?
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, C4.Dic14⋊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, C22.D28⋊12C2, C22.2(D4⋊2D7), C23.D14⋊20C2, 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
Subgroups: 1004 in 238 conjugacy classes, 99 normal (43 characteristic)
C1, C2 [×3], C2 [×5], C4 [×2], C4 [×10], C22, C22 [×2], C22 [×11], C7, C2×C4 [×2], C2×C4 [×2], C2×C4 [×15], D4 [×10], C23, C23 [×2], C23, D7, C14 [×3], C14 [×4], C42 [×3], C22⋊C4 [×2], C22⋊C4 [×8], C4⋊C4, C4⋊C4 [×9], C22×C4, C22×C4 [×5], C2×D4, C2×D4 [×2], C2×D4 [×3], Dic7 [×7], C28 [×2], C28 [×3], D14 [×3], C2×C14, C2×C14 [×2], C2×C14 [×8], C2×C4⋊C4, C42⋊C2, C4×D4 [×4], C4⋊D4, C4⋊D4 [×3], C22.D4 [×2], C42.C2, C42⋊2C2 [×2], C4×D7 [×2], C2×Dic7 [×3], C2×Dic7 [×4], C2×Dic7 [×4], C7⋊D4 [×4], C2×C28 [×2], C2×C28 [×2], C2×C28 [×2], C7×D4 [×6], C22×D7, C22×C14, C22×C14 [×2], C22.47C24, C4×Dic7, C4×Dic7 [×2], Dic7⋊C4, Dic7⋊C4 [×2], C4⋊Dic7 [×2], C4⋊Dic7 [×4], D14⋊C4, D14⋊C4 [×2], C23.D7, C23.D7 [×4], C7×C22⋊C4 [×2], C7×C4⋊C4, C2×C4×D7, C22×Dic7 [×4], C2×C7⋊D4, C2×C7⋊D4 [×2], C22×C28, D4×C14, D4×C14 [×2], C23.D14 [×2], C22.D28 [×2], C4.Dic14, C4⋊C4⋊7D7, C2×C4⋊Dic7, C4×C7⋊D4, D4×Dic7, D4×Dic7 [×2], C28⋊2D4, Dic7⋊D4 [×2], C7×C4⋊D4, C14.1152+ (1+4)
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×4], C24, D14 [×7], C2×C4○D4 [×2], 2+ (1+4), C22×D7 [×7], C22.47C24, D4⋊2D7 [×4], C23×D7, C2×D4⋊2D7 [×2], D4⋊8D14, C14.1152+ (1+4)
Generators and relations
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 >
►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)
(1 128 23 187)(2 129 24 188)(3 130 25 189)(4 131 26 190)(5 132 27 191)(6 133 28 192)(7 134 15 193)(8 135 16 194)(9 136 17 195)(10 137 18 196)(11 138 19 183)(12 139 20 184)(13 140 21 185)(14 127 22 186)(29 216 171 205)(30 217 172 206)(31 218 173 207)(32 219 174 208)(33 220 175 209)(34 221 176 210)(35 222 177 197)(36 223 178 198)(37 224 179 199)(38 211 180 200)(39 212 181 201)(40 213 182 202)(41 214 169 203)(42 215 170 204)(43 168 61 71)(44 155 62 72)(45 156 63 73)(46 157 64 74)(47 158 65 75)(48 159 66 76)(49 160 67 77)(50 161 68 78)(51 162 69 79)(52 163 70 80)(53 164 57 81)(54 165 58 82)(55 166 59 83)(56 167 60 84)(85 148 124 102)(86 149 125 103)(87 150 126 104)(88 151 113 105)(89 152 114 106)(90 153 115 107)(91 154 116 108)(92 141 117 109)(93 142 118 110)(94 143 119 111)(95 144 120 112)(96 145 121 99)(97 146 122 100)(98 147 123 101)
(1 165 8 158)(2 164 9 157)(3 163 10 156)(4 162 11 155)(5 161 12 168)(6 160 13 167)(7 159 14 166)(15 76 22 83)(16 75 23 82)(17 74 24 81)(18 73 25 80)(19 72 26 79)(20 71 27 78)(21 84 28 77)(29 116 36 123)(30 115 37 122)(31 114 38 121)(32 113 39 120)(33 126 40 119)(34 125 41 118)(35 124 42 117)(43 132 50 139)(44 131 51 138)(45 130 52 137)(46 129 53 136)(47 128 54 135)(48 127 55 134)(49 140 56 133)(57 195 64 188)(58 194 65 187)(59 193 66 186)(60 192 67 185)(61 191 68 184)(62 190 69 183)(63 189 70 196)(85 170 92 177)(86 169 93 176)(87 182 94 175)(88 181 95 174)(89 180 96 173)(90 179 97 172)(91 178 98 171)(99 207 106 200)(100 206 107 199)(101 205 108 198)(102 204 109 197)(103 203 110 210)(104 202 111 209)(105 201 112 208)(141 222 148 215)(142 221 149 214)(143 220 150 213)(144 219 151 212)(145 218 152 211)(146 217 153 224)(147 216 154 223)
(1 32 23 174)(2 31 24 173)(3 30 25 172)(4 29 26 171)(5 42 27 170)(6 41 28 169)(7 40 15 182)(8 39 16 181)(9 38 17 180)(10 37 18 179)(11 36 19 178)(12 35 20 177)(13 34 21 176)(14 33 22 175)(43 141 61 109)(44 154 62 108)(45 153 63 107)(46 152 64 106)(47 151 65 105)(48 150 66 104)(49 149 67 103)(50 148 68 102)(51 147 69 101)(52 146 70 100)(53 145 57 99)(54 144 58 112)(55 143 59 111)(56 142 60 110)(71 85 168 124)(72 98 155 123)(73 97 156 122)(74 96 157 121)(75 95 158 120)(76 94 159 119)(77 93 160 118)(78 92 161 117)(79 91 162 116)(80 90 163 115)(81 89 164 114)(82 88 165 113)(83 87 166 126)(84 86 167 125)(127 213 186 202)(128 212 187 201)(129 211 188 200)(130 224 189 199)(131 223 190 198)(132 222 191 197)(133 221 192 210)(134 220 193 209)(135 219 194 208)(136 218 195 207)(137 217 196 206)(138 216 183 205)(139 215 184 204)(140 214 185 203)
(1 47 8 54)(2 46 9 53)(3 45 10 52)(4 44 11 51)(5 43 12 50)(6 56 13 49)(7 55 14 48)(15 59 22 66)(16 58 23 65)(17 57 24 64)(18 70 25 63)(19 69 26 62)(20 68 27 61)(21 67 28 60)(29 101 36 108)(30 100 37 107)(31 99 38 106)(32 112 39 105)(33 111 40 104)(34 110 41 103)(35 109 42 102)(71 184 78 191)(72 183 79 190)(73 196 80 189)(74 195 81 188)(75 194 82 187)(76 193 83 186)(77 192 84 185)(85 222 92 215)(86 221 93 214)(87 220 94 213)(88 219 95 212)(89 218 96 211)(90 217 97 224)(91 216 98 223)(113 208 120 201)(114 207 121 200)(115 206 122 199)(116 205 123 198)(117 204 124 197)(118 203 125 210)(119 202 126 209)(127 159 134 166)(128 158 135 165)(129 157 136 164)(130 156 137 163)(131 155 138 162)(132 168 139 161)(133 167 140 160)(141 170 148 177)(142 169 149 176)(143 182 150 175)(144 181 151 174)(145 180 152 173)(146 179 153 172)(147 178 154 171)
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), (1,128,23,187)(2,129,24,188)(3,130,25,189)(4,131,26,190)(5,132,27,191)(6,133,28,192)(7,134,15,193)(8,135,16,194)(9,136,17,195)(10,137,18,196)(11,138,19,183)(12,139,20,184)(13,140,21,185)(14,127,22,186)(29,216,171,205)(30,217,172,206)(31,218,173,207)(32,219,174,208)(33,220,175,209)(34,221,176,210)(35,222,177,197)(36,223,178,198)(37,224,179,199)(38,211,180,200)(39,212,181,201)(40,213,182,202)(41,214,169,203)(42,215,170,204)(43,168,61,71)(44,155,62,72)(45,156,63,73)(46,157,64,74)(47,158,65,75)(48,159,66,76)(49,160,67,77)(50,161,68,78)(51,162,69,79)(52,163,70,80)(53,164,57,81)(54,165,58,82)(55,166,59,83)(56,167,60,84)(85,148,124,102)(86,149,125,103)(87,150,126,104)(88,151,113,105)(89,152,114,106)(90,153,115,107)(91,154,116,108)(92,141,117,109)(93,142,118,110)(94,143,119,111)(95,144,120,112)(96,145,121,99)(97,146,122,100)(98,147,123,101), (1,165,8,158)(2,164,9,157)(3,163,10,156)(4,162,11,155)(5,161,12,168)(6,160,13,167)(7,159,14,166)(15,76,22,83)(16,75,23,82)(17,74,24,81)(18,73,25,80)(19,72,26,79)(20,71,27,78)(21,84,28,77)(29,116,36,123)(30,115,37,122)(31,114,38,121)(32,113,39,120)(33,126,40,119)(34,125,41,118)(35,124,42,117)(43,132,50,139)(44,131,51,138)(45,130,52,137)(46,129,53,136)(47,128,54,135)(48,127,55,134)(49,140,56,133)(57,195,64,188)(58,194,65,187)(59,193,66,186)(60,192,67,185)(61,191,68,184)(62,190,69,183)(63,189,70,196)(85,170,92,177)(86,169,93,176)(87,182,94,175)(88,181,95,174)(89,180,96,173)(90,179,97,172)(91,178,98,171)(99,207,106,200)(100,206,107,199)(101,205,108,198)(102,204,109,197)(103,203,110,210)(104,202,111,209)(105,201,112,208)(141,222,148,215)(142,221,149,214)(143,220,150,213)(144,219,151,212)(145,218,152,211)(146,217,153,224)(147,216,154,223), (1,32,23,174)(2,31,24,173)(3,30,25,172)(4,29,26,171)(5,42,27,170)(6,41,28,169)(7,40,15,182)(8,39,16,181)(9,38,17,180)(10,37,18,179)(11,36,19,178)(12,35,20,177)(13,34,21,176)(14,33,22,175)(43,141,61,109)(44,154,62,108)(45,153,63,107)(46,152,64,106)(47,151,65,105)(48,150,66,104)(49,149,67,103)(50,148,68,102)(51,147,69,101)(52,146,70,100)(53,145,57,99)(54,144,58,112)(55,143,59,111)(56,142,60,110)(71,85,168,124)(72,98,155,123)(73,97,156,122)(74,96,157,121)(75,95,158,120)(76,94,159,119)(77,93,160,118)(78,92,161,117)(79,91,162,116)(80,90,163,115)(81,89,164,114)(82,88,165,113)(83,87,166,126)(84,86,167,125)(127,213,186,202)(128,212,187,201)(129,211,188,200)(130,224,189,199)(131,223,190,198)(132,222,191,197)(133,221,192,210)(134,220,193,209)(135,219,194,208)(136,218,195,207)(137,217,196,206)(138,216,183,205)(139,215,184,204)(140,214,185,203), (1,47,8,54)(2,46,9,53)(3,45,10,52)(4,44,11,51)(5,43,12,50)(6,56,13,49)(7,55,14,48)(15,59,22,66)(16,58,23,65)(17,57,24,64)(18,70,25,63)(19,69,26,62)(20,68,27,61)(21,67,28,60)(29,101,36,108)(30,100,37,107)(31,99,38,106)(32,112,39,105)(33,111,40,104)(34,110,41,103)(35,109,42,102)(71,184,78,191)(72,183,79,190)(73,196,80,189)(74,195,81,188)(75,194,82,187)(76,193,83,186)(77,192,84,185)(85,222,92,215)(86,221,93,214)(87,220,94,213)(88,219,95,212)(89,218,96,211)(90,217,97,224)(91,216,98,223)(113,208,120,201)(114,207,121,200)(115,206,122,199)(116,205,123,198)(117,204,124,197)(118,203,125,210)(119,202,126,209)(127,159,134,166)(128,158,135,165)(129,157,136,164)(130,156,137,163)(131,155,138,162)(132,168,139,161)(133,167,140,160)(141,170,148,177)(142,169,149,176)(143,182,150,175)(144,181,151,174)(145,180,152,173)(146,179,153,172)(147,178,154,171)>;
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), (1,128,23,187)(2,129,24,188)(3,130,25,189)(4,131,26,190)(5,132,27,191)(6,133,28,192)(7,134,15,193)(8,135,16,194)(9,136,17,195)(10,137,18,196)(11,138,19,183)(12,139,20,184)(13,140,21,185)(14,127,22,186)(29,216,171,205)(30,217,172,206)(31,218,173,207)(32,219,174,208)(33,220,175,209)(34,221,176,210)(35,222,177,197)(36,223,178,198)(37,224,179,199)(38,211,180,200)(39,212,181,201)(40,213,182,202)(41,214,169,203)(42,215,170,204)(43,168,61,71)(44,155,62,72)(45,156,63,73)(46,157,64,74)(47,158,65,75)(48,159,66,76)(49,160,67,77)(50,161,68,78)(51,162,69,79)(52,163,70,80)(53,164,57,81)(54,165,58,82)(55,166,59,83)(56,167,60,84)(85,148,124,102)(86,149,125,103)(87,150,126,104)(88,151,113,105)(89,152,114,106)(90,153,115,107)(91,154,116,108)(92,141,117,109)(93,142,118,110)(94,143,119,111)(95,144,120,112)(96,145,121,99)(97,146,122,100)(98,147,123,101), (1,165,8,158)(2,164,9,157)(3,163,10,156)(4,162,11,155)(5,161,12,168)(6,160,13,167)(7,159,14,166)(15,76,22,83)(16,75,23,82)(17,74,24,81)(18,73,25,80)(19,72,26,79)(20,71,27,78)(21,84,28,77)(29,116,36,123)(30,115,37,122)(31,114,38,121)(32,113,39,120)(33,126,40,119)(34,125,41,118)(35,124,42,117)(43,132,50,139)(44,131,51,138)(45,130,52,137)(46,129,53,136)(47,128,54,135)(48,127,55,134)(49,140,56,133)(57,195,64,188)(58,194,65,187)(59,193,66,186)(60,192,67,185)(61,191,68,184)(62,190,69,183)(63,189,70,196)(85,170,92,177)(86,169,93,176)(87,182,94,175)(88,181,95,174)(89,180,96,173)(90,179,97,172)(91,178,98,171)(99,207,106,200)(100,206,107,199)(101,205,108,198)(102,204,109,197)(103,203,110,210)(104,202,111,209)(105,201,112,208)(141,222,148,215)(142,221,149,214)(143,220,150,213)(144,219,151,212)(145,218,152,211)(146,217,153,224)(147,216,154,223), (1,32,23,174)(2,31,24,173)(3,30,25,172)(4,29,26,171)(5,42,27,170)(6,41,28,169)(7,40,15,182)(8,39,16,181)(9,38,17,180)(10,37,18,179)(11,36,19,178)(12,35,20,177)(13,34,21,176)(14,33,22,175)(43,141,61,109)(44,154,62,108)(45,153,63,107)(46,152,64,106)(47,151,65,105)(48,150,66,104)(49,149,67,103)(50,148,68,102)(51,147,69,101)(52,146,70,100)(53,145,57,99)(54,144,58,112)(55,143,59,111)(56,142,60,110)(71,85,168,124)(72,98,155,123)(73,97,156,122)(74,96,157,121)(75,95,158,120)(76,94,159,119)(77,93,160,118)(78,92,161,117)(79,91,162,116)(80,90,163,115)(81,89,164,114)(82,88,165,113)(83,87,166,126)(84,86,167,125)(127,213,186,202)(128,212,187,201)(129,211,188,200)(130,224,189,199)(131,223,190,198)(132,222,191,197)(133,221,192,210)(134,220,193,209)(135,219,194,208)(136,218,195,207)(137,217,196,206)(138,216,183,205)(139,215,184,204)(140,214,185,203), (1,47,8,54)(2,46,9,53)(3,45,10,52)(4,44,11,51)(5,43,12,50)(6,56,13,49)(7,55,14,48)(15,59,22,66)(16,58,23,65)(17,57,24,64)(18,70,25,63)(19,69,26,62)(20,68,27,61)(21,67,28,60)(29,101,36,108)(30,100,37,107)(31,99,38,106)(32,112,39,105)(33,111,40,104)(34,110,41,103)(35,109,42,102)(71,184,78,191)(72,183,79,190)(73,196,80,189)(74,195,81,188)(75,194,82,187)(76,193,83,186)(77,192,84,185)(85,222,92,215)(86,221,93,214)(87,220,94,213)(88,219,95,212)(89,218,96,211)(90,217,97,224)(91,216,98,223)(113,208,120,201)(114,207,121,200)(115,206,122,199)(116,205,123,198)(117,204,124,197)(118,203,125,210)(119,202,126,209)(127,159,134,166)(128,158,135,165)(129,157,136,164)(130,156,137,163)(131,155,138,162)(132,168,139,161)(133,167,140,160)(141,170,148,177)(142,169,149,176)(143,182,150,175)(144,181,151,174)(145,180,152,173)(146,179,153,172)(147,178,154,171) );
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)], [(1,128,23,187),(2,129,24,188),(3,130,25,189),(4,131,26,190),(5,132,27,191),(6,133,28,192),(7,134,15,193),(8,135,16,194),(9,136,17,195),(10,137,18,196),(11,138,19,183),(12,139,20,184),(13,140,21,185),(14,127,22,186),(29,216,171,205),(30,217,172,206),(31,218,173,207),(32,219,174,208),(33,220,175,209),(34,221,176,210),(35,222,177,197),(36,223,178,198),(37,224,179,199),(38,211,180,200),(39,212,181,201),(40,213,182,202),(41,214,169,203),(42,215,170,204),(43,168,61,71),(44,155,62,72),(45,156,63,73),(46,157,64,74),(47,158,65,75),(48,159,66,76),(49,160,67,77),(50,161,68,78),(51,162,69,79),(52,163,70,80),(53,164,57,81),(54,165,58,82),(55,166,59,83),(56,167,60,84),(85,148,124,102),(86,149,125,103),(87,150,126,104),(88,151,113,105),(89,152,114,106),(90,153,115,107),(91,154,116,108),(92,141,117,109),(93,142,118,110),(94,143,119,111),(95,144,120,112),(96,145,121,99),(97,146,122,100),(98,147,123,101)], [(1,165,8,158),(2,164,9,157),(3,163,10,156),(4,162,11,155),(5,161,12,168),(6,160,13,167),(7,159,14,166),(15,76,22,83),(16,75,23,82),(17,74,24,81),(18,73,25,80),(19,72,26,79),(20,71,27,78),(21,84,28,77),(29,116,36,123),(30,115,37,122),(31,114,38,121),(32,113,39,120),(33,126,40,119),(34,125,41,118),(35,124,42,117),(43,132,50,139),(44,131,51,138),(45,130,52,137),(46,129,53,136),(47,128,54,135),(48,127,55,134),(49,140,56,133),(57,195,64,188),(58,194,65,187),(59,193,66,186),(60,192,67,185),(61,191,68,184),(62,190,69,183),(63,189,70,196),(85,170,92,177),(86,169,93,176),(87,182,94,175),(88,181,95,174),(89,180,96,173),(90,179,97,172),(91,178,98,171),(99,207,106,200),(100,206,107,199),(101,205,108,198),(102,204,109,197),(103,203,110,210),(104,202,111,209),(105,201,112,208),(141,222,148,215),(142,221,149,214),(143,220,150,213),(144,219,151,212),(145,218,152,211),(146,217,153,224),(147,216,154,223)], [(1,32,23,174),(2,31,24,173),(3,30,25,172),(4,29,26,171),(5,42,27,170),(6,41,28,169),(7,40,15,182),(8,39,16,181),(9,38,17,180),(10,37,18,179),(11,36,19,178),(12,35,20,177),(13,34,21,176),(14,33,22,175),(43,141,61,109),(44,154,62,108),(45,153,63,107),(46,152,64,106),(47,151,65,105),(48,150,66,104),(49,149,67,103),(50,148,68,102),(51,147,69,101),(52,146,70,100),(53,145,57,99),(54,144,58,112),(55,143,59,111),(56,142,60,110),(71,85,168,124),(72,98,155,123),(73,97,156,122),(74,96,157,121),(75,95,158,120),(76,94,159,119),(77,93,160,118),(78,92,161,117),(79,91,162,116),(80,90,163,115),(81,89,164,114),(82,88,165,113),(83,87,166,126),(84,86,167,125),(127,213,186,202),(128,212,187,201),(129,211,188,200),(130,224,189,199),(131,223,190,198),(132,222,191,197),(133,221,192,210),(134,220,193,209),(135,219,194,208),(136,218,195,207),(137,217,196,206),(138,216,183,205),(139,215,184,204),(140,214,185,203)], [(1,47,8,54),(2,46,9,53),(3,45,10,52),(4,44,11,51),(5,43,12,50),(6,56,13,49),(7,55,14,48),(15,59,22,66),(16,58,23,65),(17,57,24,64),(18,70,25,63),(19,69,26,62),(20,68,27,61),(21,67,28,60),(29,101,36,108),(30,100,37,107),(31,99,38,106),(32,112,39,105),(33,111,40,104),(34,110,41,103),(35,109,42,102),(71,184,78,191),(72,183,79,190),(73,196,80,189),(74,195,81,188),(75,194,82,187),(76,193,83,186),(77,192,84,185),(85,222,92,215),(86,221,93,214),(87,220,94,213),(88,219,95,212),(89,218,96,211),(90,217,97,224),(91,216,98,223),(113,208,120,201),(114,207,121,200),(115,206,122,199),(116,205,123,198),(117,204,124,197),(118,203,125,210),(119,202,126,209),(127,159,134,166),(128,158,135,165),(129,157,136,164),(130,156,137,163),(131,155,138,162),(132,168,139,161),(133,167,140,160),(141,170,148,177),(142,169,149,176),(143,182,150,175),(144,181,151,174),(145,180,152,173),(146,179,153,172),(147,178,154,171)])
Matrix representation ►G ⊆ 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] >;
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 | C4.Dic14 | 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 |
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
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