G = C14.1482+ 1+4 order 448 = 26·7
57th non-split extension by C14 of 2+ 1+4 acting via 2+ 1+4/C4○D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.1482+ 1+4, (C7×Q8)⋊19D4, C7⋊5(Q8⋊6D4), C28⋊7D4⋊40C2, C28⋊2D4⋊44C2, C28⋊D4⋊31C2, (Q8×Dic7)⋊30C2, Q8⋊10(C7⋊D4), C28.268(C2×D4), Dic7⋊9(C4○D4), (C2×D4).239D14, (C2×Q8).211D14, (C2×C14).320C24, (C2×C28).562C23, D14⋊C4.91C22, (C22×C4).290D14, C14.170(C22×D4), C2.72(D4⋊8D14), (C2×D28).185C22, (D4×C14).278C22, C4⋊Dic7.261C22, (Q8×C14).246C22, C22.329(C23×D7), C23.141(C22×D7), Dic7⋊C4.175C22, (C22×C14).246C23, (C22×C28).298C22, (C4×Dic7).177C22, (C2×Dic7).166C23, (C22×D7).141C23, C23.D7.138C22, (C2×C4○D4)⋊12D7, (C4×C7⋊D4)⋊31C2, C4.74(C2×C7⋊D4), (C14×C4○D4)⋊12C2, C2.107(D7×C4○D4), (C2×Q8⋊2D7)⋊19C2, C14.219(C2×C4○D4), (C2×C4×D7).171C22, C2.43(C22×C7⋊D4), (C2×C4).642(C22×D7), (C2×C7⋊D4).143C22, SmallGroup(448,1287)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.1482+ 1+4
G = < a,b,c,d,e | a14=b4=c2=e2=1, d2=b2, ab=ba, ac=ca, ad=da, eae=a-1, cbc=b-1, bd=db, be=eb, cd=dc, ece=a7c, ede=a7b2d >
Subgroups: 1460 in 312 conjugacy classes, 113 normal (22 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, C2×C14, C2×C14, C4×D4, C4×Q8, C4⋊D4, C4⋊1D4, C2×C4○D4, C2×C4○D4, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C7×Q8, C22×D7, C22×C14, Q8⋊6D4, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C2×C4×D7, C2×D28, Q8⋊2D7, C2×C7⋊D4, C22×C28, D4×C14, Q8×C14, C7×C4○D4, C4×C7⋊D4, C28⋊7D4, C28⋊2D4, C28⋊D4, Q8×Dic7, C2×Q8⋊2D7, C14×C4○D4, C14.1482+ 1+4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C22×D4, C2×C4○D4, 2+ 1+4, C7⋊D4, C22×D7, Q8⋊6D4, C2×C7⋊D4, C23×D7, D7×C4○D4, D4⋊8D14, C22×C7⋊D4, C14.1482+ 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 89 27 102)(2 90 28 103)(3 91 15 104)(4 92 16 105)(5 93 17 106)(6 94 18 107)(7 95 19 108)(8 96 20 109)(9 97 21 110)(10 98 22 111)(11 85 23 112)(12 86 24 99)(13 87 25 100)(14 88 26 101)(29 73 49 63)(30 74 50 64)(31 75 51 65)(32 76 52 66)(33 77 53 67)(34 78 54 68)(35 79 55 69)(36 80 56 70)(37 81 43 57)(38 82 44 58)(39 83 45 59)(40 84 46 60)(41 71 47 61)(42 72 48 62)(113 222 127 205)(114 223 128 206)(115 224 129 207)(116 211 130 208)(117 212 131 209)(118 213 132 210)(119 214 133 197)(120 215 134 198)(121 216 135 199)(122 217 136 200)(123 218 137 201)(124 219 138 202)(125 220 139 203)(126 221 140 204)(141 181 158 183)(142 182 159 184)(143 169 160 185)(144 170 161 186)(145 171 162 187)(146 172 163 188)(147 173 164 189)(148 174 165 190)(149 175 166 191)(150 176 167 192)(151 177 168 193)(152 178 155 194)(153 179 156 195)(154 180 157 196)
(1 125)(2 126)(3 113)(4 114)(5 115)(6 116)(7 117)(8 118)(9 119)(10 120)(11 121)(12 122)(13 123)(14 124)(15 127)(16 128)(17 129)(18 130)(19 131)(20 132)(21 133)(22 134)(23 135)(24 136)(25 137)(26 138)(27 139)(28 140)(29 143)(30 144)(31 145)(32 146)(33 147)(34 148)(35 149)(36 150)(37 151)(38 152)(39 153)(40 154)(41 141)(42 142)(43 168)(44 155)(45 156)(46 157)(47 158)(48 159)(49 160)(50 161)(51 162)(52 163)(53 164)(54 165)(55 166)(56 167)(57 177)(58 178)(59 179)(60 180)(61 181)(62 182)(63 169)(64 170)(65 171)(66 172)(67 173)(68 174)(69 175)(70 176)(71 183)(72 184)(73 185)(74 186)(75 187)(76 188)(77 189)(78 190)(79 191)(80 192)(81 193)(82 194)(83 195)(84 196)(85 199)(86 200)(87 201)(88 202)(89 203)(90 204)(91 205)(92 206)(93 207)(94 208)(95 209)(96 210)(97 197)(98 198)(99 217)(100 218)(101 219)(102 220)(103 221)(104 222)(105 223)(106 224)(107 211)(108 212)(109 213)(110 214)(111 215)(112 216)
(1 47 27 41)(2 48 28 42)(3 49 15 29)(4 50 16 30)(5 51 17 31)(6 52 18 32)(7 53 19 33)(8 54 20 34)(9 55 21 35)(10 56 22 36)(11 43 23 37)(12 44 24 38)(13 45 25 39)(14 46 26 40)(57 112 81 85)(58 99 82 86)(59 100 83 87)(60 101 84 88)(61 102 71 89)(62 103 72 90)(63 104 73 91)(64 105 74 92)(65 106 75 93)(66 107 76 94)(67 108 77 95)(68 109 78 96)(69 110 79 97)(70 111 80 98)(113 160 127 143)(114 161 128 144)(115 162 129 145)(116 163 130 146)(117 164 131 147)(118 165 132 148)(119 166 133 149)(120 167 134 150)(121 168 135 151)(122 155 136 152)(123 156 137 153)(124 157 138 154)(125 158 139 141)(126 159 140 142)(169 222 185 205)(170 223 186 206)(171 224 187 207)(172 211 188 208)(173 212 189 209)(174 213 190 210)(175 214 191 197)(176 215 192 198)(177 216 193 199)(178 217 194 200)(179 218 195 201)(180 219 196 202)(181 220 183 203)(182 221 184 204)
(1 148)(2 147)(3 146)(4 145)(5 144)(6 143)(7 142)(8 141)(9 154)(10 153)(11 152)(12 151)(13 150)(14 149)(15 163)(16 162)(17 161)(18 160)(19 159)(20 158)(21 157)(22 156)(23 155)(24 168)(25 167)(26 166)(27 165)(28 164)(29 123)(30 122)(31 121)(32 120)(33 119)(34 118)(35 117)(36 116)(37 115)(38 114)(39 113)(40 126)(41 125)(42 124)(43 129)(44 128)(45 127)(46 140)(47 139)(48 138)(49 137)(50 136)(51 135)(52 134)(53 133)(54 132)(55 131)(56 130)(57 207)(58 206)(59 205)(60 204)(61 203)(62 202)(63 201)(64 200)(65 199)(66 198)(67 197)(68 210)(69 209)(70 208)(71 220)(72 219)(73 218)(74 217)(75 216)(76 215)(77 214)(78 213)(79 212)(80 211)(81 224)(82 223)(83 222)(84 221)(85 178)(86 177)(87 176)(88 175)(89 174)(90 173)(91 172)(92 171)(93 170)(94 169)(95 182)(96 181)(97 180)(98 179)(99 193)(100 192)(101 191)(102 190)(103 189)(104 188)(105 187)(106 186)(107 185)(108 184)(109 183)(110 196)(111 195)(112 194)
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), (1,89,27,102)(2,90,28,103)(3,91,15,104)(4,92,16,105)(5,93,17,106)(6,94,18,107)(7,95,19,108)(8,96,20,109)(9,97,21,110)(10,98,22,111)(11,85,23,112)(12,86,24,99)(13,87,25,100)(14,88,26,101)(29,73,49,63)(30,74,50,64)(31,75,51,65)(32,76,52,66)(33,77,53,67)(34,78,54,68)(35,79,55,69)(36,80,56,70)(37,81,43,57)(38,82,44,58)(39,83,45,59)(40,84,46,60)(41,71,47,61)(42,72,48,62)(113,222,127,205)(114,223,128,206)(115,224,129,207)(116,211,130,208)(117,212,131,209)(118,213,132,210)(119,214,133,197)(120,215,134,198)(121,216,135,199)(122,217,136,200)(123,218,137,201)(124,219,138,202)(125,220,139,203)(126,221,140,204)(141,181,158,183)(142,182,159,184)(143,169,160,185)(144,170,161,186)(145,171,162,187)(146,172,163,188)(147,173,164,189)(148,174,165,190)(149,175,166,191)(150,176,167,192)(151,177,168,193)(152,178,155,194)(153,179,156,195)(154,180,157,196), (1,125)(2,126)(3,113)(4,114)(5,115)(6,116)(7,117)(8,118)(9,119)(10,120)(11,121)(12,122)(13,123)(14,124)(15,127)(16,128)(17,129)(18,130)(19,131)(20,132)(21,133)(22,134)(23,135)(24,136)(25,137)(26,138)(27,139)(28,140)(29,143)(30,144)(31,145)(32,146)(33,147)(34,148)(35,149)(36,150)(37,151)(38,152)(39,153)(40,154)(41,141)(42,142)(43,168)(44,155)(45,156)(46,157)(47,158)(48,159)(49,160)(50,161)(51,162)(52,163)(53,164)(54,165)(55,166)(56,167)(57,177)(58,178)(59,179)(60,180)(61,181)(62,182)(63,169)(64,170)(65,171)(66,172)(67,173)(68,174)(69,175)(70,176)(71,183)(72,184)(73,185)(74,186)(75,187)(76,188)(77,189)(78,190)(79,191)(80,192)(81,193)(82,194)(83,195)(84,196)(85,199)(86,200)(87,201)(88,202)(89,203)(90,204)(91,205)(92,206)(93,207)(94,208)(95,209)(96,210)(97,197)(98,198)(99,217)(100,218)(101,219)(102,220)(103,221)(104,222)(105,223)(106,224)(107,211)(108,212)(109,213)(110,214)(111,215)(112,216), (1,47,27,41)(2,48,28,42)(3,49,15,29)(4,50,16,30)(5,51,17,31)(6,52,18,32)(7,53,19,33)(8,54,20,34)(9,55,21,35)(10,56,22,36)(11,43,23,37)(12,44,24,38)(13,45,25,39)(14,46,26,40)(57,112,81,85)(58,99,82,86)(59,100,83,87)(60,101,84,88)(61,102,71,89)(62,103,72,90)(63,104,73,91)(64,105,74,92)(65,106,75,93)(66,107,76,94)(67,108,77,95)(68,109,78,96)(69,110,79,97)(70,111,80,98)(113,160,127,143)(114,161,128,144)(115,162,129,145)(116,163,130,146)(117,164,131,147)(118,165,132,148)(119,166,133,149)(120,167,134,150)(121,168,135,151)(122,155,136,152)(123,156,137,153)(124,157,138,154)(125,158,139,141)(126,159,140,142)(169,222,185,205)(170,223,186,206)(171,224,187,207)(172,211,188,208)(173,212,189,209)(174,213,190,210)(175,214,191,197)(176,215,192,198)(177,216,193,199)(178,217,194,200)(179,218,195,201)(180,219,196,202)(181,220,183,203)(182,221,184,204), (1,148)(2,147)(3,146)(4,145)(5,144)(6,143)(7,142)(8,141)(9,154)(10,153)(11,152)(12,151)(13,150)(14,149)(15,163)(16,162)(17,161)(18,160)(19,159)(20,158)(21,157)(22,156)(23,155)(24,168)(25,167)(26,166)(27,165)(28,164)(29,123)(30,122)(31,121)(32,120)(33,119)(34,118)(35,117)(36,116)(37,115)(38,114)(39,113)(40,126)(41,125)(42,124)(43,129)(44,128)(45,127)(46,140)(47,139)(48,138)(49,137)(50,136)(51,135)(52,134)(53,133)(54,132)(55,131)(56,130)(57,207)(58,206)(59,205)(60,204)(61,203)(62,202)(63,201)(64,200)(65,199)(66,198)(67,197)(68,210)(69,209)(70,208)(71,220)(72,219)(73,218)(74,217)(75,216)(76,215)(77,214)(78,213)(79,212)(80,211)(81,224)(82,223)(83,222)(84,221)(85,178)(86,177)(87,176)(88,175)(89,174)(90,173)(91,172)(92,171)(93,170)(94,169)(95,182)(96,181)(97,180)(98,179)(99,193)(100,192)(101,191)(102,190)(103,189)(104,188)(105,187)(106,186)(107,185)(108,184)(109,183)(110,196)(111,195)(112,194)>;
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), (1,89,27,102)(2,90,28,103)(3,91,15,104)(4,92,16,105)(5,93,17,106)(6,94,18,107)(7,95,19,108)(8,96,20,109)(9,97,21,110)(10,98,22,111)(11,85,23,112)(12,86,24,99)(13,87,25,100)(14,88,26,101)(29,73,49,63)(30,74,50,64)(31,75,51,65)(32,76,52,66)(33,77,53,67)(34,78,54,68)(35,79,55,69)(36,80,56,70)(37,81,43,57)(38,82,44,58)(39,83,45,59)(40,84,46,60)(41,71,47,61)(42,72,48,62)(113,222,127,205)(114,223,128,206)(115,224,129,207)(116,211,130,208)(117,212,131,209)(118,213,132,210)(119,214,133,197)(120,215,134,198)(121,216,135,199)(122,217,136,200)(123,218,137,201)(124,219,138,202)(125,220,139,203)(126,221,140,204)(141,181,158,183)(142,182,159,184)(143,169,160,185)(144,170,161,186)(145,171,162,187)(146,172,163,188)(147,173,164,189)(148,174,165,190)(149,175,166,191)(150,176,167,192)(151,177,168,193)(152,178,155,194)(153,179,156,195)(154,180,157,196), (1,125)(2,126)(3,113)(4,114)(5,115)(6,116)(7,117)(8,118)(9,119)(10,120)(11,121)(12,122)(13,123)(14,124)(15,127)(16,128)(17,129)(18,130)(19,131)(20,132)(21,133)(22,134)(23,135)(24,136)(25,137)(26,138)(27,139)(28,140)(29,143)(30,144)(31,145)(32,146)(33,147)(34,148)(35,149)(36,150)(37,151)(38,152)(39,153)(40,154)(41,141)(42,142)(43,168)(44,155)(45,156)(46,157)(47,158)(48,159)(49,160)(50,161)(51,162)(52,163)(53,164)(54,165)(55,166)(56,167)(57,177)(58,178)(59,179)(60,180)(61,181)(62,182)(63,169)(64,170)(65,171)(66,172)(67,173)(68,174)(69,175)(70,176)(71,183)(72,184)(73,185)(74,186)(75,187)(76,188)(77,189)(78,190)(79,191)(80,192)(81,193)(82,194)(83,195)(84,196)(85,199)(86,200)(87,201)(88,202)(89,203)(90,204)(91,205)(92,206)(93,207)(94,208)(95,209)(96,210)(97,197)(98,198)(99,217)(100,218)(101,219)(102,220)(103,221)(104,222)(105,223)(106,224)(107,211)(108,212)(109,213)(110,214)(111,215)(112,216), (1,47,27,41)(2,48,28,42)(3,49,15,29)(4,50,16,30)(5,51,17,31)(6,52,18,32)(7,53,19,33)(8,54,20,34)(9,55,21,35)(10,56,22,36)(11,43,23,37)(12,44,24,38)(13,45,25,39)(14,46,26,40)(57,112,81,85)(58,99,82,86)(59,100,83,87)(60,101,84,88)(61,102,71,89)(62,103,72,90)(63,104,73,91)(64,105,74,92)(65,106,75,93)(66,107,76,94)(67,108,77,95)(68,109,78,96)(69,110,79,97)(70,111,80,98)(113,160,127,143)(114,161,128,144)(115,162,129,145)(116,163,130,146)(117,164,131,147)(118,165,132,148)(119,166,133,149)(120,167,134,150)(121,168,135,151)(122,155,136,152)(123,156,137,153)(124,157,138,154)(125,158,139,141)(126,159,140,142)(169,222,185,205)(170,223,186,206)(171,224,187,207)(172,211,188,208)(173,212,189,209)(174,213,190,210)(175,214,191,197)(176,215,192,198)(177,216,193,199)(178,217,194,200)(179,218,195,201)(180,219,196,202)(181,220,183,203)(182,221,184,204), (1,148)(2,147)(3,146)(4,145)(5,144)(6,143)(7,142)(8,141)(9,154)(10,153)(11,152)(12,151)(13,150)(14,149)(15,163)(16,162)(17,161)(18,160)(19,159)(20,158)(21,157)(22,156)(23,155)(24,168)(25,167)(26,166)(27,165)(28,164)(29,123)(30,122)(31,121)(32,120)(33,119)(34,118)(35,117)(36,116)(37,115)(38,114)(39,113)(40,126)(41,125)(42,124)(43,129)(44,128)(45,127)(46,140)(47,139)(48,138)(49,137)(50,136)(51,135)(52,134)(53,133)(54,132)(55,131)(56,130)(57,207)(58,206)(59,205)(60,204)(61,203)(62,202)(63,201)(64,200)(65,199)(66,198)(67,197)(68,210)(69,209)(70,208)(71,220)(72,219)(73,218)(74,217)(75,216)(76,215)(77,214)(78,213)(79,212)(80,211)(81,224)(82,223)(83,222)(84,221)(85,178)(86,177)(87,176)(88,175)(89,174)(90,173)(91,172)(92,171)(93,170)(94,169)(95,182)(96,181)(97,180)(98,179)(99,193)(100,192)(101,191)(102,190)(103,189)(104,188)(105,187)(106,186)(107,185)(108,184)(109,183)(110,196)(111,195)(112,194) );
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)], [(1,89,27,102),(2,90,28,103),(3,91,15,104),(4,92,16,105),(5,93,17,106),(6,94,18,107),(7,95,19,108),(8,96,20,109),(9,97,21,110),(10,98,22,111),(11,85,23,112),(12,86,24,99),(13,87,25,100),(14,88,26,101),(29,73,49,63),(30,74,50,64),(31,75,51,65),(32,76,52,66),(33,77,53,67),(34,78,54,68),(35,79,55,69),(36,80,56,70),(37,81,43,57),(38,82,44,58),(39,83,45,59),(40,84,46,60),(41,71,47,61),(42,72,48,62),(113,222,127,205),(114,223,128,206),(115,224,129,207),(116,211,130,208),(117,212,131,209),(118,213,132,210),(119,214,133,197),(120,215,134,198),(121,216,135,199),(122,217,136,200),(123,218,137,201),(124,219,138,202),(125,220,139,203),(126,221,140,204),(141,181,158,183),(142,182,159,184),(143,169,160,185),(144,170,161,186),(145,171,162,187),(146,172,163,188),(147,173,164,189),(148,174,165,190),(149,175,166,191),(150,176,167,192),(151,177,168,193),(152,178,155,194),(153,179,156,195),(154,180,157,196)], [(1,125),(2,126),(3,113),(4,114),(5,115),(6,116),(7,117),(8,118),(9,119),(10,120),(11,121),(12,122),(13,123),(14,124),(15,127),(16,128),(17,129),(18,130),(19,131),(20,132),(21,133),(22,134),(23,135),(24,136),(25,137),(26,138),(27,139),(28,140),(29,143),(30,144),(31,145),(32,146),(33,147),(34,148),(35,149),(36,150),(37,151),(38,152),(39,153),(40,154),(41,141),(42,142),(43,168),(44,155),(45,156),(46,157),(47,158),(48,159),(49,160),(50,161),(51,162),(52,163),(53,164),(54,165),(55,166),(56,167),(57,177),(58,178),(59,179),(60,180),(61,181),(62,182),(63,169),(64,170),(65,171),(66,172),(67,173),(68,174),(69,175),(70,176),(71,183),(72,184),(73,185),(74,186),(75,187),(76,188),(77,189),(78,190),(79,191),(80,192),(81,193),(82,194),(83,195),(84,196),(85,199),(86,200),(87,201),(88,202),(89,203),(90,204),(91,205),(92,206),(93,207),(94,208),(95,209),(96,210),(97,197),(98,198),(99,217),(100,218),(101,219),(102,220),(103,221),(104,222),(105,223),(106,224),(107,211),(108,212),(109,213),(110,214),(111,215),(112,216)], [(1,47,27,41),(2,48,28,42),(3,49,15,29),(4,50,16,30),(5,51,17,31),(6,52,18,32),(7,53,19,33),(8,54,20,34),(9,55,21,35),(10,56,22,36),(11,43,23,37),(12,44,24,38),(13,45,25,39),(14,46,26,40),(57,112,81,85),(58,99,82,86),(59,100,83,87),(60,101,84,88),(61,102,71,89),(62,103,72,90),(63,104,73,91),(64,105,74,92),(65,106,75,93),(66,107,76,94),(67,108,77,95),(68,109,78,96),(69,110,79,97),(70,111,80,98),(113,160,127,143),(114,161,128,144),(115,162,129,145),(116,163,130,146),(117,164,131,147),(118,165,132,148),(119,166,133,149),(120,167,134,150),(121,168,135,151),(122,155,136,152),(123,156,137,153),(124,157,138,154),(125,158,139,141),(126,159,140,142),(169,222,185,205),(170,223,186,206),(171,224,187,207),(172,211,188,208),(173,212,189,209),(174,213,190,210),(175,214,191,197),(176,215,192,198),(177,216,193,199),(178,217,194,200),(179,218,195,201),(180,219,196,202),(181,220,183,203),(182,221,184,204)], [(1,148),(2,147),(3,146),(4,145),(5,144),(6,143),(7,142),(8,141),(9,154),(10,153),(11,152),(12,151),(13,150),(14,149),(15,163),(16,162),(17,161),(18,160),(19,159),(20,158),(21,157),(22,156),(23,155),(24,168),(25,167),(26,166),(27,165),(28,164),(29,123),(30,122),(31,121),(32,120),(33,119),(34,118),(35,117),(36,116),(37,115),(38,114),(39,113),(40,126),(41,125),(42,124),(43,129),(44,128),(45,127),(46,140),(47,139),(48,138),(49,137),(50,136),(51,135),(52,134),(53,133),(54,132),(55,131),(56,130),(57,207),(58,206),(59,205),(60,204),(61,203),(62,202),(63,201),(64,200),(65,199),(66,198),(67,197),(68,210),(69,209),(70,208),(71,220),(72,219),(73,218),(74,217),(75,216),(76,215),(77,214),(78,213),(79,212),(80,211),(81,224),(82,223),(83,222),(84,221),(85,178),(86,177),(87,176),(88,175),(89,174),(90,173),(91,172),(92,171),(93,170),(94,169),(95,182),(96,181),(97,180),(98,179),(99,193),(100,192),(101,191),(102,190),(103,189),(104,188),(105,187),(106,186),(107,185),(108,184),(109,183),(110,196),(111,195),(112,194)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14AA | 28A | ··· | 28L | 28M | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 4 | 4 | 4 | 28 | 28 | 28 | 2 | ··· | 2 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | C7⋊D4 | 2+ 1+4 | D7×C4○D4 | D4⋊8D14 |
| kernel | C14.1482+ 1+4 | C4×C7⋊D4 | C28⋊7D4 | C28⋊2D4 | C28⋊D4 | Q8×Dic7 | C2×Q8⋊2D7 | C14×C4○D4 | C7×Q8 | C2×C4○D4 | Dic7 | C22×C4 | C2×D4 | C2×Q8 | Q8 | C14 | C2 | C2 |
| # reps | 1 | 3 | 3 | 3 | 3 | 1 | 1 | 1 | 4 | 3 | 4 | 9 | 9 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of C14.1482+ 1+4 ►in GL4(𝔽29) generated by
| 19 | 19 | 0 | 0 |
| 10 | 7 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 28 |
| 28 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 28 | 5 |
| 0 | 0 | 17 | 1 |
| 9 | 14 | 0 | 0 |
| 15 | 20 | 0 | 0 |
| 0 | 0 | 1 | 24 |
| 0 | 0 | 0 | 28 |
| 9 | 14 | 0 | 0 |
| 15 | 20 | 0 | 0 |
| 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 12 |
| 1 | 0 | 0 | 0 |
| 7 | 28 | 0 | 0 |
| 0 | 0 | 12 | 27 |
| 0 | 0 | 28 | 17 |
G:=sub<GL(4,GF(29))| [19,10,0,0,19,7,0,0,0,0,28,0,0,0,0,28],[28,0,0,0,0,28,0,0,0,0,28,17,0,0,5,1],[9,15,0,0,14,20,0,0,0,0,1,0,0,0,24,28],[9,15,0,0,14,20,0,0,0,0,12,0,0,0,0,12],[1,7,0,0,0,28,0,0,0,0,12,28,0,0,27,17] >;
C14.1482+ 1+4 in GAP, Magma, Sage, TeX
C_{14}._{148}2_+^{1+4} % in TeX
G:=Group("C14.148ES+(2,2)"); // GroupNames label
G:=SmallGroup(448,1287);
// by ID
G=gap.SmallGroup(448,1287);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,758,219,1571,80,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=c^2=e^2=1,d^2=b^2,a*b=b*a,a*c=c*a,a*d=d*a,e*a*e=a^-1,c*b*c=b^-1,b*d=d*b,b*e=e*b,c*d=d*c,e*c*e=a^7*c,e*d*e=a^7*b^2*d>;
// generators/relations