183),(114,131,221,196),(115,130,222,195),(116,129,223,194),(117,128,224,193),(118,127,211,192),(119,140,212,191),(120,139,213,190),(121,138,214,189),(122,137,215,188),(123,136,216,187),(124,135,217,186),(125,134,218,185),(126,133,219,184)], [(1,27,8,20),(2,28,9,21),(3,15,10,22),(4,16,11,23),(5,17,12,24),(6,18,13,25),(7,19,14,26),(29,141,36,148),(30,142,37,149),(31,143,38,150),(32,144,39,151),(33,145,40,152),(34,146,41,153),(35,147,42,154),(43,108,50,101),(44,109,51,102),(45,110,52,103),(46,111,53,104),(47,112,54,105),(48,99,55,106),(49,100,56,107),(57,206,64,199),(58,207,65,200),(59,208,66,201),(60,209,67,202),(61,210,68,203),(62,197,69,204),(63,198,70,205),(71,176,78,169),(72,177,79,170),(73,178,80,171),(74,179,81,172),(75,180,82,173),(76,181,83,174),(77,182,84,175),(85,165,92,158),(86,166,93,159),(87,167,94,160),(88,168,95,161),(89,155,96,162),(90,156,97,163),(91,157,98,164),(113,140,120,133),(114,127,121,134),(115,128,122,135),(116,129,123,136),(117,130,124,137),(118,131,125,138),(119,132,126,139),(183,219,190,212),(184,220,191,213),(185,221,192,214),(186,222,193,215),(187,223,194,216),(188,224,195,217),(189,211,196,218)], [(1,194,204,136),(2,193,205,135),(3,192,206,134),(4,191,207,133),(5,190,208,132),(6,189,209,131),(7,188,210,130),(8,187,197,129),(9,186,198,128),(10,185,199,127),(11,184,200,140),(12,183,201,139),(13,196,202,138),(14,195,203,137),(15,221,64,121),(16,220,65,120),(17,219,66,119),(18,218,67,118),(19,217,68,117),(20,216,69,116),(21,215,70,115),(22,214,57,114),(23,213,58,113),(24,212,59,126),(25,211,60,125),(26,224,61,124),(27,223,62,123),(28,222,63,122),(29,161,112,73),(30,160,99,72),(31,159,100,71),(32,158,101,84),(33,157,102,83),(34,156,103,82),(35,155,104,81),(36,168,105,80),(37,167,106,79),(38,166,107,78),(39,165,108,77),(40,164,109,76),(41,163,110,75),(42,162,111,74),(43,182,144,92),(44,181,145,91),(45,180,146,90),(46,179,147,89),(47,178,148,88),(48,177,149,87),(49,176,150,86),(50,175,151,85),(51,174,152,98),(52,173,153,97),(53,172,154,96),(54,171,141,95),(55,170,142,94),(56,169,143,93)], [(1,105,8,112),(2,104,9,111),(3,103,10,110),(4,102,11,109),(5,101,12,108),(6,100,13,107),(7,99,14,106),(15,45,22,52),(16,44,23,51),(17,43,24,50),(18,56,25,49),(19,55,26,48),(20,54,27,47),(21,53,28,46),(29,204,36,197),(30,203,37,210),(31,202,38,209),(32,201,39,208),(33,200,40,207),(34,199,41,206),(35,198,42,205),(57,153,64,146),(58,152,65,145),(59,151,66,144),(60,150,67,143),(61,149,68,142),(62,148,69,141),(63,147,70,154),(71,138,78,131),(72,137,79,130),(73,136,80,129),(74,135,81,128),(75,134,82,127),(76,133,83,140),(77,132,84,139),(85,219,92,212),(86,218,93,211),(87,217,94,224),(88,216,95,223),(89,215,96,222),(90,214,97,221),(91,213,98,220),(113,174,120,181),(114,173,121,180),(115,172,122,179),(116,171,123,178),(117,170,124,177),(118,169,125,176),(119,182,126,175),(155,186,162,193),(156,185,163,192),(157,184,164,191),(158,183,165,190),(159,196,166,189),(160,195,167,188),(161,194,168,187)])
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 | C14.542+ 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 C14.542+ 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] >;
C14.542+ 1+4 in GAP, Magma, Sage, TeX
C_{14}._{54}2_+^{1+4} % in TeX
G:=Group("C14.54ES+(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