G = C14.1152+ 1+4 order 448 = 26·7
24th non-split extension by C14 of 2+ 1+4 acting via 2+ 1+4/C4○D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.1152+ 1+4, C4⋊D4⋊21D7, C28⋊2D4⋊26C2, C4⋊C4.184D14, (D4×Dic7)⋊25C2, (C2×D4).157D14, (C2×C28).44C23, C22⋊C4.10D14, C28.3Q8⋊20C2, Dic7⋊D4⋊16C2, C28.205(C4○D4), C4.98(D4⋊2D7), (C2×C14).162C24, (C22×C4).229D14, C2.30(D4⋊8D14), C23.22(C22×D7), D14⋊C4.106C22, (D4×C14).127C22, C23.D14⋊20C2, C22.2(D4⋊2D7), C22.D28⋊12C2, Dic7⋊C4.20C22, C4⋊Dic7.209C22, (C4×Dic7).98C22, (C22×D7).69C23, C22.183(C23×D7), C23.D7.28C22, (C22×C28).245C22, (C22×C14).190C23, C7⋊8(C22.47C24), (C2×Dic7).230C23, (C22×Dic7).114C22, (C4×C7⋊D4)⋊21C2, C4⋊C4⋊7D7⋊22C2, (C7×C4⋊D4)⋊24C2, (C2×C4⋊Dic7)⋊41C2, C14.86(C2×C4○D4), (C2×C4×D7).88C22, C2.41(C2×D4⋊2D7), (C2×C14).24(C4○D4), (C7×C4⋊C4).149C22, (C2×C4).589(C22×D7), (C2×C7⋊D4).119C22, (C7×C22⋊C4).18C22, SmallGroup(448,1071)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.1152+ 1+4
G = < a,b,c,d,e | a14=b4=1, c2=e2=a7, d2=b2, ab=ba, cac-1=dad-1=eae-1=a-1, cbc-1=b-1, dbd-1=a7b, be=eb, cd=dc, ce=ec, ede-1=a7b2d >
Subgroups: 1004 in 238 conjugacy classes, 99 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, 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, C2×C14, 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, D14⋊C4, C23.D7, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C2×C4×D7, C22×Dic7, C2×C7⋊D4, C2×C7⋊D4, C22×C28, D4×C14, D4×C14, C23.D14, C22.D28, C28.3Q8, C4⋊C4⋊7D7, C2×C4⋊Dic7, C4×C7⋊D4, D4×Dic7, D4×Dic7, C28⋊2D4, Dic7⋊D4, C7×C4⋊D4, C14.1152+ 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⋊8D14, C14.1152+ 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)
(1 156 139 211)(2 157 140 212)(3 158 127 213)(4 159 128 214)(5 160 129 215)(6 161 130 216)(7 162 131 217)(8 163 132 218)(9 164 133 219)(10 165 134 220)(11 166 135 221)(12 167 136 222)(13 168 137 223)(14 155 138 224)(15 68 94 204)(16 69 95 205)(17 70 96 206)(18 57 97 207)(19 58 98 208)(20 59 85 209)(21 60 86 210)(22 61 87 197)(23 62 88 198)(24 63 89 199)(25 64 90 200)(26 65 91 201)(27 66 92 202)(28 67 93 203)(29 84 105 145)(30 71 106 146)(31 72 107 147)(32 73 108 148)(33 74 109 149)(34 75 110 150)(35 76 111 151)(36 77 112 152)(37 78 99 153)(38 79 100 154)(39 80 101 141)(40 81 102 142)(41 82 103 143)(42 83 104 144)(43 174 116 196)(44 175 117 183)(45 176 118 184)(46 177 119 185)(47 178 120 186)(48 179 121 187)(49 180 122 188)(50 181 123 189)(51 182 124 190)(52 169 125 191)(53 170 126 192)(54 171 113 193)(55 172 114 194)(56 173 115 195)
(1 97 8 90)(2 96 9 89)(3 95 10 88)(4 94 11 87)(5 93 12 86)(6 92 13 85)(7 91 14 98)(15 135 22 128)(16 134 23 127)(17 133 24 140)(18 132 25 139)(19 131 26 138)(20 130 27 137)(21 129 28 136)(29 191 36 184)(30 190 37 183)(31 189 38 196)(32 188 39 195)(33 187 40 194)(34 186 41 193)(35 185 42 192)(43 147 50 154)(44 146 51 153)(45 145 52 152)(46 144 53 151)(47 143 54 150)(48 142 55 149)(49 141 56 148)(57 163 64 156)(58 162 65 155)(59 161 66 168)(60 160 67 167)(61 159 68 166)(62 158 69 165)(63 157 70 164)(71 124 78 117)(72 123 79 116)(73 122 80 115)(74 121 81 114)(75 120 82 113)(76 119 83 126)(77 118 84 125)(99 175 106 182)(100 174 107 181)(101 173 108 180)(102 172 109 179)(103 171 110 178)(104 170 111 177)(105 169 112 176)(197 214 204 221)(198 213 205 220)(199 212 206 219)(200 211 207 218)(201 224 208 217)(202 223 209 216)(203 222 210 215)
(1 169 139 191)(2 182 140 190)(3 181 127 189)(4 180 128 188)(5 179 129 187)(6 178 130 186)(7 177 131 185)(8 176 132 184)(9 175 133 183)(10 174 134 196)(11 173 135 195)(12 172 136 194)(13 171 137 193)(14 170 138 192)(15 39 94 101)(16 38 95 100)(17 37 96 99)(18 36 97 112)(19 35 98 111)(20 34 85 110)(21 33 86 109)(22 32 87 108)(23 31 88 107)(24 30 89 106)(25 29 90 105)(26 42 91 104)(27 41 92 103)(28 40 93 102)(43 158 116 213)(44 157 117 212)(45 156 118 211)(46 155 119 224)(47 168 120 223)(48 167 121 222)(49 166 122 221)(50 165 123 220)(51 164 124 219)(52 163 125 218)(53 162 126 217)(54 161 113 216)(55 160 114 215)(56 159 115 214)(57 84 207 145)(58 83 208 144)(59 82 209 143)(60 81 210 142)(61 80 197 141)(62 79 198 154)(63 78 199 153)(64 77 200 152)(65 76 201 151)(66 75 202 150)(67 74 203 149)(68 73 204 148)(69 72 205 147)(70 71 206 146)
(1 64 8 57)(2 63 9 70)(3 62 10 69)(4 61 11 68)(5 60 12 67)(6 59 13 66)(7 58 14 65)(15 214 22 221)(16 213 23 220)(17 212 24 219)(18 211 25 218)(19 224 26 217)(20 223 27 216)(21 222 28 215)(29 118 36 125)(30 117 37 124)(31 116 38 123)(32 115 39 122)(33 114 40 121)(34 113 41 120)(35 126 42 119)(43 100 50 107)(44 99 51 106)(45 112 52 105)(46 111 53 104)(47 110 54 103)(48 109 55 102)(49 108 56 101)(71 183 78 190)(72 196 79 189)(73 195 80 188)(74 194 81 187)(75 193 82 186)(76 192 83 185)(77 191 84 184)(85 168 92 161)(86 167 93 160)(87 166 94 159)(88 165 95 158)(89 164 96 157)(90 163 97 156)(91 162 98 155)(127 198 134 205)(128 197 135 204)(129 210 136 203)(130 209 137 202)(131 208 138 201)(132 207 139 200)(133 206 140 199)(141 180 148 173)(142 179 149 172)(143 178 150 171)(144 177 151 170)(145 176 152 169)(146 175 153 182)(147 174 154 181)
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), (1,156,139,211)(2,157,140,212)(3,158,127,213)(4,159,128,214)(5,160,129,215)(6,161,130,216)(7,162,131,217)(8,163,132,218)(9,164,133,219)(10,165,134,220)(11,166,135,221)(12,167,136,222)(13,168,137,223)(14,155,138,224)(15,68,94,204)(16,69,95,205)(17,70,96,206)(18,57,97,207)(19,58,98,208)(20,59,85,209)(21,60,86,210)(22,61,87,197)(23,62,88,198)(24,63,89,199)(25,64,90,200)(26,65,91,201)(27,66,92,202)(28,67,93,203)(29,84,105,145)(30,71,106,146)(31,72,107,147)(32,73,108,148)(33,74,109,149)(34,75,110,150)(35,76,111,151)(36,77,112,152)(37,78,99,153)(38,79,100,154)(39,80,101,141)(40,81,102,142)(41,82,103,143)(42,83,104,144)(43,174,116,196)(44,175,117,183)(45,176,118,184)(46,177,119,185)(47,178,120,186)(48,179,121,187)(49,180,122,188)(50,181,123,189)(51,182,124,190)(52,169,125,191)(53,170,126,192)(54,171,113,193)(55,172,114,194)(56,173,115,195), (1,97,8,90)(2,96,9,89)(3,95,10,88)(4,94,11,87)(5,93,12,86)(6,92,13,85)(7,91,14,98)(15,135,22,128)(16,134,23,127)(17,133,24,140)(18,132,25,139)(19,131,26,138)(20,130,27,137)(21,129,28,136)(29,191,36,184)(30,190,37,183)(31,189,38,196)(32,188,39,195)(33,187,40,194)(34,186,41,193)(35,185,42,192)(43,147,50,154)(44,146,51,153)(45,145,52,152)(46,144,53,151)(47,143,54,150)(48,142,55,149)(49,141,56,148)(57,163,64,156)(58,162,65,155)(59,161,66,168)(60,160,67,167)(61,159,68,166)(62,158,69,165)(63,157,70,164)(71,124,78,117)(72,123,79,116)(73,122,80,115)(74,121,81,114)(75,120,82,113)(76,119,83,126)(77,118,84,125)(99,175,106,182)(100,174,107,181)(101,173,108,180)(102,172,109,179)(103,171,110,178)(104,170,111,177)(105,169,112,176)(197,214,204,221)(198,213,205,220)(199,212,206,219)(200,211,207,218)(201,224,208,217)(202,223,209,216)(203,222,210,215), (1,169,139,191)(2,182,140,190)(3,181,127,189)(4,180,128,188)(5,179,129,187)(6,178,130,186)(7,177,131,185)(8,176,132,184)(9,175,133,183)(10,174,134,196)(11,173,135,195)(12,172,136,194)(13,171,137,193)(14,170,138,192)(15,39,94,101)(16,38,95,100)(17,37,96,99)(18,36,97,112)(19,35,98,111)(20,34,85,110)(21,33,86,109)(22,32,87,108)(23,31,88,107)(24,30,89,106)(25,29,90,105)(26,42,91,104)(27,41,92,103)(28,40,93,102)(43,158,116,213)(44,157,117,212)(45,156,118,211)(46,155,119,224)(47,168,120,223)(48,167,121,222)(49,166,122,221)(50,165,123,220)(51,164,124,219)(52,163,125,218)(53,162,126,217)(54,161,113,216)(55,160,114,215)(56,159,115,214)(57,84,207,145)(58,83,208,144)(59,82,209,143)(60,81,210,142)(61,80,197,141)(62,79,198,154)(63,78,199,153)(64,77,200,152)(65,76,201,151)(66,75,202,150)(67,74,203,149)(68,73,204,148)(69,72,205,147)(70,71,206,146), (1,64,8,57)(2,63,9,70)(3,62,10,69)(4,61,11,68)(5,60,12,67)(6,59,13,66)(7,58,14,65)(15,214,22,221)(16,213,23,220)(17,212,24,219)(18,211,25,218)(19,224,26,217)(20,223,27,216)(21,222,28,215)(29,118,36,125)(30,117,37,124)(31,116,38,123)(32,115,39,122)(33,114,40,121)(34,113,41,120)(35,126,42,119)(43,100,50,107)(44,99,51,106)(45,112,52,105)(46,111,53,104)(47,110,54,103)(48,109,55,102)(49,108,56,101)(71,183,78,190)(72,196,79,189)(73,195,80,188)(74,194,81,187)(75,193,82,186)(76,192,83,185)(77,191,84,184)(85,168,92,161)(86,167,93,160)(87,166,94,159)(88,165,95,158)(89,164,96,157)(90,163,97,156)(91,162,98,155)(127,198,134,205)(128,197,135,204)(129,210,136,203)(130,209,137,202)(131,208,138,201)(132,207,139,200)(133,206,140,199)(141,180,148,173)(142,179,149,172)(143,178,150,171)(144,177,151,170)(145,176,152,169)(146,175,153,182)(147,174,154,181)>;
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), (1,156,139,211)(2,157,140,212)(3,158,127,213)(4,159,128,214)(5,160,129,215)(6,161,130,216)(7,162,131,217)(8,163,132,218)(9,164,133,219)(10,165,134,220)(11,166,135,221)(12,167,136,222)(13,168,137,223)(14,155,138,224)(15,68,94,204)(16,69,95,205)(17,70,96,206)(18,57,97,207)(19,58,98,208)(20,59,85,209)(21,60,86,210)(22,61,87,197)(23,62,88,198)(24,63,89,199)(25,64,90,200)(26,65,91,201)(27,66,92,202)(28,67,93,203)(29,84,105,145)(30,71,106,146)(31,72,107,147)(32,73,108,148)(33,74,109,149)(34,75,110,150)(35,76,111,151)(36,77,112,152)(37,78,99,153)(38,79,100,154)(39,80,101,141)(40,81,102,142)(41,82,103,143)(42,83,104,144)(43,174,116,196)(44,175,117,183)(45,176,118,184)(46,177,119,185)(47,178,120,186)(48,179,121,187)(49,180,122,188)(50,181,123,189)(51,182,124,190)(52,169,125,191)(53,170,126,192)(54,171,113,193)(55,172,114,194)(56,173,115,195), (1,97,8,90)(2,96,9,89)(3,95,10,88)(4,94,11,87)(5,93,12,86)(6,92,13,85)(7,91,14,98)(15,135,22,128)(16,134,23,127)(17,133,24,140)(18,132,25,139)(19,131,26,138)(20,130,27,137)(21,129,28,136)(29,191,36,184)(30,190,37,183)(31,189,38,196)(32,188,39,195)(33,187,40,194)(34,186,41,193)(35,185,42,192)(43,147,50,154)(44,146,51,153)(45,145,52,152)(46,144,53,151)(47,143,54,150)(48,142,55,149)(49,141,56,148)(57,163,64,156)(58,162,65,155)(59,161,66,168)(60,160,67,167)(61,159,68,166)(62,158,69,165)(63,157,70,164)(71,124,78,117)(72,123,79,116)(73,122,80,115)(74,121,81,114)(75,120,82,113)(76,119,83,126)(77,118,84,125)(99,175,106,182)(100,174,107,181)(101,173,108,180)(102,172,109,179)(103,171,110,178)(104,170,111,177)(105,169,112,176)(197,214,204,221)(198,213,205,220)(199,212,206,219)(200,211,207,218)(201,224,208,217)(202,223,209,216)(203,222,210,215), (1,169,139,191)(2,182,140,190)(3,181,127,189)(4,180,128,188)(5,179,129,187)(6,178,130,186)(7,177,131,185)(8,176,132,184)(9,175,133,183)(10,174,134,196)(11,173,135,195)(12,172,136,194)(13,171,137,193)(14,170,138,192)(15,39,94,101)(16,38,95,100)(17,37,96,99)(18,36,97,112)(19,35,98,111)(20,34,85,110)(21,33,86,109)(22,32,87,108)(23,31,88,107)(24,30,89,106)(25,29,90,105)(26,42,91,104)(27,41,92,103)(28,40,93,102)(43,158,116,213)(44,157,117,212)(45,156,118,211)(46,155,119,224)(47,168,120,223)(48,167,121,222)(49,166,122,221)(50,165,123,220)(51,164,124,219)(52,163,125,218)(53,162,126,217)(54,161,113,216)(55,160,114,215)(56,159,115,214)(57,84,207,145)(58,83,208,144)(59,82,209,143)(60,81,210,142)(61,80,197,141)(62,79,198,154)(63,78,199,153)(64,77,200,152)(65,76,201,151)(66,75,202,150)(67,74,203,149)(68,73,204,148)(69,72,205,147)(70,71,206,146), (1,64,8,57)(2,63,9,70)(3,62,10,69)(4,61,11,68)(5,60,12,67)(6,59,13,66)(7,58,14,65)(15,214,22,221)(16,213,23,220)(17,212,24,219)(18,211,25,218)(19,224,26,217)(20,223,27,216)(21,222,28,215)(29,118,36,125)(30,117,37,124)(31,116,38,123)(32,115,39,122)(33,114,40,121)(34,113,41,120)(35,126,42,119)(43,100,50,107)(44,99,51,106)(45,112,52,105)(46,111,53,104)(47,110,54,103)(48,109,55,102)(49,108,56,101)(71,183,78,190)(72,196,79,189)(73,195,80,188)(74,194,81,187)(75,193,82,186)(76,192,83,185)(77,191,84,184)(85,168,92,161)(86,167,93,160)(87,166,94,159)(88,165,95,158)(89,164,96,157)(90,163,97,156)(91,162,98,155)(127,198,134,205)(128,197,135,204)(129,210,136,203)(130,209,137,202)(131,208,138,201)(132,207,139,200)(133,206,140,199)(141,180,148,173)(142,179,149,172)(143,178,150,171)(144,177,151,170)(145,176,152,169)(146,175,153,182)(147,174,154,181) );
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)], [(1,156,139,211),(2,157,140,212),(3,158,127,213),(4,159,128,214),(5,160,129,215),(6,161,130,216),(7,162,131,217),(8,163,132,218),(9,164,133,219),(10,165,134,220),(11,166,135,221),(12,167,136,222),(13,168,137,223),(14,155,138,224),(15,68,94,204),(16,69,95,205),(17,70,96,206),(18,57,97,207),(19,58,98,208),(20,59,85,209),(21,60,86,210),(22,61,87,197),(23,62,88,198),(24,63,89,199),(25,64,90,200),(26,65,91,201),(27,66,92,202),(28,67,93,203),(29,84,105,145),(30,71,106,146),(31,72,107,147),(32,73,108,148),(33,74,109,149),(34,75,110,150),(35,76,111,151),(36,77,112,152),(37,78,99,153),(38,79,100,154),(39,80,101,141),(40,81,102,142),(41,82,103,143),(42,83,104,144),(43,174,116,196),(44,175,117,183),(45,176,118,184),(46,177,119,185),(47,178,120,186),(48,179,121,187),(49,180,122,188),(50,181,123,189),(51,182,124,190),(52,169,125,191),(53,170,126,192),(54,171,113,193),(55,172,114,194),(56,173,115,195)], [(1,97,8,90),(2,96,9,89),(3,95,10,88),(4,94,11,87),(5,93,12,86),(6,92,13,85),(7,91,14,98),(15,135,22,128),(16,134,23,127),(17,133,24,140),(18,132,25,139),(19,131,26,138),(20,130,27,137),(21,129,28,136),(29,191,36,184),(30,190,37,183),(31,189,38,196),(32,188,39,195),(33,187,40,194),(34,186,41,193),(35,185,42,192),(43,147,50,154),(44,146,51,153),(45,145,52,152),(46,144,53,151),(47,143,54,150),(48,142,55,149),(49,141,56,148),(57,163,64,156),(58,162,65,155),(59,161,66,168),(60,160,67,167),(61,159,68,166),(62,158,69,165),(63,157,70,164),(71,124,78,117),(72,123,79,116),(73,122,80,115),(74,121,81,114),(75,120,82,113),(76,119,83,126),(77,118,84,125),(99,175,106,182),(100,174,107,181),(101,173,108,180),(102,172,109,179),(103,171,110,178),(104,170,111,177),(105,169,112,176),(197,214,204,221),(198,213,205,220),(199,212,206,219),(200,211,207,218),(201,224,208,217),(202,223,209,216),(203,222,210,215)], [(1,169,139,191),(2,182,140,190),(3,181,127,189),(4,180,128,188),(5,179,129,187),(6,178,130,186),(7,177,131,185),(8,176,132,184),(9,175,133,183),(10,174,134,196),(11,173,135,195),(12,172,136,194),(13,171,137,193),(14,170,138,192),(15,39,94,101),(16,38,95,100),(17,37,96,99),(18,36,97,112),(19,35,98,111),(20,34,85,110),(21,33,86,109),(22,32,87,108),(23,31,88,107),(24,30,89,106),(25,29,90,105),(26,42,91,104),(27,41,92,103),(28,40,93,102),(43,158,116,213),(44,157,117,212),(45,156,118,211),(46,155,119,224),(47,168,120,223),(48,167,121,222),(49,166,122,221),(50,165,123,220),(51,164,124,219),(52,163,125,218),(53,162,126,217),(54,161,113,216),(55,160,114,215),(56,159,115,214),(57,84,207,145),(58,83,208,144),(59,82,209,143),(60,81,210,142),(61,80,197,141),(62,79,198,154),(63,78,199,153),(64,77,200,152),(65,76,201,151),(66,75,202,150),(67,74,203,149),(68,73,204,148),(69,72,205,147),(70,71,206,146)], [(1,64,8,57),(2,63,9,70),(3,62,10,69),(4,61,11,68),(5,60,12,67),(6,59,13,66),(7,58,14,65),(15,214,22,221),(16,213,23,220),(17,212,24,219),(18,211,25,218),(19,224,26,217),(20,223,27,216),(21,222,28,215),(29,118,36,125),(30,117,37,124),(31,116,38,123),(32,115,39,122),(33,114,40,121),(34,113,41,120),(35,126,42,119),(43,100,50,107),(44,99,51,106),(45,112,52,105),(46,111,53,104),(47,110,54,103),(48,109,55,102),(49,108,56,101),(71,183,78,190),(72,196,79,189),(73,195,80,188),(74,194,81,187),(75,193,82,186),(76,192,83,185),(77,191,84,184),(85,168,92,161),(86,167,93,160),(87,166,94,159),(88,165,95,158),(89,164,96,157),(90,163,97,156),(91,162,98,155),(127,198,134,205),(128,197,135,204),(129,210,136,203),(130,209,137,202),(131,208,138,201),(132,207,139,200),(133,206,140,199),(141,180,148,173),(142,179,149,172),(143,178,150,171),(144,177,151,170),(145,176,152,169),(146,175,153,182),(147,174,154,181)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | 4B | 4C | 4D | 4E | 4F | ··· | 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 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 28 | 2 | 2 | 4 | 4 | 4 | 14 | ··· | 14 | 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⋊2D7 | D4⋊8D14 |
| kernel | C14.1152+ 1+4 | C23.D14 | C22.D28 | C28.3Q8 | C4⋊C4⋊7D7 | C2×C4⋊Dic7 | C4×C7⋊D4 | D4×Dic7 | C28⋊2D4 | Dic7⋊D4 | C7×C4⋊D4 | C4⋊D4 | C28 | C2×C14 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C14 | C4 | C22 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 3 | 1 | 2 | 1 | 3 | 4 | 4 | 6 | 3 | 3 | 9 | 1 | 6 | 6 | 6 |
Matrix representation of C14.1152+ 1+4 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 25 | 0 | 0 |
| 0 | 0 | 4 | 25 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 1 | 23 | 0 | 0 | 0 | 0 |
| 10 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 12 | 15 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 16 | 0 | 0 |
| 0 | 0 | 13 | 24 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 17 | 14 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 16 | 0 | 0 |
| 0 | 0 | 13 | 24 | 0 | 0 |
| 0 | 0 | 0 | 0 | 21 | 18 |
| 0 | 0 | 0 | 0 | 11 | 8 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 16 | 0 | 0 |
| 0 | 0 | 13 | 24 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 0 | 0 | 0 | 0 | 17 | 0 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,11,4,0,0,0,0,25,25,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[1,10,0,0,0,0,23,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,28,0],[12,0,0,0,0,0,15,17,0,0,0,0,0,0,5,13,0,0,0,0,16,24,0,0,0,0,0,0,17,0,0,0,0,0,0,17],[17,0,0,0,0,0,14,12,0,0,0,0,0,0,5,13,0,0,0,0,16,24,0,0,0,0,0,0,21,11,0,0,0,0,18,8],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,5,13,0,0,0,0,16,24,0,0,0,0,0,0,0,17,0,0,0,0,17,0] >;
C14.1152+ 1+4 in GAP, Magma, Sage, TeX
C_{14}._{115}2_+^{1+4} % in TeX
G:=Group("C14.115ES+(2,2)"); // GroupNames label
G:=SmallGroup(448,1071);
// by ID
G=gap.SmallGroup(448,1071);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,100,675,570,185,136,18822]);
// 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,c*a*c^-1=d*a*d^-1=e*a*e^-1=a^-1,c*b*c^-1=b^-1,d*b*d^-1=a^7*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=a^7*b^2*d>;
// generators/relations