G = C14.1182+ 1+4 order 448 = 26·7
27th non-split extension by C14 of 2+ 1+4 acting via 2+ 1+4/C4○D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.1182+ 1+4, C7⋊D4⋊2Q8, C28⋊Q8⋊26C2, C7⋊5(D4⋊3Q8), C22⋊Q8⋊12D7, D14.9(C2×Q8), C4⋊C4.192D14, (Q8×Dic7)⋊13C2, C22.1(Q8×D7), D14⋊3Q8⋊17C2, D14⋊2Q8⋊28C2, Dic7.Q8⋊18C2, (C2×C28).58C23, (C2×Q8).129D14, C22⋊C4.60D14, Dic7.11(C2×Q8), C28.210(C4○D4), C4.99(D4⋊2D7), C14.37(C22×Q8), (C2×C14).179C24, D14⋊C4.24C22, Dic7⋊4D4.2C2, (C22×C4).241D14, C2.36(D4⋊8D14), C22⋊Dic14⋊25C2, C4⋊Dic7.374C22, (Q8×C14).110C22, (C2×Dic7).90C23, C22.200(C23×D7), C23.192(C22×D7), Dic7⋊C4.118C22, (C22×C14).207C23, (C22×C28).258C22, (C4×Dic7).108C22, (C22×D7).201C23, C23.D7.119C22, (C2×Dic14).160C22, (C22×Dic7).120C22, (D7×C4⋊C4)⋊27C2, C2.20(C2×Q8×D7), (C4×C7⋊D4).8C2, (C2×C14).8(C2×Q8), (C2×C4⋊Dic7)⋊42C2, C14.90(C2×C4○D4), (C7×C22⋊Q8)⋊15C2, (C2×C4×D7).99C22, C2.46(C2×D4⋊2D7), (C7×C4⋊C4).161C22, (C2×C4).184(C22×D7), (C2×C7⋊D4).126C22, (C7×C22⋊C4).34C22, SmallGroup(448,1088)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.1182+ 1+4
G = < a,b,c,d,e | a14=b4=c2=1, d2=b2, e2=a7, ab=ba, cac=a-1, ad=da, ae=ea, cbc=a7b-1, bd=db, ebe-1=a7b, cd=dc, ce=ec, ede-1=b2d >
Subgroups: 956 in 228 conjugacy classes, 107 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, C2×Q8, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C14, C2×C4⋊C4, C4×D4, C4×Q8, C22⋊Q8, C22⋊Q8, C42.C2, C4⋊Q8, Dic14, C4×D7, C2×Dic7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×Q8, C22×D7, C22×C14, D4⋊3Q8, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, D14⋊C4, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×C4×D7, C22×Dic7, C2×C7⋊D4, C22×C28, Q8×C14, C22⋊Dic14, Dic7⋊4D4, C28⋊Q8, Dic7.Q8, D7×C4⋊C4, D14⋊2Q8, C2×C4⋊Dic7, C4×C7⋊D4, Q8×Dic7, D14⋊3Q8, C7×C22⋊Q8, C14.1182+ 1+4
Quotients: C1, C2, C22, Q8, C23, D7, C2×Q8, C4○D4, C24, D14, C22×Q8, C2×C4○D4, 2+ 1+4, C22×D7, D4⋊3Q8, D4⋊2D7, Q8×D7, C23×D7, C2×D4⋊2D7, C2×Q8×D7, D4⋊8D14, C14.1182+ 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)
(1 205 18 77)(2 206 19 78)(3 207 20 79)(4 208 21 80)(5 209 22 81)(6 210 23 82)(7 197 24 83)(8 198 25 84)(9 199 26 71)(10 200 27 72)(11 201 28 73)(12 202 15 74)(13 203 16 75)(14 204 17 76)(29 118 47 224)(30 119 48 211)(31 120 49 212)(32 121 50 213)(33 122 51 214)(34 123 52 215)(35 124 53 216)(36 125 54 217)(37 126 55 218)(38 113 56 219)(39 114 43 220)(40 115 44 221)(41 116 45 222)(42 117 46 223)(57 132 179 90)(58 133 180 91)(59 134 181 92)(60 135 182 93)(61 136 169 94)(62 137 170 95)(63 138 171 96)(64 139 172 97)(65 140 173 98)(66 127 174 85)(67 128 175 86)(68 129 176 87)(69 130 177 88)(70 131 178 89)(99 150 189 159)(100 151 190 160)(101 152 191 161)(102 153 192 162)(103 154 193 163)(104 141 194 164)(105 142 195 165)(106 143 196 166)(107 144 183 167)(108 145 184 168)(109 146 185 155)(110 147 186 156)(111 148 187 157)(112 149 188 158)
(2 14)(3 13)(4 12)(5 11)(6 10)(7 9)(15 21)(16 20)(17 19)(22 28)(23 27)(24 26)(29 41)(30 40)(31 39)(32 38)(33 37)(34 36)(43 49)(44 48)(45 47)(50 56)(51 55)(52 54)(57 69)(58 68)(59 67)(60 66)(61 65)(62 64)(71 204)(72 203)(73 202)(74 201)(75 200)(76 199)(77 198)(78 197)(79 210)(80 209)(81 208)(82 207)(83 206)(84 205)(85 128)(86 127)(87 140)(88 139)(89 138)(90 137)(91 136)(92 135)(93 134)(94 133)(95 132)(96 131)(97 130)(98 129)(99 103)(100 102)(104 112)(105 111)(106 110)(107 109)(113 220)(114 219)(115 218)(116 217)(117 216)(118 215)(119 214)(120 213)(121 212)(122 211)(123 224)(124 223)(125 222)(126 221)(141 165)(142 164)(143 163)(144 162)(145 161)(146 160)(147 159)(148 158)(149 157)(150 156)(151 155)(152 168)(153 167)(154 166)(169 173)(170 172)(174 182)(175 181)(176 180)(177 179)(183 185)(186 196)(187 195)(188 194)(189 193)(190 192)
(1 178 18 70)(2 179 19 57)(3 180 20 58)(4 181 21 59)(5 182 22 60)(6 169 23 61)(7 170 24 62)(8 171 25 63)(9 172 26 64)(10 173 27 65)(11 174 28 66)(12 175 15 67)(13 176 16 68)(14 177 17 69)(29 185 47 109)(30 186 48 110)(31 187 49 111)(32 188 50 112)(33 189 51 99)(34 190 52 100)(35 191 53 101)(36 192 54 102)(37 193 55 103)(38 194 56 104)(39 195 43 105)(40 196 44 106)(41 183 45 107)(42 184 46 108)(71 139 199 97)(72 140 200 98)(73 127 201 85)(74 128 202 86)(75 129 203 87)(76 130 204 88)(77 131 205 89)(78 132 206 90)(79 133 207 91)(80 134 208 92)(81 135 209 93)(82 136 210 94)(83 137 197 95)(84 138 198 96)(113 164 219 141)(114 165 220 142)(115 166 221 143)(116 167 222 144)(117 168 223 145)(118 155 224 146)(119 156 211 147)(120 157 212 148)(121 158 213 149)(122 159 214 150)(123 160 215 151)(124 161 216 152)(125 162 217 153)(126 163 218 154)
(1 101 8 108)(2 102 9 109)(3 103 10 110)(4 104 11 111)(5 105 12 112)(6 106 13 99)(7 107 14 100)(15 188 22 195)(16 189 23 196)(17 190 24 183)(18 191 25 184)(19 192 26 185)(20 193 27 186)(21 194 28 187)(29 57 36 64)(30 58 37 65)(31 59 38 66)(32 60 39 67)(33 61 40 68)(34 62 41 69)(35 63 42 70)(43 175 50 182)(44 176 51 169)(45 177 52 170)(46 178 53 171)(47 179 54 172)(48 180 55 173)(49 181 56 174)(71 162 78 155)(72 163 79 156)(73 164 80 157)(74 165 81 158)(75 166 82 159)(76 167 83 160)(77 168 84 161)(85 219 92 212)(86 220 93 213)(87 221 94 214)(88 222 95 215)(89 223 96 216)(90 224 97 217)(91 211 98 218)(113 134 120 127)(114 135 121 128)(115 136 122 129)(116 137 123 130)(117 138 124 131)(118 139 125 132)(119 140 126 133)(141 208 148 201)(142 209 149 202)(143 210 150 203)(144 197 151 204)(145 198 152 205)(146 199 153 206)(147 200 154 207)
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), (1,205,18,77)(2,206,19,78)(3,207,20,79)(4,208,21,80)(5,209,22,81)(6,210,23,82)(7,197,24,83)(8,198,25,84)(9,199,26,71)(10,200,27,72)(11,201,28,73)(12,202,15,74)(13,203,16,75)(14,204,17,76)(29,118,47,224)(30,119,48,211)(31,120,49,212)(32,121,50,213)(33,122,51,214)(34,123,52,215)(35,124,53,216)(36,125,54,217)(37,126,55,218)(38,113,56,219)(39,114,43,220)(40,115,44,221)(41,116,45,222)(42,117,46,223)(57,132,179,90)(58,133,180,91)(59,134,181,92)(60,135,182,93)(61,136,169,94)(62,137,170,95)(63,138,171,96)(64,139,172,97)(65,140,173,98)(66,127,174,85)(67,128,175,86)(68,129,176,87)(69,130,177,88)(70,131,178,89)(99,150,189,159)(100,151,190,160)(101,152,191,161)(102,153,192,162)(103,154,193,163)(104,141,194,164)(105,142,195,165)(106,143,196,166)(107,144,183,167)(108,145,184,168)(109,146,185,155)(110,147,186,156)(111,148,187,157)(112,149,188,158), (2,14)(3,13)(4,12)(5,11)(6,10)(7,9)(15,21)(16,20)(17,19)(22,28)(23,27)(24,26)(29,41)(30,40)(31,39)(32,38)(33,37)(34,36)(43,49)(44,48)(45,47)(50,56)(51,55)(52,54)(57,69)(58,68)(59,67)(60,66)(61,65)(62,64)(71,204)(72,203)(73,202)(74,201)(75,200)(76,199)(77,198)(78,197)(79,210)(80,209)(81,208)(82,207)(83,206)(84,205)(85,128)(86,127)(87,140)(88,139)(89,138)(90,137)(91,136)(92,135)(93,134)(94,133)(95,132)(96,131)(97,130)(98,129)(99,103)(100,102)(104,112)(105,111)(106,110)(107,109)(113,220)(114,219)(115,218)(116,217)(117,216)(118,215)(119,214)(120,213)(121,212)(122,211)(123,224)(124,223)(125,222)(126,221)(141,165)(142,164)(143,163)(144,162)(145,161)(146,160)(147,159)(148,158)(149,157)(150,156)(151,155)(152,168)(153,167)(154,166)(169,173)(170,172)(174,182)(175,181)(176,180)(177,179)(183,185)(186,196)(187,195)(188,194)(189,193)(190,192), (1,178,18,70)(2,179,19,57)(3,180,20,58)(4,181,21,59)(5,182,22,60)(6,169,23,61)(7,170,24,62)(8,171,25,63)(9,172,26,64)(10,173,27,65)(11,174,28,66)(12,175,15,67)(13,176,16,68)(14,177,17,69)(29,185,47,109)(30,186,48,110)(31,187,49,111)(32,188,50,112)(33,189,51,99)(34,190,52,100)(35,191,53,101)(36,192,54,102)(37,193,55,103)(38,194,56,104)(39,195,43,105)(40,196,44,106)(41,183,45,107)(42,184,46,108)(71,139,199,97)(72,140,200,98)(73,127,201,85)(74,128,202,86)(75,129,203,87)(76,130,204,88)(77,131,205,89)(78,132,206,90)(79,133,207,91)(80,134,208,92)(81,135,209,93)(82,136,210,94)(83,137,197,95)(84,138,198,96)(113,164,219,141)(114,165,220,142)(115,166,221,143)(116,167,222,144)(117,168,223,145)(118,155,224,146)(119,156,211,147)(120,157,212,148)(121,158,213,149)(122,159,214,150)(123,160,215,151)(124,161,216,152)(125,162,217,153)(126,163,218,154), (1,101,8,108)(2,102,9,109)(3,103,10,110)(4,104,11,111)(5,105,12,112)(6,106,13,99)(7,107,14,100)(15,188,22,195)(16,189,23,196)(17,190,24,183)(18,191,25,184)(19,192,26,185)(20,193,27,186)(21,194,28,187)(29,57,36,64)(30,58,37,65)(31,59,38,66)(32,60,39,67)(33,61,40,68)(34,62,41,69)(35,63,42,70)(43,175,50,182)(44,176,51,169)(45,177,52,170)(46,178,53,171)(47,179,54,172)(48,180,55,173)(49,181,56,174)(71,162,78,155)(72,163,79,156)(73,164,80,157)(74,165,81,158)(75,166,82,159)(76,167,83,160)(77,168,84,161)(85,219,92,212)(86,220,93,213)(87,221,94,214)(88,222,95,215)(89,223,96,216)(90,224,97,217)(91,211,98,218)(113,134,120,127)(114,135,121,128)(115,136,122,129)(116,137,123,130)(117,138,124,131)(118,139,125,132)(119,140,126,133)(141,208,148,201)(142,209,149,202)(143,210,150,203)(144,197,151,204)(145,198,152,205)(146,199,153,206)(147,200,154,207)>;
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), (1,205,18,77)(2,206,19,78)(3,207,20,79)(4,208,21,80)(5,209,22,81)(6,210,23,82)(7,197,24,83)(8,198,25,84)(9,199,26,71)(10,200,27,72)(11,201,28,73)(12,202,15,74)(13,203,16,75)(14,204,17,76)(29,118,47,224)(30,119,48,211)(31,120,49,212)(32,121,50,213)(33,122,51,214)(34,123,52,215)(35,124,53,216)(36,125,54,217)(37,126,55,218)(38,113,56,219)(39,114,43,220)(40,115,44,221)(41,116,45,222)(42,117,46,223)(57,132,179,90)(58,133,180,91)(59,134,181,92)(60,135,182,93)(61,136,169,94)(62,137,170,95)(63,138,171,96)(64,139,172,97)(65,140,173,98)(66,127,174,85)(67,128,175,86)(68,129,176,87)(69,130,177,88)(70,131,178,89)(99,150,189,159)(100,151,190,160)(101,152,191,161)(102,153,192,162)(103,154,193,163)(104,141,194,164)(105,142,195,165)(106,143,196,166)(107,144,183,167)(108,145,184,168)(109,146,185,155)(110,147,186,156)(111,148,187,157)(112,149,188,158), (2,14)(3,13)(4,12)(5,11)(6,10)(7,9)(15,21)(16,20)(17,19)(22,28)(23,27)(24,26)(29,41)(30,40)(31,39)(32,38)(33,37)(34,36)(43,49)(44,48)(45,47)(50,56)(51,55)(52,54)(57,69)(58,68)(59,67)(60,66)(61,65)(62,64)(71,204)(72,203)(73,202)(74,201)(75,200)(76,199)(77,198)(78,197)(79,210)(80,209)(81,208)(82,207)(83,206)(84,205)(85,128)(86,127)(87,140)(88,139)(89,138)(90,137)(91,136)(92,135)(93,134)(94,133)(95,132)(96,131)(97,130)(98,129)(99,103)(100,102)(104,112)(105,111)(106,110)(107,109)(113,220)(114,219)(115,218)(116,217)(117,216)(118,215)(119,214)(120,213)(121,212)(122,211)(123,224)(124,223)(125,222)(126,221)(141,165)(142,164)(143,163)(144,162)(145,161)(146,160)(147,159)(148,158)(149,157)(150,156)(151,155)(152,168)(153,167)(154,166)(169,173)(170,172)(174,182)(175,181)(176,180)(177,179)(183,185)(186,196)(187,195)(188,194)(189,193)(190,192), (1,178,18,70)(2,179,19,57)(3,180,20,58)(4,181,21,59)(5,182,22,60)(6,169,23,61)(7,170,24,62)(8,171,25,63)(9,172,26,64)(10,173,27,65)(11,174,28,66)(12,175,15,67)(13,176,16,68)(14,177,17,69)(29,185,47,109)(30,186,48,110)(31,187,49,111)(32,188,50,112)(33,189,51,99)(34,190,52,100)(35,191,53,101)(36,192,54,102)(37,193,55,103)(38,194,56,104)(39,195,43,105)(40,196,44,106)(41,183,45,107)(42,184,46,108)(71,139,199,97)(72,140,200,98)(73,127,201,85)(74,128,202,86)(75,129,203,87)(76,130,204,88)(77,131,205,89)(78,132,206,90)(79,133,207,91)(80,134,208,92)(81,135,209,93)(82,136,210,94)(83,137,197,95)(84,138,198,96)(113,164,219,141)(114,165,220,142)(115,166,221,143)(116,167,222,144)(117,168,223,145)(118,155,224,146)(119,156,211,147)(120,157,212,148)(121,158,213,149)(122,159,214,150)(123,160,215,151)(124,161,216,152)(125,162,217,153)(126,163,218,154), (1,101,8,108)(2,102,9,109)(3,103,10,110)(4,104,11,111)(5,105,12,112)(6,106,13,99)(7,107,14,100)(15,188,22,195)(16,189,23,196)(17,190,24,183)(18,191,25,184)(19,192,26,185)(20,193,27,186)(21,194,28,187)(29,57,36,64)(30,58,37,65)(31,59,38,66)(32,60,39,67)(33,61,40,68)(34,62,41,69)(35,63,42,70)(43,175,50,182)(44,176,51,169)(45,177,52,170)(46,178,53,171)(47,179,54,172)(48,180,55,173)(49,181,56,174)(71,162,78,155)(72,163,79,156)(73,164,80,157)(74,165,81,158)(75,166,82,159)(76,167,83,160)(77,168,84,161)(85,219,92,212)(86,220,93,213)(87,221,94,214)(88,222,95,215)(89,223,96,216)(90,224,97,217)(91,211,98,218)(113,134,120,127)(114,135,121,128)(115,136,122,129)(116,137,123,130)(117,138,124,131)(118,139,125,132)(119,140,126,133)(141,208,148,201)(142,209,149,202)(143,210,150,203)(144,197,151,204)(145,198,152,205)(146,199,153,206)(147,200,154,207) );
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)], [(1,205,18,77),(2,206,19,78),(3,207,20,79),(4,208,21,80),(5,209,22,81),(6,210,23,82),(7,197,24,83),(8,198,25,84),(9,199,26,71),(10,200,27,72),(11,201,28,73),(12,202,15,74),(13,203,16,75),(14,204,17,76),(29,118,47,224),(30,119,48,211),(31,120,49,212),(32,121,50,213),(33,122,51,214),(34,123,52,215),(35,124,53,216),(36,125,54,217),(37,126,55,218),(38,113,56,219),(39,114,43,220),(40,115,44,221),(41,116,45,222),(42,117,46,223),(57,132,179,90),(58,133,180,91),(59,134,181,92),(60,135,182,93),(61,136,169,94),(62,137,170,95),(63,138,171,96),(64,139,172,97),(65,140,173,98),(66,127,174,85),(67,128,175,86),(68,129,176,87),(69,130,177,88),(70,131,178,89),(99,150,189,159),(100,151,190,160),(101,152,191,161),(102,153,192,162),(103,154,193,163),(104,141,194,164),(105,142,195,165),(106,143,196,166),(107,144,183,167),(108,145,184,168),(109,146,185,155),(110,147,186,156),(111,148,187,157),(112,149,188,158)], [(2,14),(3,13),(4,12),(5,11),(6,10),(7,9),(15,21),(16,20),(17,19),(22,28),(23,27),(24,26),(29,41),(30,40),(31,39),(32,38),(33,37),(34,36),(43,49),(44,48),(45,47),(50,56),(51,55),(52,54),(57,69),(58,68),(59,67),(60,66),(61,65),(62,64),(71,204),(72,203),(73,202),(74,201),(75,200),(76,199),(77,198),(78,197),(79,210),(80,209),(81,208),(82,207),(83,206),(84,205),(85,128),(86,127),(87,140),(88,139),(89,138),(90,137),(91,136),(92,135),(93,134),(94,133),(95,132),(96,131),(97,130),(98,129),(99,103),(100,102),(104,112),(105,111),(106,110),(107,109),(113,220),(114,219),(115,218),(116,217),(117,216),(118,215),(119,214),(120,213),(121,212),(122,211),(123,224),(124,223),(125,222),(126,221),(141,165),(142,164),(143,163),(144,162),(145,161),(146,160),(147,159),(148,158),(149,157),(150,156),(151,155),(152,168),(153,167),(154,166),(169,173),(170,172),(174,182),(175,181),(176,180),(177,179),(183,185),(186,196),(187,195),(188,194),(189,193),(190,192)], [(1,178,18,70),(2,179,19,57),(3,180,20,58),(4,181,21,59),(5,182,22,60),(6,169,23,61),(7,170,24,62),(8,171,25,63),(9,172,26,64),(10,173,27,65),(11,174,28,66),(12,175,15,67),(13,176,16,68),(14,177,17,69),(29,185,47,109),(30,186,48,110),(31,187,49,111),(32,188,50,112),(33,189,51,99),(34,190,52,100),(35,191,53,101),(36,192,54,102),(37,193,55,103),(38,194,56,104),(39,195,43,105),(40,196,44,106),(41,183,45,107),(42,184,46,108),(71,139,199,97),(72,140,200,98),(73,127,201,85),(74,128,202,86),(75,129,203,87),(76,130,204,88),(77,131,205,89),(78,132,206,90),(79,133,207,91),(80,134,208,92),(81,135,209,93),(82,136,210,94),(83,137,197,95),(84,138,198,96),(113,164,219,141),(114,165,220,142),(115,166,221,143),(116,167,222,144),(117,168,223,145),(118,155,224,146),(119,156,211,147),(120,157,212,148),(121,158,213,149),(122,159,214,150),(123,160,215,151),(124,161,216,152),(125,162,217,153),(126,163,218,154)], [(1,101,8,108),(2,102,9,109),(3,103,10,110),(4,104,11,111),(5,105,12,112),(6,106,13,99),(7,107,14,100),(15,188,22,195),(16,189,23,196),(17,190,24,183),(18,191,25,184),(19,192,26,185),(20,193,27,186),(21,194,28,187),(29,57,36,64),(30,58,37,65),(31,59,38,66),(32,60,39,67),(33,61,40,68),(34,62,41,69),(35,63,42,70),(43,175,50,182),(44,176,51,169),(45,177,52,170),(46,178,53,171),(47,179,54,172),(48,180,55,173),(49,181,56,174),(71,162,78,155),(72,163,79,156),(73,164,80,157),(74,165,81,158),(75,166,82,159),(76,167,83,160),(77,168,84,161),(85,219,92,212),(86,220,93,213),(87,221,94,214),(88,222,95,215),(89,223,96,216),(90,224,97,217),(91,211,98,218),(113,134,120,127),(114,135,121,128),(115,136,122,129),(116,137,123,130),(117,138,124,131),(118,139,125,132),(119,140,126,133),(141,208,148,201),(142,209,149,202),(143,210,150,203),(144,197,151,204),(145,198,152,205),(146,199,153,206),(147,200,154,207)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | ··· | 4G | 4H | ··· | 4M | 4N | 4O | 4P | 4Q | 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 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 14 | 14 | 2 | 2 | 4 | ··· | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 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 | C2 | Q8 | D7 | C4○D4 | D14 | D14 | D14 | D14 | 2+ 1+4 | D4⋊2D7 | Q8×D7 | D4⋊8D14 |
| kernel | C14.1182+ 1+4 | C22⋊Dic14 | Dic7⋊4D4 | C28⋊Q8 | Dic7.Q8 | D7×C4⋊C4 | D14⋊2Q8 | C2×C4⋊Dic7 | C4×C7⋊D4 | Q8×Dic7 | D14⋊3Q8 | C7×C22⋊Q8 | C7⋊D4 | C22⋊Q8 | C28 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×Q8 | C14 | C4 | C22 | C2 |
| # reps | 1 | 2 | 2 | 1 | 2 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 4 | 3 | 4 | 6 | 9 | 3 | 3 | 1 | 6 | 6 | 6 |
Matrix representation of C14.1182+ 1+4 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 10 | 0 | 0 |
| 0 | 0 | 19 | 22 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 27 |
| 0 | 0 | 0 | 0 | 12 | 20 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 7 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 2 |
| 0 | 0 | 0 | 0 | 17 | 9 |
| 17 | 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 | 8 | 22 |
| 0 | 0 | 0 | 0 | 1 | 21 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,10,19,0,0,0,0,10,22,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,9,12,0,0,0,0,27,20],[1,0,0,0,0,0,0,28,0,0,0,0,0,0,1,7,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,20,17,0,0,0,0,2,9],[17,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,8,1,0,0,0,0,22,21] >;
C14.1182+ 1+4 in GAP, Magma, Sage, TeX
C_{14}._{118}2_+^{1+4} % in TeX
G:=Group("C14.118ES+(2,2)"); // GroupNames label
G:=SmallGroup(448,1088);
// by ID
G=gap.SmallGroup(448,1088);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,100,570,185,192,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=c^2=1,d^2=b^2,e^2=a^7,a*b=b*a,c*a*c=a^-1,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,c*e=e*c,e*d*e^-1=b^2*d>;
// generators/relations