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G = C14.632+ 1+4order 448 = 26·7

63rd non-split extension by C14 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C14.632+ 1+4, C14.832- 1+4, C4⋊C4.107D14, D14⋊Q831C2, D14.7(C4○D4), (C2×D4).100D14, C282D4.11C2, Dic7.Q827C2, C22⋊C4.28D14, C4.Dic1429C2, C22.D49D7, Dic74D422C2, D14.D433C2, C28.48D422C2, (C2×C14).204C24, (C2×C28).180C23, (C22×C4).259D14, C2.65(D46D14), C23.28(C22×D7), D14⋊C4.108C22, C22⋊Dic1433C2, (D4×C14).142C22, C23.D1432C2, Dic7⋊C4.42C22, C4⋊Dic7.228C22, (C22×C14).36C23, C22.225(C23×D7), C23.D7.44C22, C23.18D1415C2, (C22×C28).115C22, C76(C22.33C24), (C2×Dic14).37C22, (C2×Dic7).106C23, (C4×Dic7).124C22, (C22×D7).210C23, C2.44(D4.10D14), (C22×Dic7).130C22, (D7×C4⋊C4)⋊33C2, (C4×C7⋊D4)⋊7C2, C2.66(D7×C4○D4), C14.178(C2×C4○D4), (C2×C4×D7).113C22, (C2×C4).66(C22×D7), (C7×C4⋊C4).177C22, (C2×C7⋊D4).48C22, (C7×C22.D4)⋊12C2, (C7×C22⋊C4).52C22, SmallGroup(448,1113)

Series: Derived Chief Lower central Upper central

C1C2×C14 — C14.632+ 1+4
C1C7C14C2×C14C22×D7C2×C4×D7D7×C4⋊C4 — C14.632+ 1+4
C7C2×C14 — C14.632+ 1+4
C1C22C22.D4

Generators and relations for C14.632+ 1+4
 G = < a,b,c,d,e | a14=b4=e2=1, c2=a7, d2=b2, ab=ba, ac=ca, dad-1=a-1, ae=ea, cbc-1=b-1, dbd-1=ebe=a7b, cd=dc, ce=ec, ede=b2d >

Subgroups: 940 in 218 conjugacy classes, 93 normal (91 characteristic)
C1, C2 [×3], C2 [×4], C4 [×12], C22, C22 [×10], C7, C2×C4 [×5], C2×C4 [×13], D4 [×5], Q8, C23 [×2], C23, D7 [×2], C14 [×3], C14 [×2], C42 [×2], C22⋊C4 [×3], C22⋊C4 [×7], C4⋊C4 [×2], C4⋊C4 [×12], C22×C4, C22×C4 [×4], C2×D4, C2×D4 [×2], C2×Q8, Dic7 [×7], C28 [×5], D14 [×2], D14 [×2], C2×C14, C2×C14 [×6], C2×C4⋊C4, C4×D4 [×2], C4⋊D4, C22⋊Q8 [×3], C22.D4, C22.D4 [×3], C42.C2 [×2], C422C2 [×2], Dic14, C4×D7 [×4], C2×Dic7 [×7], C2×Dic7, C7⋊D4 [×4], C2×C28 [×5], C2×C28, C7×D4, C22×D7, C22×C14 [×2], C22.33C24, C4×Dic7 [×2], Dic7⋊C4 [×8], C4⋊Dic7 [×4], D14⋊C4 [×2], C23.D7 [×5], C7×C22⋊C4 [×3], C7×C4⋊C4 [×2], C2×Dic14, C2×C4×D7 [×3], C22×Dic7, C2×C7⋊D4 [×2], C22×C28, D4×C14, C22⋊Dic14, C23.D14 [×2], Dic74D4, D14.D4 [×2], Dic7.Q8, C4.Dic14, D7×C4⋊C4, D14⋊Q8, C28.48D4, C4×C7⋊D4, C23.18D14, C282D4, C7×C22.D4, C14.632+ 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], C22.33C24, C23×D7, D46D14, D7×C4○D4, D4.10D14, C14.632+ 1+4

Smallest permutation representation of C14.632+ 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)
(1 189 15 170)(2 190 16 171)(3 191 17 172)(4 192 18 173)(5 193 19 174)(6 194 20 175)(7 195 21 176)(8 196 22 177)(9 183 23 178)(10 184 24 179)(11 185 25 180)(12 186 26 181)(13 187 27 182)(14 188 28 169)(29 217 43 208)(30 218 44 209)(31 219 45 210)(32 220 46 197)(33 221 47 198)(34 222 48 199)(35 223 49 200)(36 224 50 201)(37 211 51 202)(38 212 52 203)(39 213 53 204)(40 214 54 205)(41 215 55 206)(42 216 56 207)(57 131 80 118)(58 132 81 119)(59 133 82 120)(60 134 83 121)(61 135 84 122)(62 136 71 123)(63 137 72 124)(64 138 73 125)(65 139 74 126)(66 140 75 113)(67 127 76 114)(68 128 77 115)(69 129 78 116)(70 130 79 117)(85 164 107 150)(86 165 108 151)(87 166 109 152)(88 167 110 153)(89 168 111 154)(90 155 112 141)(91 156 99 142)(92 157 100 143)(93 158 101 144)(94 159 102 145)(95 160 103 146)(96 161 104 147)(97 162 105 148)(98 163 106 149)
(1 124 8 117)(2 125 9 118)(3 126 10 119)(4 113 11 120)(5 114 12 121)(6 115 13 122)(7 116 14 123)(15 137 22 130)(16 138 23 131)(17 139 24 132)(18 140 25 133)(19 127 26 134)(20 128 27 135)(21 129 28 136)(29 150 36 143)(30 151 37 144)(31 152 38 145)(32 153 39 146)(33 154 40 147)(34 141 41 148)(35 142 42 149)(43 164 50 157)(44 165 51 158)(45 166 52 159)(46 167 53 160)(47 168 54 161)(48 155 55 162)(49 156 56 163)(57 171 64 178)(58 172 65 179)(59 173 66 180)(60 174 67 181)(61 175 68 182)(62 176 69 169)(63 177 70 170)(71 195 78 188)(72 196 79 189)(73 183 80 190)(74 184 81 191)(75 185 82 192)(76 186 83 193)(77 187 84 194)(85 201 92 208)(86 202 93 209)(87 203 94 210)(88 204 95 197)(89 205 96 198)(90 206 97 199)(91 207 98 200)(99 216 106 223)(100 217 107 224)(101 218 108 211)(102 219 109 212)(103 220 110 213)(104 221 111 214)(105 222 112 215)
(1 55 15 41)(2 54 16 40)(3 53 17 39)(4 52 18 38)(5 51 19 37)(6 50 20 36)(7 49 21 35)(8 48 22 34)(9 47 23 33)(10 46 24 32)(11 45 25 31)(12 44 26 30)(13 43 27 29)(14 56 28 42)(57 104 80 96)(58 103 81 95)(59 102 82 94)(60 101 83 93)(61 100 84 92)(62 99 71 91)(63 112 72 90)(64 111 73 89)(65 110 74 88)(66 109 75 87)(67 108 76 86)(68 107 77 85)(69 106 78 98)(70 105 79 97)(113 159 140 145)(114 158 127 144)(115 157 128 143)(116 156 129 142)(117 155 130 141)(118 168 131 154)(119 167 132 153)(120 166 133 152)(121 165 134 151)(122 164 135 150)(123 163 136 149)(124 162 137 148)(125 161 138 147)(126 160 139 146)(169 223 188 200)(170 222 189 199)(171 221 190 198)(172 220 191 197)(173 219 192 210)(174 218 193 209)(175 217 194 208)(176 216 195 207)(177 215 196 206)(178 214 183 205)(179 213 184 204)(180 212 185 203)(181 211 186 202)(182 224 187 201)
(1 41)(2 42)(3 29)(4 30)(5 31)(6 32)(7 33)(8 34)(9 35)(10 36)(11 37)(12 38)(13 39)(14 40)(15 55)(16 56)(17 43)(18 44)(19 45)(20 46)(21 47)(22 48)(23 49)(24 50)(25 51)(26 52)(27 53)(28 54)(57 98)(58 85)(59 86)(60 87)(61 88)(62 89)(63 90)(64 91)(65 92)(66 93)(67 94)(68 95)(69 96)(70 97)(71 111)(72 112)(73 99)(74 100)(75 101)(76 102)(77 103)(78 104)(79 105)(80 106)(81 107)(82 108)(83 109)(84 110)(113 151)(114 152)(115 153)(116 154)(117 141)(118 142)(119 143)(120 144)(121 145)(122 146)(123 147)(124 148)(125 149)(126 150)(127 166)(128 167)(129 168)(130 155)(131 156)(132 157)(133 158)(134 159)(135 160)(136 161)(137 162)(138 163)(139 164)(140 165)(169 198)(170 199)(171 200)(172 201)(173 202)(174 203)(175 204)(176 205)(177 206)(178 207)(179 208)(180 209)(181 210)(182 197)(183 216)(184 217)(185 218)(186 219)(187 220)(188 221)(189 222)(190 223)(191 224)(192 211)(193 212)(194 213)(195 214)(196 215)

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

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

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

64 conjugacy classes

class 1 2A2B2C2D2E2F2G4A4B4C4D4E4F4G4H4I···4N7A7B7C14A···14I14J···14O14P14Q14R28A···28L28M···28U
order12222222444444444···477714···1414···1414141428···2828···28
size1111441414224444141428···282222···24···48884···48···8

64 irreducible representations

dim1111111111111122222244444
type++++++++++++++++++++--
imageC1C2C2C2C2C2C2C2C2C2C2C2C2C2D7C4○D4D14D14D14D142+ 1+42- 1+4D46D14D7×C4○D4D4.10D14
kernelC14.632+ 1+4C22⋊Dic14C23.D14Dic74D4D14.D4Dic7.Q8C4.Dic14D7×C4⋊C4D14⋊Q8C28.48D4C4×C7⋊D4C23.18D14C282D4C7×C22.D4C22.D4D14C22⋊C4C4⋊C4C22×C4C2×D4C14C14C2C2C2
# reps1121211111111134963311666

Matrix representation of C14.632+ 1+4 in GL8(𝔽29)

2121000000
826000000
002800000
000280000
000028000
000002800
000000280
000000028
,
280000000
028000000
000120000
001700000
0000230170
000017817
000020060
00001192722
,
280000000
028000000
001200000
000120000
000070180
000017231411
0000230220
00001423236
,
280000000
261000000
00100000
000280000
0000212800
00007800
00002012171
00002610012
,
280000000
028000000
002800000
00010000
0000212800
00005800
00002012171
00002110212

G:=sub<GL(8,GF(29))| [21,8,0,0,0,0,0,0,21,26,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,0,17,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,23,1,20,11,0,0,0,0,0,7,0,9,0,0,0,0,17,8,6,27,0,0,0,0,0,17,0,22],[28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,7,17,23,14,0,0,0,0,0,23,0,23,0,0,0,0,18,14,22,23,0,0,0,0,0,11,0,6],[28,26,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,21,7,20,26,0,0,0,0,28,8,12,10,0,0,0,0,0,0,17,0,0,0,0,0,0,0,1,12],[28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,21,5,20,21,0,0,0,0,28,8,12,10,0,0,0,0,0,0,17,2,0,0,0,0,0,0,1,12] >;

C14.632+ 1+4 in GAP, Magma, Sage, TeX

C_{14}._{63}2_+^{1+4}
% in TeX

G:=Group("C14.63ES+(2,2)");
// GroupNames label

G:=SmallGroup(448,1113);
// by ID

G=gap.SmallGroup(448,1113);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,219,184,675,297,18822]);
// Polycyclic

G:=Group<a,b,c,d,e|a^14=b^4=e^2=1,c^2=a^7,d^2=b^2,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,a*e=e*a,c*b*c^-1=b^-1,d*b*d^-1=e*b*e=a^7*b,c*d=d*c,c*e=e*c,e*d*e=b^2*d>;
// generators/relations

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