G = C14.852- 1+4 order 448 = 26·7
40th non-split extension by C14 of 2- 1+4 acting via 2- 1+4/C4○D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.852- 1+4, C14.1232+ 1+4, C4⋊C4.108D14, (D4×Dic7)⋊29C2, D14⋊2Q8⋊33C2, (C2×D4).167D14, Dic7.Q8⋊30C2, D14⋊C4.9C22, C22⋊C4.69D14, C28.3Q8⋊30C2, Dic7⋊4D4⋊26C2, D14.D4⋊37C2, (C2×C28).183C23, (C2×C14).209C24, Dic7⋊D4.3C2, C22.D4⋊14D7, (C22×C4).262D14, C2.45(D4⋊8D14), C23.33(C22×D7), C22⋊Dic14⋊35C2, (D4×C14).147C22, C23.23D14⋊8C2, C22.D28⋊23C2, C23.D14⋊35C2, Dic7⋊C4.10C22, C4⋊Dic7.313C22, (C22×C14).41C23, (C22×C28).87C22, (C22×D7).90C23, C22.230(C23×D7), C23.D7.47C22, C22.12(D4⋊2D7), C7⋊7(C22.33C24), (C4×Dic7).128C22, (C2×Dic7).108C23, C2.46(D4.10D14), (C2×Dic14).171C22, (C22×Dic7).135C22, C4⋊C4⋊D7⋊31C2, (C2×C4⋊Dic7)⋊27C2, C14.92(C2×C4○D4), C2.54(C2×D4⋊2D7), (C2×C4×D7).116C22, (C2×C14).48(C4○D4), (C7×C4⋊C4).182C22, (C2×C4).190(C22×D7), (C2×C7⋊D4).53C22, (C7×C22.D4)⋊17C2, (C7×C22⋊C4).57C22, SmallGroup(448,1118)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.852- 1+4
G = < a,b,c,d,e | a14=b4=c2=1, d2=a7b2, e2=b2, ab=ba, ac=ca, dad-1=a-1, ae=ea, cbc=b-1, dbd-1=ebe-1=a7b, cd=dc, ce=ec, ede-1=b2d >
Subgroups: 940 in 218 conjugacy classes, 95 normal (91 characteristic)
C1, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, Dic7, C28, D14, C2×C14, C2×C14, C2×C14, C2×C4⋊C4, C4×D4, C4⋊D4, C22⋊Q8, C22.D4, C22.D4, C42.C2, C42⋊2C2, Dic14, C4×D7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C22.33C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C22×Dic7, C2×C7⋊D4, C22×C28, D4×C14, C22⋊Dic14, C23.D14, Dic7⋊4D4, D14.D4, C22.D28, Dic7.Q8, C28.3Q8, D14⋊2Q8, C4⋊C4⋊D7, C2×C4⋊Dic7, C23.23D14, D4×Dic7, Dic7⋊D4, C7×C22.D4, C14.852- 1+4
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, 2- 1+4, C22×D7, C22.33C24, D4⋊2D7, C23×D7, C2×D4⋊2D7, D4⋊8D14, D4.10D14, C14.852- 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)
(1 121 105 181)(2 122 106 182)(3 123 107 169)(4 124 108 170)(5 125 109 171)(6 126 110 172)(7 113 111 173)(8 114 112 174)(9 115 99 175)(10 116 100 176)(11 117 101 177)(12 118 102 178)(13 119 103 179)(14 120 104 180)(15 47 129 82)(16 48 130 83)(17 49 131 84)(18 50 132 71)(19 51 133 72)(20 52 134 73)(21 53 135 74)(22 54 136 75)(23 55 137 76)(24 56 138 77)(25 43 139 78)(26 44 140 79)(27 45 127 80)(28 46 128 81)(29 97 150 161)(30 98 151 162)(31 85 152 163)(32 86 153 164)(33 87 154 165)(34 88 141 166)(35 89 142 167)(36 90 143 168)(37 91 144 155)(38 92 145 156)(39 93 146 157)(40 94 147 158)(41 95 148 159)(42 96 149 160)(57 204 188 212)(58 205 189 213)(59 206 190 214)(60 207 191 215)(61 208 192 216)(62 209 193 217)(63 210 194 218)(64 197 195 219)(65 198 196 220)(66 199 183 221)(67 200 184 222)(68 201 185 223)(69 202 186 224)(70 203 187 211)
(15 129)(16 130)(17 131)(18 132)(19 133)(20 134)(21 135)(22 136)(23 137)(24 138)(25 139)(26 140)(27 127)(28 128)(57 188)(58 189)(59 190)(60 191)(61 192)(62 193)(63 194)(64 195)(65 196)(66 183)(67 184)(68 185)(69 186)(70 187)(85 163)(86 164)(87 165)(88 166)(89 167)(90 168)(91 155)(92 156)(93 157)(94 158)(95 159)(96 160)(97 161)(98 162)(113 173)(114 174)(115 175)(116 176)(117 177)(118 178)(119 179)(120 180)(121 181)(122 182)(123 169)(124 170)(125 171)(126 172)
(1 202 112 217)(2 201 99 216)(3 200 100 215)(4 199 101 214)(5 198 102 213)(6 197 103 212)(7 210 104 211)(8 209 105 224)(9 208 106 223)(10 207 107 222)(11 206 108 221)(12 205 109 220)(13 204 110 219)(14 203 111 218)(15 160 136 89)(16 159 137 88)(17 158 138 87)(18 157 139 86)(19 156 140 85)(20 155 127 98)(21 168 128 97)(22 167 129 96)(23 166 130 95)(24 165 131 94)(25 164 132 93)(26 163 133 92)(27 162 134 91)(28 161 135 90)(29 81 143 53)(30 80 144 52)(31 79 145 51)(32 78 146 50)(33 77 147 49)(34 76 148 48)(35 75 149 47)(36 74 150 46)(37 73 151 45)(38 72 152 44)(39 71 153 43)(40 84 154 56)(41 83 141 55)(42 82 142 54)(57 119 195 172)(58 118 196 171)(59 117 183 170)(60 116 184 169)(61 115 185 182)(62 114 186 181)(63 113 187 180)(64 126 188 179)(65 125 189 178)(66 124 190 177)(67 123 191 176)(68 122 192 175)(69 121 193 174)(70 120 194 173)
(1 38 105 145)(2 39 106 146)(3 40 107 147)(4 41 108 148)(5 42 109 149)(6 29 110 150)(7 30 111 151)(8 31 112 152)(9 32 99 153)(10 33 100 154)(11 34 101 141)(12 35 102 142)(13 36 103 143)(14 37 104 144)(15 189 129 58)(16 190 130 59)(17 191 131 60)(18 192 132 61)(19 193 133 62)(20 194 134 63)(21 195 135 64)(22 196 136 65)(23 183 137 66)(24 184 138 67)(25 185 139 68)(26 186 140 69)(27 187 127 70)(28 188 128 57)(43 216 78 208)(44 217 79 209)(45 218 80 210)(46 219 81 197)(47 220 82 198)(48 221 83 199)(49 222 84 200)(50 223 71 201)(51 224 72 202)(52 211 73 203)(53 212 74 204)(54 213 75 205)(55 214 76 206)(56 215 77 207)(85 181 163 121)(86 182 164 122)(87 169 165 123)(88 170 166 124)(89 171 167 125)(90 172 168 126)(91 173 155 113)(92 174 156 114)(93 175 157 115)(94 176 158 116)(95 177 159 117)(96 178 160 118)(97 179 161 119)(98 180 162 120)
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), (1,121,105,181)(2,122,106,182)(3,123,107,169)(4,124,108,170)(5,125,109,171)(6,126,110,172)(7,113,111,173)(8,114,112,174)(9,115,99,175)(10,116,100,176)(11,117,101,177)(12,118,102,178)(13,119,103,179)(14,120,104,180)(15,47,129,82)(16,48,130,83)(17,49,131,84)(18,50,132,71)(19,51,133,72)(20,52,134,73)(21,53,135,74)(22,54,136,75)(23,55,137,76)(24,56,138,77)(25,43,139,78)(26,44,140,79)(27,45,127,80)(28,46,128,81)(29,97,150,161)(30,98,151,162)(31,85,152,163)(32,86,153,164)(33,87,154,165)(34,88,141,166)(35,89,142,167)(36,90,143,168)(37,91,144,155)(38,92,145,156)(39,93,146,157)(40,94,147,158)(41,95,148,159)(42,96,149,160)(57,204,188,212)(58,205,189,213)(59,206,190,214)(60,207,191,215)(61,208,192,216)(62,209,193,217)(63,210,194,218)(64,197,195,219)(65,198,196,220)(66,199,183,221)(67,200,184,222)(68,201,185,223)(69,202,186,224)(70,203,187,211), (15,129)(16,130)(17,131)(18,132)(19,133)(20,134)(21,135)(22,136)(23,137)(24,138)(25,139)(26,140)(27,127)(28,128)(57,188)(58,189)(59,190)(60,191)(61,192)(62,193)(63,194)(64,195)(65,196)(66,183)(67,184)(68,185)(69,186)(70,187)(85,163)(86,164)(87,165)(88,166)(89,167)(90,168)(91,155)(92,156)(93,157)(94,158)(95,159)(96,160)(97,161)(98,162)(113,173)(114,174)(115,175)(116,176)(117,177)(118,178)(119,179)(120,180)(121,181)(122,182)(123,169)(124,170)(125,171)(126,172), (1,202,112,217)(2,201,99,216)(3,200,100,215)(4,199,101,214)(5,198,102,213)(6,197,103,212)(7,210,104,211)(8,209,105,224)(9,208,106,223)(10,207,107,222)(11,206,108,221)(12,205,109,220)(13,204,110,219)(14,203,111,218)(15,160,136,89)(16,159,137,88)(17,158,138,87)(18,157,139,86)(19,156,140,85)(20,155,127,98)(21,168,128,97)(22,167,129,96)(23,166,130,95)(24,165,131,94)(25,164,132,93)(26,163,133,92)(27,162,134,91)(28,161,135,90)(29,81,143,53)(30,80,144,52)(31,79,145,51)(32,78,146,50)(33,77,147,49)(34,76,148,48)(35,75,149,47)(36,74,150,46)(37,73,151,45)(38,72,152,44)(39,71,153,43)(40,84,154,56)(41,83,141,55)(42,82,142,54)(57,119,195,172)(58,118,196,171)(59,117,183,170)(60,116,184,169)(61,115,185,182)(62,114,186,181)(63,113,187,180)(64,126,188,179)(65,125,189,178)(66,124,190,177)(67,123,191,176)(68,122,192,175)(69,121,193,174)(70,120,194,173), (1,38,105,145)(2,39,106,146)(3,40,107,147)(4,41,108,148)(5,42,109,149)(6,29,110,150)(7,30,111,151)(8,31,112,152)(9,32,99,153)(10,33,100,154)(11,34,101,141)(12,35,102,142)(13,36,103,143)(14,37,104,144)(15,189,129,58)(16,190,130,59)(17,191,131,60)(18,192,132,61)(19,193,133,62)(20,194,134,63)(21,195,135,64)(22,196,136,65)(23,183,137,66)(24,184,138,67)(25,185,139,68)(26,186,140,69)(27,187,127,70)(28,188,128,57)(43,216,78,208)(44,217,79,209)(45,218,80,210)(46,219,81,197)(47,220,82,198)(48,221,83,199)(49,222,84,200)(50,223,71,201)(51,224,72,202)(52,211,73,203)(53,212,74,204)(54,213,75,205)(55,214,76,206)(56,215,77,207)(85,181,163,121)(86,182,164,122)(87,169,165,123)(88,170,166,124)(89,171,167,125)(90,172,168,126)(91,173,155,113)(92,174,156,114)(93,175,157,115)(94,176,158,116)(95,177,159,117)(96,178,160,118)(97,179,161,119)(98,180,162,120)>;
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), (1,121,105,181)(2,122,106,182)(3,123,107,169)(4,124,108,170)(5,125,109,171)(6,126,110,172)(7,113,111,173)(8,114,112,174)(9,115,99,175)(10,116,100,176)(11,117,101,177)(12,118,102,178)(13,119,103,179)(14,120,104,180)(15,47,129,82)(16,48,130,83)(17,49,131,84)(18,50,132,71)(19,51,133,72)(20,52,134,73)(21,53,135,74)(22,54,136,75)(23,55,137,76)(24,56,138,77)(25,43,139,78)(26,44,140,79)(27,45,127,80)(28,46,128,81)(29,97,150,161)(30,98,151,162)(31,85,152,163)(32,86,153,164)(33,87,154,165)(34,88,141,166)(35,89,142,167)(36,90,143,168)(37,91,144,155)(38,92,145,156)(39,93,146,157)(40,94,147,158)(41,95,148,159)(42,96,149,160)(57,204,188,212)(58,205,189,213)(59,206,190,214)(60,207,191,215)(61,208,192,216)(62,209,193,217)(63,210,194,218)(64,197,195,219)(65,198,196,220)(66,199,183,221)(67,200,184,222)(68,201,185,223)(69,202,186,224)(70,203,187,211), (15,129)(16,130)(17,131)(18,132)(19,133)(20,134)(21,135)(22,136)(23,137)(24,138)(25,139)(26,140)(27,127)(28,128)(57,188)(58,189)(59,190)(60,191)(61,192)(62,193)(63,194)(64,195)(65,196)(66,183)(67,184)(68,185)(69,186)(70,187)(85,163)(86,164)(87,165)(88,166)(89,167)(90,168)(91,155)(92,156)(93,157)(94,158)(95,159)(96,160)(97,161)(98,162)(113,173)(114,174)(115,175)(116,176)(117,177)(118,178)(119,179)(120,180)(121,181)(122,182)(123,169)(124,170)(125,171)(126,172), (1,202,112,217)(2,201,99,216)(3,200,100,215)(4,199,101,214)(5,198,102,213)(6,197,103,212)(7,210,104,211)(8,209,105,224)(9,208,106,223)(10,207,107,222)(11,206,108,221)(12,205,109,220)(13,204,110,219)(14,203,111,218)(15,160,136,89)(16,159,137,88)(17,158,138,87)(18,157,139,86)(19,156,140,85)(20,155,127,98)(21,168,128,97)(22,167,129,96)(23,166,130,95)(24,165,131,94)(25,164,132,93)(26,163,133,92)(27,162,134,91)(28,161,135,90)(29,81,143,53)(30,80,144,52)(31,79,145,51)(32,78,146,50)(33,77,147,49)(34,76,148,48)(35,75,149,47)(36,74,150,46)(37,73,151,45)(38,72,152,44)(39,71,153,43)(40,84,154,56)(41,83,141,55)(42,82,142,54)(57,119,195,172)(58,118,196,171)(59,117,183,170)(60,116,184,169)(61,115,185,182)(62,114,186,181)(63,113,187,180)(64,126,188,179)(65,125,189,178)(66,124,190,177)(67,123,191,176)(68,122,192,175)(69,121,193,174)(70,120,194,173), (1,38,105,145)(2,39,106,146)(3,40,107,147)(4,41,108,148)(5,42,109,149)(6,29,110,150)(7,30,111,151)(8,31,112,152)(9,32,99,153)(10,33,100,154)(11,34,101,141)(12,35,102,142)(13,36,103,143)(14,37,104,144)(15,189,129,58)(16,190,130,59)(17,191,131,60)(18,192,132,61)(19,193,133,62)(20,194,134,63)(21,195,135,64)(22,196,136,65)(23,183,137,66)(24,184,138,67)(25,185,139,68)(26,186,140,69)(27,187,127,70)(28,188,128,57)(43,216,78,208)(44,217,79,209)(45,218,80,210)(46,219,81,197)(47,220,82,198)(48,221,83,199)(49,222,84,200)(50,223,71,201)(51,224,72,202)(52,211,73,203)(53,212,74,204)(54,213,75,205)(55,214,76,206)(56,215,77,207)(85,181,163,121)(86,182,164,122)(87,169,165,123)(88,170,166,124)(89,171,167,125)(90,172,168,126)(91,173,155,113)(92,174,156,114)(93,175,157,115)(94,176,158,116)(95,177,159,117)(96,178,160,118)(97,179,161,119)(98,180,162,120) );
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)], [(1,121,105,181),(2,122,106,182),(3,123,107,169),(4,124,108,170),(5,125,109,171),(6,126,110,172),(7,113,111,173),(8,114,112,174),(9,115,99,175),(10,116,100,176),(11,117,101,177),(12,118,102,178),(13,119,103,179),(14,120,104,180),(15,47,129,82),(16,48,130,83),(17,49,131,84),(18,50,132,71),(19,51,133,72),(20,52,134,73),(21,53,135,74),(22,54,136,75),(23,55,137,76),(24,56,138,77),(25,43,139,78),(26,44,140,79),(27,45,127,80),(28,46,128,81),(29,97,150,161),(30,98,151,162),(31,85,152,163),(32,86,153,164),(33,87,154,165),(34,88,141,166),(35,89,142,167),(36,90,143,168),(37,91,144,155),(38,92,145,156),(39,93,146,157),(40,94,147,158),(41,95,148,159),(42,96,149,160),(57,204,188,212),(58,205,189,213),(59,206,190,214),(60,207,191,215),(61,208,192,216),(62,209,193,217),(63,210,194,218),(64,197,195,219),(65,198,196,220),(66,199,183,221),(67,200,184,222),(68,201,185,223),(69,202,186,224),(70,203,187,211)], [(15,129),(16,130),(17,131),(18,132),(19,133),(20,134),(21,135),(22,136),(23,137),(24,138),(25,139),(26,140),(27,127),(28,128),(57,188),(58,189),(59,190),(60,191),(61,192),(62,193),(63,194),(64,195),(65,196),(66,183),(67,184),(68,185),(69,186),(70,187),(85,163),(86,164),(87,165),(88,166),(89,167),(90,168),(91,155),(92,156),(93,157),(94,158),(95,159),(96,160),(97,161),(98,162),(113,173),(114,174),(115,175),(116,176),(117,177),(118,178),(119,179),(120,180),(121,181),(122,182),(123,169),(124,170),(125,171),(126,172)], [(1,202,112,217),(2,201,99,216),(3,200,100,215),(4,199,101,214),(5,198,102,213),(6,197,103,212),(7,210,104,211),(8,209,105,224),(9,208,106,223),(10,207,107,222),(11,206,108,221),(12,205,109,220),(13,204,110,219),(14,203,111,218),(15,160,136,89),(16,159,137,88),(17,158,138,87),(18,157,139,86),(19,156,140,85),(20,155,127,98),(21,168,128,97),(22,167,129,96),(23,166,130,95),(24,165,131,94),(25,164,132,93),(26,163,133,92),(27,162,134,91),(28,161,135,90),(29,81,143,53),(30,80,144,52),(31,79,145,51),(32,78,146,50),(33,77,147,49),(34,76,148,48),(35,75,149,47),(36,74,150,46),(37,73,151,45),(38,72,152,44),(39,71,153,43),(40,84,154,56),(41,83,141,55),(42,82,142,54),(57,119,195,172),(58,118,196,171),(59,117,183,170),(60,116,184,169),(61,115,185,182),(62,114,186,181),(63,113,187,180),(64,126,188,179),(65,125,189,178),(66,124,190,177),(67,123,191,176),(68,122,192,175),(69,121,193,174),(70,120,194,173)], [(1,38,105,145),(2,39,106,146),(3,40,107,147),(4,41,108,148),(5,42,109,149),(6,29,110,150),(7,30,111,151),(8,31,112,152),(9,32,99,153),(10,33,100,154),(11,34,101,141),(12,35,102,142),(13,36,103,143),(14,37,104,144),(15,189,129,58),(16,190,130,59),(17,191,131,60),(18,192,132,61),(19,193,133,62),(20,194,134,63),(21,195,135,64),(22,196,136,65),(23,183,137,66),(24,184,138,67),(25,185,139,68),(26,186,140,69),(27,187,127,70),(28,188,128,57),(43,216,78,208),(44,217,79,209),(45,218,80,210),(46,219,81,197),(47,220,82,198),(48,221,83,199),(49,222,84,200),(50,223,71,201),(51,224,72,202),(52,211,73,203),(53,212,74,204),(54,213,75,205),(55,214,76,206),(56,215,77,207),(85,181,163,121),(86,182,164,122),(87,169,165,123),(88,170,166,124),(89,171,167,125),(90,172,168,126),(91,173,155,113),(92,174,156,114),(93,175,157,115),(94,176,158,116),(95,177,159,117),(96,178,160,118),(97,179,161,119),(98,180,162,120)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | ··· | 4E | 4F | 4G | 4H | 4I | 4J | ··· | 4N | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 14P | 14Q | 14R | 28A | ··· | 28L | 28M | ··· | 28U |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 2 | 2 | 4 | 28 | 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⋊2D7 | D4⋊8D14 | D4.10D14 |
| kernel | C14.852- 1+4 | C22⋊Dic14 | C23.D14 | Dic7⋊4D4 | D14.D4 | C22.D28 | Dic7.Q8 | C28.3Q8 | D14⋊2Q8 | C4⋊C4⋊D7 | C2×C4⋊Dic7 | C23.23D14 | D4×Dic7 | Dic7⋊D4 | C7×C22.D4 | C22.D4 | C2×C14 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C14 | C14 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 9 | 6 | 3 | 3 | 1 | 1 | 6 | 6 | 6 |
Matrix representation of C14.852- 1+4 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 8 | 0 | 0 |
| 0 | 0 | 21 | 8 | 0 | 0 |
| 0 | 0 | 2 | 16 | 1 | 8 |
| 0 | 0 | 25 | 2 | 12 | 10 |
| 24 | 16 | 0 | 0 | 0 | 0 |
| 13 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 13 | 22 | 21 |
| 0 | 0 | 11 | 2 | 26 | 15 |
| 0 | 0 | 9 | 28 | 28 | 0 |
| 0 | 0 | 3 | 17 | 15 | 0 |
| 28 | 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 | 9 | 28 | 28 | 0 |
| 0 | 0 | 10 | 15 | 0 | 28 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 8 | 0 | 0 |
| 0 | 0 | 3 | 8 | 0 | 0 |
| 0 | 0 | 4 | 0 | 7 | 26 |
| 0 | 0 | 18 | 1 | 16 | 22 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 11 | 0 | 0 |
| 0 | 0 | 18 | 27 | 0 | 0 |
| 0 | 0 | 19 | 21 | 8 | 18 |
| 0 | 0 | 20 | 12 | 27 | 21 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,3,21,2,25,0,0,8,8,16,2,0,0,0,0,1,12,0,0,0,0,8,10],[24,13,0,0,0,0,16,5,0,0,0,0,0,0,28,11,9,3,0,0,13,2,28,17,0,0,22,26,28,15,0,0,21,15,0,0],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,9,10,0,0,0,1,28,15,0,0,0,0,28,0,0,0,0,0,0,28],[0,12,0,0,0,0,12,0,0,0,0,0,0,0,21,3,4,18,0,0,8,8,0,1,0,0,0,0,7,16,0,0,0,0,26,22],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,2,18,19,20,0,0,11,27,21,12,0,0,0,0,8,27,0,0,0,0,18,21] >;
C14.852- 1+4 in GAP, Magma, Sage, TeX
C_{14}._{85}2_-^{1+4} % in TeX
G:=Group("C14.85ES-(2,2)"); // GroupNames label
G:=SmallGroup(448,1118);
// by ID
G=gap.SmallGroup(448,1118);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,387,100,675,409,136,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=c^2=1,d^2=a^7*b^2,e^2=b^2,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,a*e=e*a,c*b*c=b^-1,d*b*d^-1=e*b*e^-1=a^7*b,c*d=d*c,c*e=e*c,e*d*e^-1=b^2*d>;
// generators/relations