G = C14.652+ 1+4 order 448 = 26·7
65th non-split extension by C14 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.652+ 1+4, C14.842- 1+4, C28⋊Q8⋊33C2, C4⋊C4.199D14, D14⋊Q8⋊32C2, (C2×D4).102D14, C22⋊C4.29D14, Dic7⋊3Q8⋊32C2, D14.D4⋊35C2, C28.48D4⋊23C2, C28.17D4⋊22C2, (C2×C14).206C24, (C2×C28).181C23, D14⋊C4.34C22, Dic7.9(C4○D4), Dic7⋊D4.2C2, (C22×C4).260D14, C22.D4⋊11D7, C4⋊Dic7.49C22, C2.67(D4⋊6D14), C23.30(C22×D7), Dic7.D4⋊34C2, C22⋊Dic14⋊34C2, (D4×C14).144C22, C23.D14⋊34C2, Dic7⋊C4.44C22, (C22×C14).38C23, (C22×D7).87C23, C22.227(C23×D7), C23.D7.45C22, C23.11D14⋊15C2, (C22×C28).116C22, C7⋊7(C22.36C24), (C2×Dic7).107C23, (C4×Dic7).125C22, C2.45(D4.10D14), (C2×Dic14).169C22, (C22×Dic7).132C22, (C4×C7⋊D4)⋊8C2, C2.68(D7×C4○D4), C4⋊C4⋊D7⋊30C2, C14.180(C2×C4○D4), (C2×C4×D7).212C22, (C2×C4).68(C22×D7), (C7×C4⋊C4).179C22, (C2×C7⋊D4).50C22, (C7×C22.D4)⋊14C2, (C7×C22⋊C4).54C22, SmallGroup(448,1115)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.652+ 1+4
G = < a,b,c,d,e | a14=b4=e2=1, c2=a7, d2=a7b2, ab=ba, ac=ca, dad-1=a-1, ae=ea, cbc-1=a7b-1, bd=db, ebe=a7b, cd=dc, ce=ec, ede=a7b2d >
Subgroups: 940 in 216 conjugacy classes, 93 normal (91 characteristic)
C1, C2 [×3], C2 [×3], C4 [×13], C22, C22 [×9], C7, C2×C4 [×5], C2×C4 [×11], D4 [×4], Q8 [×4], C23 [×2], C23, D7, C14 [×3], C14 [×2], C42 [×4], C22⋊C4 [×3], C22⋊C4 [×9], C4⋊C4 [×2], C4⋊C4 [×8], C22×C4, C22×C4 [×2], C2×D4, C2×D4 [×2], C2×Q8 [×3], Dic7 [×2], Dic7 [×6], C28 [×5], D14 [×3], C2×C14, C2×C14 [×6], C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8 [×3], C22.D4, C22.D4, C4.4D4 [×3], C42⋊2C2 [×2], C4⋊Q8, Dic14 [×4], C4×D7, C2×Dic7 [×7], C2×Dic7 [×2], C7⋊D4 [×3], C2×C28 [×5], C2×C28, C7×D4, C22×D7, C22×C14 [×2], C22.36C24, C4×Dic7 [×4], Dic7⋊C4 [×6], C4⋊Dic7 [×2], D14⋊C4 [×4], C23.D7 [×5], C7×C22⋊C4 [×3], C7×C4⋊C4 [×2], C2×Dic14 [×3], C2×C4×D7, C22×Dic7, C2×C7⋊D4 [×2], C22×C28, D4×C14, C23.11D14, C22⋊Dic14, C23.D14, D14.D4, Dic7.D4 [×2], Dic7⋊3Q8, C28⋊Q8, D14⋊Q8, C4⋊C4⋊D7, C28.48D4, C4×C7⋊D4, C28.17D4, Dic7⋊D4, C7×C22.D4, C14.652+ 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], C22.36C24, C23×D7, D4⋊6D14, D7×C4○D4, D4.10D14, C14.652+ 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)
(1 104 25 91)(2 105 26 92)(3 106 27 93)(4 107 28 94)(5 108 15 95)(6 109 16 96)(7 110 17 97)(8 111 18 98)(9 112 19 85)(10 99 20 86)(11 100 21 87)(12 101 22 88)(13 102 23 89)(14 103 24 90)(29 75 45 65)(30 76 46 66)(31 77 47 67)(32 78 48 68)(33 79 49 69)(34 80 50 70)(35 81 51 57)(36 82 52 58)(37 83 53 59)(38 84 54 60)(39 71 55 61)(40 72 56 62)(41 73 43 63)(42 74 44 64)(113 223 130 201)(114 224 131 202)(115 211 132 203)(116 212 133 204)(117 213 134 205)(118 214 135 206)(119 215 136 207)(120 216 137 208)(121 217 138 209)(122 218 139 210)(123 219 140 197)(124 220 127 198)(125 221 128 199)(126 222 129 200)(141 185 162 174)(142 186 163 175)(143 187 164 176)(144 188 165 177)(145 189 166 178)(146 190 167 179)(147 191 168 180)(148 192 155 181)(149 193 156 182)(150 194 157 169)(151 195 158 170)(152 196 159 171)(153 183 160 172)(154 184 161 173)
(1 64 8 57)(2 65 9 58)(3 66 10 59)(4 67 11 60)(5 68 12 61)(6 69 13 62)(7 70 14 63)(15 78 22 71)(16 79 23 72)(17 80 24 73)(18 81 25 74)(19 82 26 75)(20 83 27 76)(21 84 28 77)(29 92 36 85)(30 93 37 86)(31 94 38 87)(32 95 39 88)(33 96 40 89)(34 97 41 90)(35 98 42 91)(43 103 50 110)(44 104 51 111)(45 105 52 112)(46 106 53 99)(47 107 54 100)(48 108 55 101)(49 109 56 102)(113 172 120 179)(114 173 121 180)(115 174 122 181)(116 175 123 182)(117 176 124 169)(118 177 125 170)(119 178 126 171)(127 194 134 187)(128 195 135 188)(129 196 136 189)(130 183 137 190)(131 184 138 191)(132 185 139 192)(133 186 140 193)(141 203 148 210)(142 204 149 197)(143 205 150 198)(144 206 151 199)(145 207 152 200)(146 208 153 201)(147 209 154 202)(155 218 162 211)(156 219 163 212)(157 220 164 213)(158 221 165 214)(159 222 166 215)(160 223 167 216)(161 224 168 217)
(1 126 18 136)(2 125 19 135)(3 124 20 134)(4 123 21 133)(5 122 22 132)(6 121 23 131)(7 120 24 130)(8 119 25 129)(9 118 26 128)(10 117 27 127)(11 116 28 140)(12 115 15 139)(13 114 16 138)(14 113 17 137)(29 151 52 165)(30 150 53 164)(31 149 54 163)(32 148 55 162)(33 147 56 161)(34 146 43 160)(35 145 44 159)(36 144 45 158)(37 143 46 157)(38 142 47 156)(39 141 48 155)(40 154 49 168)(41 153 50 167)(42 152 51 166)(57 178 74 196)(58 177 75 195)(59 176 76 194)(60 175 77 193)(61 174 78 192)(62 173 79 191)(63 172 80 190)(64 171 81 189)(65 170 82 188)(66 169 83 187)(67 182 84 186)(68 181 71 185)(69 180 72 184)(70 179 73 183)(85 206 105 221)(86 205 106 220)(87 204 107 219)(88 203 108 218)(89 202 109 217)(90 201 110 216)(91 200 111 215)(92 199 112 214)(93 198 99 213)(94 197 100 212)(95 210 101 211)(96 209 102 224)(97 208 103 223)(98 207 104 222)
(29 36)(30 37)(31 38)(32 39)(33 40)(34 41)(35 42)(43 50)(44 51)(45 52)(46 53)(47 54)(48 55)(49 56)(85 92)(86 93)(87 94)(88 95)(89 96)(90 97)(91 98)(99 106)(100 107)(101 108)(102 109)(103 110)(104 111)(105 112)(113 137)(114 138)(115 139)(116 140)(117 127)(118 128)(119 129)(120 130)(121 131)(122 132)(123 133)(124 134)(125 135)(126 136)(141 162)(142 163)(143 164)(144 165)(145 166)(146 167)(147 168)(148 155)(149 156)(150 157)(151 158)(152 159)(153 160)(154 161)(169 187)(170 188)(171 189)(172 190)(173 191)(174 192)(175 193)(176 194)(177 195)(178 196)(179 183)(180 184)(181 185)(182 186)(197 219)(198 220)(199 221)(200 222)(201 223)(202 224)(203 211)(204 212)(205 213)(206 214)(207 215)(208 216)(209 217)(210 218)
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), (1,104,25,91)(2,105,26,92)(3,106,27,93)(4,107,28,94)(5,108,15,95)(6,109,16,96)(7,110,17,97)(8,111,18,98)(9,112,19,85)(10,99,20,86)(11,100,21,87)(12,101,22,88)(13,102,23,89)(14,103,24,90)(29,75,45,65)(30,76,46,66)(31,77,47,67)(32,78,48,68)(33,79,49,69)(34,80,50,70)(35,81,51,57)(36,82,52,58)(37,83,53,59)(38,84,54,60)(39,71,55,61)(40,72,56,62)(41,73,43,63)(42,74,44,64)(113,223,130,201)(114,224,131,202)(115,211,132,203)(116,212,133,204)(117,213,134,205)(118,214,135,206)(119,215,136,207)(120,216,137,208)(121,217,138,209)(122,218,139,210)(123,219,140,197)(124,220,127,198)(125,221,128,199)(126,222,129,200)(141,185,162,174)(142,186,163,175)(143,187,164,176)(144,188,165,177)(145,189,166,178)(146,190,167,179)(147,191,168,180)(148,192,155,181)(149,193,156,182)(150,194,157,169)(151,195,158,170)(152,196,159,171)(153,183,160,172)(154,184,161,173), (1,64,8,57)(2,65,9,58)(3,66,10,59)(4,67,11,60)(5,68,12,61)(6,69,13,62)(7,70,14,63)(15,78,22,71)(16,79,23,72)(17,80,24,73)(18,81,25,74)(19,82,26,75)(20,83,27,76)(21,84,28,77)(29,92,36,85)(30,93,37,86)(31,94,38,87)(32,95,39,88)(33,96,40,89)(34,97,41,90)(35,98,42,91)(43,103,50,110)(44,104,51,111)(45,105,52,112)(46,106,53,99)(47,107,54,100)(48,108,55,101)(49,109,56,102)(113,172,120,179)(114,173,121,180)(115,174,122,181)(116,175,123,182)(117,176,124,169)(118,177,125,170)(119,178,126,171)(127,194,134,187)(128,195,135,188)(129,196,136,189)(130,183,137,190)(131,184,138,191)(132,185,139,192)(133,186,140,193)(141,203,148,210)(142,204,149,197)(143,205,150,198)(144,206,151,199)(145,207,152,200)(146,208,153,201)(147,209,154,202)(155,218,162,211)(156,219,163,212)(157,220,164,213)(158,221,165,214)(159,222,166,215)(160,223,167,216)(161,224,168,217), (1,126,18,136)(2,125,19,135)(3,124,20,134)(4,123,21,133)(5,122,22,132)(6,121,23,131)(7,120,24,130)(8,119,25,129)(9,118,26,128)(10,117,27,127)(11,116,28,140)(12,115,15,139)(13,114,16,138)(14,113,17,137)(29,151,52,165)(30,150,53,164)(31,149,54,163)(32,148,55,162)(33,147,56,161)(34,146,43,160)(35,145,44,159)(36,144,45,158)(37,143,46,157)(38,142,47,156)(39,141,48,155)(40,154,49,168)(41,153,50,167)(42,152,51,166)(57,178,74,196)(58,177,75,195)(59,176,76,194)(60,175,77,193)(61,174,78,192)(62,173,79,191)(63,172,80,190)(64,171,81,189)(65,170,82,188)(66,169,83,187)(67,182,84,186)(68,181,71,185)(69,180,72,184)(70,179,73,183)(85,206,105,221)(86,205,106,220)(87,204,107,219)(88,203,108,218)(89,202,109,217)(90,201,110,216)(91,200,111,215)(92,199,112,214)(93,198,99,213)(94,197,100,212)(95,210,101,211)(96,209,102,224)(97,208,103,223)(98,207,104,222), (29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56)(85,92)(86,93)(87,94)(88,95)(89,96)(90,97)(91,98)(99,106)(100,107)(101,108)(102,109)(103,110)(104,111)(105,112)(113,137)(114,138)(115,139)(116,140)(117,127)(118,128)(119,129)(120,130)(121,131)(122,132)(123,133)(124,134)(125,135)(126,136)(141,162)(142,163)(143,164)(144,165)(145,166)(146,167)(147,168)(148,155)(149,156)(150,157)(151,158)(152,159)(153,160)(154,161)(169,187)(170,188)(171,189)(172,190)(173,191)(174,192)(175,193)(176,194)(177,195)(178,196)(179,183)(180,184)(181,185)(182,186)(197,219)(198,220)(199,221)(200,222)(201,223)(202,224)(203,211)(204,212)(205,213)(206,214)(207,215)(208,216)(209,217)(210,218)>;
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), (1,104,25,91)(2,105,26,92)(3,106,27,93)(4,107,28,94)(5,108,15,95)(6,109,16,96)(7,110,17,97)(8,111,18,98)(9,112,19,85)(10,99,20,86)(11,100,21,87)(12,101,22,88)(13,102,23,89)(14,103,24,90)(29,75,45,65)(30,76,46,66)(31,77,47,67)(32,78,48,68)(33,79,49,69)(34,80,50,70)(35,81,51,57)(36,82,52,58)(37,83,53,59)(38,84,54,60)(39,71,55,61)(40,72,56,62)(41,73,43,63)(42,74,44,64)(113,223,130,201)(114,224,131,202)(115,211,132,203)(116,212,133,204)(117,213,134,205)(118,214,135,206)(119,215,136,207)(120,216,137,208)(121,217,138,209)(122,218,139,210)(123,219,140,197)(124,220,127,198)(125,221,128,199)(126,222,129,200)(141,185,162,174)(142,186,163,175)(143,187,164,176)(144,188,165,177)(145,189,166,178)(146,190,167,179)(147,191,168,180)(148,192,155,181)(149,193,156,182)(150,194,157,169)(151,195,158,170)(152,196,159,171)(153,183,160,172)(154,184,161,173), (1,64,8,57)(2,65,9,58)(3,66,10,59)(4,67,11,60)(5,68,12,61)(6,69,13,62)(7,70,14,63)(15,78,22,71)(16,79,23,72)(17,80,24,73)(18,81,25,74)(19,82,26,75)(20,83,27,76)(21,84,28,77)(29,92,36,85)(30,93,37,86)(31,94,38,87)(32,95,39,88)(33,96,40,89)(34,97,41,90)(35,98,42,91)(43,103,50,110)(44,104,51,111)(45,105,52,112)(46,106,53,99)(47,107,54,100)(48,108,55,101)(49,109,56,102)(113,172,120,179)(114,173,121,180)(115,174,122,181)(116,175,123,182)(117,176,124,169)(118,177,125,170)(119,178,126,171)(127,194,134,187)(128,195,135,188)(129,196,136,189)(130,183,137,190)(131,184,138,191)(132,185,139,192)(133,186,140,193)(141,203,148,210)(142,204,149,197)(143,205,150,198)(144,206,151,199)(145,207,152,200)(146,208,153,201)(147,209,154,202)(155,218,162,211)(156,219,163,212)(157,220,164,213)(158,221,165,214)(159,222,166,215)(160,223,167,216)(161,224,168,217), (1,126,18,136)(2,125,19,135)(3,124,20,134)(4,123,21,133)(5,122,22,132)(6,121,23,131)(7,120,24,130)(8,119,25,129)(9,118,26,128)(10,117,27,127)(11,116,28,140)(12,115,15,139)(13,114,16,138)(14,113,17,137)(29,151,52,165)(30,150,53,164)(31,149,54,163)(32,148,55,162)(33,147,56,161)(34,146,43,160)(35,145,44,159)(36,144,45,158)(37,143,46,157)(38,142,47,156)(39,141,48,155)(40,154,49,168)(41,153,50,167)(42,152,51,166)(57,178,74,196)(58,177,75,195)(59,176,76,194)(60,175,77,193)(61,174,78,192)(62,173,79,191)(63,172,80,190)(64,171,81,189)(65,170,82,188)(66,169,83,187)(67,182,84,186)(68,181,71,185)(69,180,72,184)(70,179,73,183)(85,206,105,221)(86,205,106,220)(87,204,107,219)(88,203,108,218)(89,202,109,217)(90,201,110,216)(91,200,111,215)(92,199,112,214)(93,198,99,213)(94,197,100,212)(95,210,101,211)(96,209,102,224)(97,208,103,223)(98,207,104,222), (29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56)(85,92)(86,93)(87,94)(88,95)(89,96)(90,97)(91,98)(99,106)(100,107)(101,108)(102,109)(103,110)(104,111)(105,112)(113,137)(114,138)(115,139)(116,140)(117,127)(118,128)(119,129)(120,130)(121,131)(122,132)(123,133)(124,134)(125,135)(126,136)(141,162)(142,163)(143,164)(144,165)(145,166)(146,167)(147,168)(148,155)(149,156)(150,157)(151,158)(152,159)(153,160)(154,161)(169,187)(170,188)(171,189)(172,190)(173,191)(174,192)(175,193)(176,194)(177,195)(178,196)(179,183)(180,184)(181,185)(182,186)(197,219)(198,220)(199,221)(200,222)(201,223)(202,224)(203,211)(204,212)(205,213)(206,214)(207,215)(208,216)(209,217)(210,218) );
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)], [(1,104,25,91),(2,105,26,92),(3,106,27,93),(4,107,28,94),(5,108,15,95),(6,109,16,96),(7,110,17,97),(8,111,18,98),(9,112,19,85),(10,99,20,86),(11,100,21,87),(12,101,22,88),(13,102,23,89),(14,103,24,90),(29,75,45,65),(30,76,46,66),(31,77,47,67),(32,78,48,68),(33,79,49,69),(34,80,50,70),(35,81,51,57),(36,82,52,58),(37,83,53,59),(38,84,54,60),(39,71,55,61),(40,72,56,62),(41,73,43,63),(42,74,44,64),(113,223,130,201),(114,224,131,202),(115,211,132,203),(116,212,133,204),(117,213,134,205),(118,214,135,206),(119,215,136,207),(120,216,137,208),(121,217,138,209),(122,218,139,210),(123,219,140,197),(124,220,127,198),(125,221,128,199),(126,222,129,200),(141,185,162,174),(142,186,163,175),(143,187,164,176),(144,188,165,177),(145,189,166,178),(146,190,167,179),(147,191,168,180),(148,192,155,181),(149,193,156,182),(150,194,157,169),(151,195,158,170),(152,196,159,171),(153,183,160,172),(154,184,161,173)], [(1,64,8,57),(2,65,9,58),(3,66,10,59),(4,67,11,60),(5,68,12,61),(6,69,13,62),(7,70,14,63),(15,78,22,71),(16,79,23,72),(17,80,24,73),(18,81,25,74),(19,82,26,75),(20,83,27,76),(21,84,28,77),(29,92,36,85),(30,93,37,86),(31,94,38,87),(32,95,39,88),(33,96,40,89),(34,97,41,90),(35,98,42,91),(43,103,50,110),(44,104,51,111),(45,105,52,112),(46,106,53,99),(47,107,54,100),(48,108,55,101),(49,109,56,102),(113,172,120,179),(114,173,121,180),(115,174,122,181),(116,175,123,182),(117,176,124,169),(118,177,125,170),(119,178,126,171),(127,194,134,187),(128,195,135,188),(129,196,136,189),(130,183,137,190),(131,184,138,191),(132,185,139,192),(133,186,140,193),(141,203,148,210),(142,204,149,197),(143,205,150,198),(144,206,151,199),(145,207,152,200),(146,208,153,201),(147,209,154,202),(155,218,162,211),(156,219,163,212),(157,220,164,213),(158,221,165,214),(159,222,166,215),(160,223,167,216),(161,224,168,217)], [(1,126,18,136),(2,125,19,135),(3,124,20,134),(4,123,21,133),(5,122,22,132),(6,121,23,131),(7,120,24,130),(8,119,25,129),(9,118,26,128),(10,117,27,127),(11,116,28,140),(12,115,15,139),(13,114,16,138),(14,113,17,137),(29,151,52,165),(30,150,53,164),(31,149,54,163),(32,148,55,162),(33,147,56,161),(34,146,43,160),(35,145,44,159),(36,144,45,158),(37,143,46,157),(38,142,47,156),(39,141,48,155),(40,154,49,168),(41,153,50,167),(42,152,51,166),(57,178,74,196),(58,177,75,195),(59,176,76,194),(60,175,77,193),(61,174,78,192),(62,173,79,191),(63,172,80,190),(64,171,81,189),(65,170,82,188),(66,169,83,187),(67,182,84,186),(68,181,71,185),(69,180,72,184),(70,179,73,183),(85,206,105,221),(86,205,106,220),(87,204,107,219),(88,203,108,218),(89,202,109,217),(90,201,110,216),(91,200,111,215),(92,199,112,214),(93,198,99,213),(94,197,100,212),(95,210,101,211),(96,209,102,224),(97,208,103,223),(98,207,104,222)], [(29,36),(30,37),(31,38),(32,39),(33,40),(34,41),(35,42),(43,50),(44,51),(45,52),(46,53),(47,54),(48,55),(49,56),(85,92),(86,93),(87,94),(88,95),(89,96),(90,97),(91,98),(99,106),(100,107),(101,108),(102,109),(103,110),(104,111),(105,112),(113,137),(114,138),(115,139),(116,140),(117,127),(118,128),(119,129),(120,130),(121,131),(122,132),(123,133),(124,134),(125,135),(126,136),(141,162),(142,163),(143,164),(144,165),(145,166),(146,167),(147,168),(148,155),(149,156),(150,157),(151,158),(152,159),(153,160),(154,161),(169,187),(170,188),(171,189),(172,190),(173,191),(174,192),(175,193),(176,194),(177,195),(178,196),(179,183),(180,184),(181,185),(182,186),(197,219),(198,220),(199,221),(200,222),(201,223),(202,224),(203,211),(204,212),(205,213),(206,214),(207,215),(208,216),(209,217),(210,218)])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | ··· | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 14P | 14Q | 14R | 28A | ··· | 28L | 28M | ··· | 28U |
| order | 1 | 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 | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 28 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | 14 | 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 | 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 | C2 | D7 | C4○D4 | D14 | D14 | D14 | D14 | 2+ 1+4 | 2- 1+4 | D4⋊6D14 | D7×C4○D4 | D4.10D14 |
| kernel | C14.652+ 1+4 | C23.11D14 | C22⋊Dic14 | C23.D14 | D14.D4 | Dic7.D4 | Dic7⋊3Q8 | C28⋊Q8 | D14⋊Q8 | C4⋊C4⋊D7 | C28.48D4 | C4×C7⋊D4 | C28.17D4 | Dic7⋊D4 | C7×C22.D4 | C22.D4 | Dic7 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C14 | C14 | C2 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 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 C14.652+ 1+4 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 0 | 0 | 0 |
| 0 | 0 | 0 | 25 | 0 | 0 |
| 0 | 0 | 0 | 0 | 7 | 0 |
| 0 | 0 | 0 | 0 | 0 | 7 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 14 | 9 | 0 | 0 |
| 0 | 0 | 20 | 15 | 0 | 0 |
| 0 | 0 | 0 | 0 | 14 | 9 |
| 0 | 0 | 0 | 0 | 20 | 15 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 20 | 15 | 0 | 0 |
| 0 | 0 | 14 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 15 |
| 0 | 0 | 0 | 0 | 14 | 9 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 1 | 0 | 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 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,25,0,0,0,0,0,0,25,0,0,0,0,0,0,7,0,0,0,0,0,0,7],[0,12,0,0,0,0,12,0,0,0,0,0,0,0,14,20,0,0,0,0,9,15,0,0,0,0,0,0,14,20,0,0,0,0,9,15],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,20,14,0,0,0,0,15,9,0,0,0,0,0,0,20,14,0,0,0,0,15,9],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,28,0,0,0,0,0,0,28,0,0],[1,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28] >;
C14.652+ 1+4 in GAP, Magma, Sage, TeX
C_{14}._{65}2_+^{1+4} % in TeX
G:=Group("C14.65ES+(2,2)"); // GroupNames label
G:=SmallGroup(448,1115);
// by ID
G=gap.SmallGroup(448,1115);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,219,675,297,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=e^2=1,c^2=a^7,d^2=a^7*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=a^7*b,c*d=d*c,c*e=e*c,e*d*e=a^7*b^2*d>;
// generators/relations