G = C14.432+ 1+4 order 448 = 26·7
43rd non-split extension by C14 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.432+ 1+4, C4⋊D4⋊17D7, C28⋊2D4⋊23C2, C4⋊C4.182D14, (D4×Dic7)⋊22C2, (C2×D4).156D14, C22⋊C4.49D14, C28.3Q8⋊19C2, Dic7⋊4D4⋊11C2, D14.30(C4○D4), C28.203(C4○D4), C4.96(D4⋊2D7), (C2×C28).596C23, (C2×C14).158C24, (C22×C4).225D14, C2.45(D4⋊6D14), C23.18(C22×D7), D14⋊C4.127C22, (D4×C14).124C22, C23.D14⋊19C2, C4⋊Dic7.372C22, (C22×C14).25C23, (C2×Dic7).77C23, (C4×Dic7).96C22, C22.179(C23×D7), C23.D7.26C22, C23.21D14⋊26C2, C23.18D14⋊11C2, Dic7⋊C4.139C22, (C22×C28).243C22, C7⋊7(C22.47C24), (C22×D7).191C23, (C22×Dic7).111C22, (D7×C4⋊C4)⋊23C2, (C4×C7⋊D4)⋊19C2, C2.42(D7×C4○D4), (C7×C4⋊D4)⋊20C2, (C2×C4×D7).86C22, C14.155(C2×C4○D4), C2.38(C2×D4⋊2D7), (C2×C4).40(C22×D7), (C7×C4⋊C4).146C22, (C2×C7⋊D4).31C22, (C7×C22⋊C4).15C22, SmallGroup(448,1067)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.432+ 1+4
G = < a,b,c,d,e | a14=b4=c2=1, d2=a7b2, e2=a7, bab-1=a-1, ac=ca, ad=da, ae=ea, cbc=a7b-1, bd=db, ebe-1=a7b, cd=dc, ece-1=a7c, ede-1=b2d >
Subgroups: 1004 in 238 conjugacy classes, 97 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, C23, C23, C23, D7, C14, C14, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×D4, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C4⋊C4, C42⋊C2, C4×D4, C4⋊D4, C4⋊D4, C22.D4, C42.C2, C42⋊2C2, C4×D7, C2×Dic7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C22×C14, C22.47C24, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C23.D7, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C2×C4×D7, C2×C4×D7, C22×Dic7, C2×C7⋊D4, C2×C7⋊D4, C22×C28, D4×C14, D4×C14, C23.D14, Dic7⋊4D4, C28.3Q8, D7×C4⋊C4, C23.21D14, C4×C7⋊D4, D4×Dic7, C23.18D14, C28⋊2D4, C28⋊2D4, C7×C4⋊D4, C14.432+ 1+4
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.47C24, D4⋊2D7, C23×D7, C2×D4⋊2D7, D4⋊6D14, D7×C4○D4, C14.432+ 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 22 42 63)(2 21 29 62)(3 20 30 61)(4 19 31 60)(5 18 32 59)(6 17 33 58)(7 16 34 57)(8 15 35 70)(9 28 36 69)(10 27 37 68)(11 26 38 67)(12 25 39 66)(13 24 40 65)(14 23 41 64)(43 109 97 84)(44 108 98 83)(45 107 85 82)(46 106 86 81)(47 105 87 80)(48 104 88 79)(49 103 89 78)(50 102 90 77)(51 101 91 76)(52 100 92 75)(53 99 93 74)(54 112 94 73)(55 111 95 72)(56 110 96 71)(113 216 140 170)(114 215 127 169)(115 214 128 182)(116 213 129 181)(117 212 130 180)(118 211 131 179)(119 224 132 178)(120 223 133 177)(121 222 134 176)(122 221 135 175)(123 220 136 174)(124 219 137 173)(125 218 138 172)(126 217 139 171)(141 205 190 167)(142 204 191 166)(143 203 192 165)(144 202 193 164)(145 201 194 163)(146 200 195 162)(147 199 196 161)(148 198 183 160)(149 197 184 159)(150 210 185 158)(151 209 186 157)(152 208 187 156)(153 207 188 155)(154 206 189 168)
(1 53)(2 54)(3 55)(4 56)(5 43)(6 44)(7 45)(8 46)(9 47)(10 48)(11 49)(12 50)(13 51)(14 52)(15 74)(16 75)(17 76)(18 77)(19 78)(20 79)(21 80)(22 81)(23 82)(24 83)(25 84)(26 71)(27 72)(28 73)(29 94)(30 95)(31 96)(32 97)(33 98)(34 85)(35 86)(36 87)(37 88)(38 89)(39 90)(40 91)(41 92)(42 93)(57 100)(58 101)(59 102)(60 103)(61 104)(62 105)(63 106)(64 107)(65 108)(66 109)(67 110)(68 111)(69 112)(70 99)(113 193)(114 194)(115 195)(116 196)(117 183)(118 184)(119 185)(120 186)(121 187)(122 188)(123 189)(124 190)(125 191)(126 192)(127 145)(128 146)(129 147)(130 148)(131 149)(132 150)(133 151)(134 152)(135 153)(136 154)(137 141)(138 142)(139 143)(140 144)(155 182)(156 169)(157 170)(158 171)(159 172)(160 173)(161 174)(162 175)(163 176)(164 177)(165 178)(166 179)(167 180)(168 181)(197 218)(198 219)(199 220)(200 221)(201 222)(202 223)(203 224)(204 211)(205 212)(206 213)(207 214)(208 215)(209 216)(210 217)
(1 151 35 193)(2 152 36 194)(3 153 37 195)(4 154 38 196)(5 141 39 183)(6 142 40 184)(7 143 41 185)(8 144 42 186)(9 145 29 187)(10 146 30 188)(11 147 31 189)(12 148 32 190)(13 149 33 191)(14 150 34 192)(15 202 63 157)(16 203 64 158)(17 204 65 159)(18 205 66 160)(19 206 67 161)(20 207 68 162)(21 208 69 163)(22 209 70 164)(23 210 57 165)(24 197 58 166)(25 198 59 167)(26 199 60 168)(27 200 61 155)(28 201 62 156)(43 137 90 117)(44 138 91 118)(45 139 92 119)(46 140 93 120)(47 127 94 121)(48 128 95 122)(49 129 96 123)(50 130 97 124)(51 131 98 125)(52 132 85 126)(53 133 86 113)(54 134 87 114)(55 135 88 115)(56 136 89 116)(71 220 103 181)(72 221 104 182)(73 222 105 169)(74 223 106 170)(75 224 107 171)(76 211 108 172)(77 212 109 173)(78 213 110 174)(79 214 111 175)(80 215 112 176)(81 216 99 177)(82 217 100 178)(83 218 101 179)(84 219 102 180)
(1 99 8 106)(2 100 9 107)(3 101 10 108)(4 102 11 109)(5 103 12 110)(6 104 13 111)(7 105 14 112)(15 93 22 86)(16 94 23 87)(17 95 24 88)(18 96 25 89)(19 97 26 90)(20 98 27 91)(21 85 28 92)(29 75 36 82)(30 76 37 83)(31 77 38 84)(32 78 39 71)(33 79 40 72)(34 80 41 73)(35 81 42 74)(43 67 50 60)(44 68 51 61)(45 69 52 62)(46 70 53 63)(47 57 54 64)(48 58 55 65)(49 59 56 66)(113 164 120 157)(114 165 121 158)(115 166 122 159)(116 167 123 160)(117 168 124 161)(118 155 125 162)(119 156 126 163)(127 203 134 210)(128 204 135 197)(129 205 136 198)(130 206 137 199)(131 207 138 200)(132 208 139 201)(133 209 140 202)(141 213 148 220)(142 214 149 221)(143 215 150 222)(144 216 151 223)(145 217 152 224)(146 218 153 211)(147 219 154 212)(169 185 176 192)(170 186 177 193)(171 187 178 194)(172 188 179 195)(173 189 180 196)(174 190 181 183)(175 191 182 184)
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), (1,22,42,63)(2,21,29,62)(3,20,30,61)(4,19,31,60)(5,18,32,59)(6,17,33,58)(7,16,34,57)(8,15,35,70)(9,28,36,69)(10,27,37,68)(11,26,38,67)(12,25,39,66)(13,24,40,65)(14,23,41,64)(43,109,97,84)(44,108,98,83)(45,107,85,82)(46,106,86,81)(47,105,87,80)(48,104,88,79)(49,103,89,78)(50,102,90,77)(51,101,91,76)(52,100,92,75)(53,99,93,74)(54,112,94,73)(55,111,95,72)(56,110,96,71)(113,216,140,170)(114,215,127,169)(115,214,128,182)(116,213,129,181)(117,212,130,180)(118,211,131,179)(119,224,132,178)(120,223,133,177)(121,222,134,176)(122,221,135,175)(123,220,136,174)(124,219,137,173)(125,218,138,172)(126,217,139,171)(141,205,190,167)(142,204,191,166)(143,203,192,165)(144,202,193,164)(145,201,194,163)(146,200,195,162)(147,199,196,161)(148,198,183,160)(149,197,184,159)(150,210,185,158)(151,209,186,157)(152,208,187,156)(153,207,188,155)(154,206,189,168), (1,53)(2,54)(3,55)(4,56)(5,43)(6,44)(7,45)(8,46)(9,47)(10,48)(11,49)(12,50)(13,51)(14,52)(15,74)(16,75)(17,76)(18,77)(19,78)(20,79)(21,80)(22,81)(23,82)(24,83)(25,84)(26,71)(27,72)(28,73)(29,94)(30,95)(31,96)(32,97)(33,98)(34,85)(35,86)(36,87)(37,88)(38,89)(39,90)(40,91)(41,92)(42,93)(57,100)(58,101)(59,102)(60,103)(61,104)(62,105)(63,106)(64,107)(65,108)(66,109)(67,110)(68,111)(69,112)(70,99)(113,193)(114,194)(115,195)(116,196)(117,183)(118,184)(119,185)(120,186)(121,187)(122,188)(123,189)(124,190)(125,191)(126,192)(127,145)(128,146)(129,147)(130,148)(131,149)(132,150)(133,151)(134,152)(135,153)(136,154)(137,141)(138,142)(139,143)(140,144)(155,182)(156,169)(157,170)(158,171)(159,172)(160,173)(161,174)(162,175)(163,176)(164,177)(165,178)(166,179)(167,180)(168,181)(197,218)(198,219)(199,220)(200,221)(201,222)(202,223)(203,224)(204,211)(205,212)(206,213)(207,214)(208,215)(209,216)(210,217), (1,151,35,193)(2,152,36,194)(3,153,37,195)(4,154,38,196)(5,141,39,183)(6,142,40,184)(7,143,41,185)(8,144,42,186)(9,145,29,187)(10,146,30,188)(11,147,31,189)(12,148,32,190)(13,149,33,191)(14,150,34,192)(15,202,63,157)(16,203,64,158)(17,204,65,159)(18,205,66,160)(19,206,67,161)(20,207,68,162)(21,208,69,163)(22,209,70,164)(23,210,57,165)(24,197,58,166)(25,198,59,167)(26,199,60,168)(27,200,61,155)(28,201,62,156)(43,137,90,117)(44,138,91,118)(45,139,92,119)(46,140,93,120)(47,127,94,121)(48,128,95,122)(49,129,96,123)(50,130,97,124)(51,131,98,125)(52,132,85,126)(53,133,86,113)(54,134,87,114)(55,135,88,115)(56,136,89,116)(71,220,103,181)(72,221,104,182)(73,222,105,169)(74,223,106,170)(75,224,107,171)(76,211,108,172)(77,212,109,173)(78,213,110,174)(79,214,111,175)(80,215,112,176)(81,216,99,177)(82,217,100,178)(83,218,101,179)(84,219,102,180), (1,99,8,106)(2,100,9,107)(3,101,10,108)(4,102,11,109)(5,103,12,110)(6,104,13,111)(7,105,14,112)(15,93,22,86)(16,94,23,87)(17,95,24,88)(18,96,25,89)(19,97,26,90)(20,98,27,91)(21,85,28,92)(29,75,36,82)(30,76,37,83)(31,77,38,84)(32,78,39,71)(33,79,40,72)(34,80,41,73)(35,81,42,74)(43,67,50,60)(44,68,51,61)(45,69,52,62)(46,70,53,63)(47,57,54,64)(48,58,55,65)(49,59,56,66)(113,164,120,157)(114,165,121,158)(115,166,122,159)(116,167,123,160)(117,168,124,161)(118,155,125,162)(119,156,126,163)(127,203,134,210)(128,204,135,197)(129,205,136,198)(130,206,137,199)(131,207,138,200)(132,208,139,201)(133,209,140,202)(141,213,148,220)(142,214,149,221)(143,215,150,222)(144,216,151,223)(145,217,152,224)(146,218,153,211)(147,219,154,212)(169,185,176,192)(170,186,177,193)(171,187,178,194)(172,188,179,195)(173,189,180,196)(174,190,181,183)(175,191,182,184)>;
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), (1,22,42,63)(2,21,29,62)(3,20,30,61)(4,19,31,60)(5,18,32,59)(6,17,33,58)(7,16,34,57)(8,15,35,70)(9,28,36,69)(10,27,37,68)(11,26,38,67)(12,25,39,66)(13,24,40,65)(14,23,41,64)(43,109,97,84)(44,108,98,83)(45,107,85,82)(46,106,86,81)(47,105,87,80)(48,104,88,79)(49,103,89,78)(50,102,90,77)(51,101,91,76)(52,100,92,75)(53,99,93,74)(54,112,94,73)(55,111,95,72)(56,110,96,71)(113,216,140,170)(114,215,127,169)(115,214,128,182)(116,213,129,181)(117,212,130,180)(118,211,131,179)(119,224,132,178)(120,223,133,177)(121,222,134,176)(122,221,135,175)(123,220,136,174)(124,219,137,173)(125,218,138,172)(126,217,139,171)(141,205,190,167)(142,204,191,166)(143,203,192,165)(144,202,193,164)(145,201,194,163)(146,200,195,162)(147,199,196,161)(148,198,183,160)(149,197,184,159)(150,210,185,158)(151,209,186,157)(152,208,187,156)(153,207,188,155)(154,206,189,168), (1,53)(2,54)(3,55)(4,56)(5,43)(6,44)(7,45)(8,46)(9,47)(10,48)(11,49)(12,50)(13,51)(14,52)(15,74)(16,75)(17,76)(18,77)(19,78)(20,79)(21,80)(22,81)(23,82)(24,83)(25,84)(26,71)(27,72)(28,73)(29,94)(30,95)(31,96)(32,97)(33,98)(34,85)(35,86)(36,87)(37,88)(38,89)(39,90)(40,91)(41,92)(42,93)(57,100)(58,101)(59,102)(60,103)(61,104)(62,105)(63,106)(64,107)(65,108)(66,109)(67,110)(68,111)(69,112)(70,99)(113,193)(114,194)(115,195)(116,196)(117,183)(118,184)(119,185)(120,186)(121,187)(122,188)(123,189)(124,190)(125,191)(126,192)(127,145)(128,146)(129,147)(130,148)(131,149)(132,150)(133,151)(134,152)(135,153)(136,154)(137,141)(138,142)(139,143)(140,144)(155,182)(156,169)(157,170)(158,171)(159,172)(160,173)(161,174)(162,175)(163,176)(164,177)(165,178)(166,179)(167,180)(168,181)(197,218)(198,219)(199,220)(200,221)(201,222)(202,223)(203,224)(204,211)(205,212)(206,213)(207,214)(208,215)(209,216)(210,217), (1,151,35,193)(2,152,36,194)(3,153,37,195)(4,154,38,196)(5,141,39,183)(6,142,40,184)(7,143,41,185)(8,144,42,186)(9,145,29,187)(10,146,30,188)(11,147,31,189)(12,148,32,190)(13,149,33,191)(14,150,34,192)(15,202,63,157)(16,203,64,158)(17,204,65,159)(18,205,66,160)(19,206,67,161)(20,207,68,162)(21,208,69,163)(22,209,70,164)(23,210,57,165)(24,197,58,166)(25,198,59,167)(26,199,60,168)(27,200,61,155)(28,201,62,156)(43,137,90,117)(44,138,91,118)(45,139,92,119)(46,140,93,120)(47,127,94,121)(48,128,95,122)(49,129,96,123)(50,130,97,124)(51,131,98,125)(52,132,85,126)(53,133,86,113)(54,134,87,114)(55,135,88,115)(56,136,89,116)(71,220,103,181)(72,221,104,182)(73,222,105,169)(74,223,106,170)(75,224,107,171)(76,211,108,172)(77,212,109,173)(78,213,110,174)(79,214,111,175)(80,215,112,176)(81,216,99,177)(82,217,100,178)(83,218,101,179)(84,219,102,180), (1,99,8,106)(2,100,9,107)(3,101,10,108)(4,102,11,109)(5,103,12,110)(6,104,13,111)(7,105,14,112)(15,93,22,86)(16,94,23,87)(17,95,24,88)(18,96,25,89)(19,97,26,90)(20,98,27,91)(21,85,28,92)(29,75,36,82)(30,76,37,83)(31,77,38,84)(32,78,39,71)(33,79,40,72)(34,80,41,73)(35,81,42,74)(43,67,50,60)(44,68,51,61)(45,69,52,62)(46,70,53,63)(47,57,54,64)(48,58,55,65)(49,59,56,66)(113,164,120,157)(114,165,121,158)(115,166,122,159)(116,167,123,160)(117,168,124,161)(118,155,125,162)(119,156,126,163)(127,203,134,210)(128,204,135,197)(129,205,136,198)(130,206,137,199)(131,207,138,200)(132,208,139,201)(133,209,140,202)(141,213,148,220)(142,214,149,221)(143,215,150,222)(144,216,151,223)(145,217,152,224)(146,218,153,211)(147,219,154,212)(169,185,176,192)(170,186,177,193)(171,187,178,194)(172,188,179,195)(173,189,180,196)(174,190,181,183)(175,191,182,184) );
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)], [(1,22,42,63),(2,21,29,62),(3,20,30,61),(4,19,31,60),(5,18,32,59),(6,17,33,58),(7,16,34,57),(8,15,35,70),(9,28,36,69),(10,27,37,68),(11,26,38,67),(12,25,39,66),(13,24,40,65),(14,23,41,64),(43,109,97,84),(44,108,98,83),(45,107,85,82),(46,106,86,81),(47,105,87,80),(48,104,88,79),(49,103,89,78),(50,102,90,77),(51,101,91,76),(52,100,92,75),(53,99,93,74),(54,112,94,73),(55,111,95,72),(56,110,96,71),(113,216,140,170),(114,215,127,169),(115,214,128,182),(116,213,129,181),(117,212,130,180),(118,211,131,179),(119,224,132,178),(120,223,133,177),(121,222,134,176),(122,221,135,175),(123,220,136,174),(124,219,137,173),(125,218,138,172),(126,217,139,171),(141,205,190,167),(142,204,191,166),(143,203,192,165),(144,202,193,164),(145,201,194,163),(146,200,195,162),(147,199,196,161),(148,198,183,160),(149,197,184,159),(150,210,185,158),(151,209,186,157),(152,208,187,156),(153,207,188,155),(154,206,189,168)], [(1,53),(2,54),(3,55),(4,56),(5,43),(6,44),(7,45),(8,46),(9,47),(10,48),(11,49),(12,50),(13,51),(14,52),(15,74),(16,75),(17,76),(18,77),(19,78),(20,79),(21,80),(22,81),(23,82),(24,83),(25,84),(26,71),(27,72),(28,73),(29,94),(30,95),(31,96),(32,97),(33,98),(34,85),(35,86),(36,87),(37,88),(38,89),(39,90),(40,91),(41,92),(42,93),(57,100),(58,101),(59,102),(60,103),(61,104),(62,105),(63,106),(64,107),(65,108),(66,109),(67,110),(68,111),(69,112),(70,99),(113,193),(114,194),(115,195),(116,196),(117,183),(118,184),(119,185),(120,186),(121,187),(122,188),(123,189),(124,190),(125,191),(126,192),(127,145),(128,146),(129,147),(130,148),(131,149),(132,150),(133,151),(134,152),(135,153),(136,154),(137,141),(138,142),(139,143),(140,144),(155,182),(156,169),(157,170),(158,171),(159,172),(160,173),(161,174),(162,175),(163,176),(164,177),(165,178),(166,179),(167,180),(168,181),(197,218),(198,219),(199,220),(200,221),(201,222),(202,223),(203,224),(204,211),(205,212),(206,213),(207,214),(208,215),(209,216),(210,217)], [(1,151,35,193),(2,152,36,194),(3,153,37,195),(4,154,38,196),(5,141,39,183),(6,142,40,184),(7,143,41,185),(8,144,42,186),(9,145,29,187),(10,146,30,188),(11,147,31,189),(12,148,32,190),(13,149,33,191),(14,150,34,192),(15,202,63,157),(16,203,64,158),(17,204,65,159),(18,205,66,160),(19,206,67,161),(20,207,68,162),(21,208,69,163),(22,209,70,164),(23,210,57,165),(24,197,58,166),(25,198,59,167),(26,199,60,168),(27,200,61,155),(28,201,62,156),(43,137,90,117),(44,138,91,118),(45,139,92,119),(46,140,93,120),(47,127,94,121),(48,128,95,122),(49,129,96,123),(50,130,97,124),(51,131,98,125),(52,132,85,126),(53,133,86,113),(54,134,87,114),(55,135,88,115),(56,136,89,116),(71,220,103,181),(72,221,104,182),(73,222,105,169),(74,223,106,170),(75,224,107,171),(76,211,108,172),(77,212,109,173),(78,213,110,174),(79,214,111,175),(80,215,112,176),(81,216,99,177),(82,217,100,178),(83,218,101,179),(84,219,102,180)], [(1,99,8,106),(2,100,9,107),(3,101,10,108),(4,102,11,109),(5,103,12,110),(6,104,13,111),(7,105,14,112),(15,93,22,86),(16,94,23,87),(17,95,24,88),(18,96,25,89),(19,97,26,90),(20,98,27,91),(21,85,28,92),(29,75,36,82),(30,76,37,83),(31,77,38,84),(32,78,39,71),(33,79,40,72),(34,80,41,73),(35,81,42,74),(43,67,50,60),(44,68,51,61),(45,69,52,62),(46,70,53,63),(47,57,54,64),(48,58,55,65),(49,59,56,66),(113,164,120,157),(114,165,121,158),(115,166,122,159),(116,167,123,160),(117,168,124,161),(118,155,125,162),(119,156,126,163),(127,203,134,210),(128,204,135,197),(129,205,136,198),(130,206,137,199),(131,207,138,200),(132,208,139,201),(133,209,140,202),(141,213,148,220),(142,214,149,221),(143,215,150,222),(144,216,151,223),(145,217,152,224),(146,218,153,211),(147,219,154,212),(169,185,176,192),(170,186,177,193),(171,187,178,194),(172,188,179,195),(173,189,180,196),(174,190,181,183),(175,191,182,184)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | 4B | 4C | 4D | 4E | 4F | 4G | ··· | 4L | 4M | 4N | 4O | 4P | 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 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 14 | 14 | 2 | 2 | 2 | 2 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | D14 | 2+ 1+4 | D4⋊2D7 | D4⋊6D14 | D7×C4○D4 |
| kernel | C14.432+ 1+4 | C23.D14 | Dic7⋊4D4 | C28.3Q8 | D7×C4⋊C4 | C23.21D14 | C4×C7⋊D4 | D4×Dic7 | C23.18D14 | C28⋊2D4 | C7×C4⋊D4 | C4⋊D4 | C28 | D14 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C14 | C4 | C2 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 2 | 3 | 1 | 3 | 4 | 4 | 6 | 3 | 3 | 9 | 1 | 6 | 6 | 6 |
Matrix representation of C14.432+ 1+4 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 21 | 0 | 0 |
| 0 | 0 | 11 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 2 | 2 | 0 | 0 | 0 | 0 |
| 13 | 27 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 1 | 0 | 0 |
| 0 | 0 | 14 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 27 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 27 | 27 | 0 | 0 | 0 | 0 |
| 17 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,0,11,0,0,0,0,21,18,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[2,13,0,0,0,0,2,27,0,0,0,0,0,0,25,14,0,0,0,0,1,4,0,0,0,0,0,0,0,12,0,0,0,0,12,0],[1,27,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0],[27,17,0,0,0,0,27,2,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,17] >;
C14.432+ 1+4 in GAP, Magma, Sage, TeX
C_{14}._{43}2_+^{1+4} % in TeX
G:=Group("C14.43ES+(2,2)"); // GroupNames label
G:=SmallGroup(448,1067);
// by ID
G=gap.SmallGroup(448,1067);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,387,100,1571,185,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=c^2=1,d^2=a^7*b^2,e^2=a^7,b*a*b^-1=a^-1,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c=a^7*b^-1,b*d=d*b,e*b*e^-1=a^7*b,c*d=d*c,e*c*e^-1=a^7*c,e*d*e^-1=b^2*d>;
// generators/relations