G = C14.732- 1+4 order 448 = 26·7
28th non-split extension by C14 of 2- 1+4 acting via 2- 1+4/C4○D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.732- 1+4, C7⋊D4⋊3D4, C28⋊Q8⋊20C2, C4⋊D4⋊14D7, C7⋊4(D4⋊6D4), C28⋊10(C4○D4), C28⋊2D4⋊20C2, C4⋊4(D4⋊2D7), C22.7(D4×D7), C4⋊C4.181D14, (D4×Dic7)⋊21C2, D14.18(C2×D4), C22⋊C4.9D14, (C2×D4).155D14, Dic7.23(C2×D4), C14.70(C22×D4), D14.D4⋊19C2, (C2×C28).174C23, (C2×C14).155C24, (C22×C4).224D14, D14⋊C4.105C22, C22⋊Dic14⋊20C2, (D4×C14).123C22, C4⋊Dic7.371C22, (C22×C14).22C23, (C4×Dic7).95C22, C23.183(C22×D7), C22.176(C23×D7), C23.18D14⋊10C2, Dic7⋊C4.117C22, (C22×C28).242C22, (C2×Dic7).228C23, (C22×D7).189C23, C23.D7.111C22, C2.31(D4.10D14), (C2×Dic14).155C22, (C22×Dic7).110C22, C2.43(C2×D4×D7), (D7×C4⋊C4)⋊22C2, (C4×C7⋊D4)⋊17C2, (C2×C14).7(C2×D4), (C7×C4⋊D4)⋊17C2, (C2×C4⋊Dic7)⋊40C2, C14.84(C2×C4○D4), (C2×D4⋊2D7)⋊15C2, (C2×C4×D7).84C22, C2.37(C2×D4⋊2D7), (C7×C4⋊C4).145C22, (C2×C4).587(C22×D7), (C2×C7⋊D4).29C22, (C7×C22⋊C4).14C22, SmallGroup(448,1064)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.732- 1+4
G = < a,b,c,d,e | a14=b4=c2=1, d2=b2, e2=a7b2, bab-1=dad-1=a-1, ac=ca, ae=ea, cbc=b-1, bd=db, be=eb, cd=dc, ce=ec, ede-1=a7b2d >
Subgroups: 1260 in 292 conjugacy classes, 107 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, 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, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C14, C2×C4⋊C4, C4×D4, C4⋊D4, C4⋊D4, C22⋊Q8, C22.D4, C4⋊Q8, C2×C4○D4, Dic14, C4×D7, C2×Dic7, C2×Dic7, C2×Dic7, C7⋊D4, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C22×C14, D4⋊6D4, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C23.D7, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×C4×D7, D4⋊2D7, C22×Dic7, C2×C7⋊D4, C2×C7⋊D4, C22×C28, D4×C14, D4×C14, C22⋊Dic14, D14.D4, C28⋊Q8, D7×C4⋊C4, C2×C4⋊Dic7, C4×C7⋊D4, D4×Dic7, C23.18D14, C28⋊2D4, C7×C4⋊D4, C2×D4⋊2D7, C14.732- 1+4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C22×D4, C2×C4○D4, 2- 1+4, C22×D7, D4⋊6D4, D4×D7, D4⋊2D7, C23×D7, C2×D4×D7, C2×D4⋊2D7, D4.10D14, C14.732- 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 79 37)(2 88 80 36)(3 87 81 35)(4 86 82 34)(5 85 83 33)(6 98 84 32)(7 97 71 31)(8 96 72 30)(9 95 73 29)(10 94 74 42)(11 93 75 41)(12 92 76 40)(13 91 77 39)(14 90 78 38)(15 141 166 102)(16 154 167 101)(17 153 168 100)(18 152 155 99)(19 151 156 112)(20 150 157 111)(21 149 158 110)(22 148 159 109)(23 147 160 108)(24 146 161 107)(25 145 162 106)(26 144 163 105)(27 143 164 104)(28 142 165 103)(43 207 60 196)(44 206 61 195)(45 205 62 194)(46 204 63 193)(47 203 64 192)(48 202 65 191)(49 201 66 190)(50 200 67 189)(51 199 68 188)(52 198 69 187)(53 197 70 186)(54 210 57 185)(55 209 58 184)(56 208 59 183)(113 181 127 216)(114 180 128 215)(115 179 129 214)(116 178 130 213)(117 177 131 212)(118 176 132 211)(119 175 133 224)(120 174 134 223)(121 173 135 222)(122 172 136 221)(123 171 137 220)(124 170 138 219)(125 169 139 218)(126 182 140 217)
(1 30)(2 31)(3 32)(4 33)(5 34)(6 35)(7 36)(8 37)(9 38)(10 39)(11 40)(12 41)(13 42)(14 29)(15 144)(16 145)(17 146)(18 147)(19 148)(20 149)(21 150)(22 151)(23 152)(24 153)(25 154)(26 141)(27 142)(28 143)(43 208)(44 209)(45 210)(46 197)(47 198)(48 199)(49 200)(50 201)(51 202)(52 203)(53 204)(54 205)(55 206)(56 207)(57 194)(58 195)(59 196)(60 183)(61 184)(62 185)(63 186)(64 187)(65 188)(66 189)(67 190)(68 191)(69 192)(70 193)(71 88)(72 89)(73 90)(74 91)(75 92)(76 93)(77 94)(78 95)(79 96)(80 97)(81 98)(82 85)(83 86)(84 87)(99 160)(100 161)(101 162)(102 163)(103 164)(104 165)(105 166)(106 167)(107 168)(108 155)(109 156)(110 157)(111 158)(112 159)(113 176)(114 177)(115 178)(116 179)(117 180)(118 181)(119 182)(120 169)(121 170)(122 171)(123 172)(124 173)(125 174)(126 175)(127 211)(128 212)(129 213)(130 214)(131 215)(132 216)(133 217)(134 218)(135 219)(136 220)(137 221)(138 222)(139 223)(140 224)
(1 193 79 204)(2 192 80 203)(3 191 81 202)(4 190 82 201)(5 189 83 200)(6 188 84 199)(7 187 71 198)(8 186 72 197)(9 185 73 210)(10 184 74 209)(11 183 75 208)(12 196 76 207)(13 195 77 206)(14 194 78 205)(15 114 166 128)(16 113 167 127)(17 126 168 140)(18 125 155 139)(19 124 156 138)(20 123 157 137)(21 122 158 136)(22 121 159 135)(23 120 160 134)(24 119 161 133)(25 118 162 132)(26 117 163 131)(27 116 164 130)(28 115 165 129)(29 57 95 54)(30 70 96 53)(31 69 97 52)(32 68 98 51)(33 67 85 50)(34 66 86 49)(35 65 87 48)(36 64 88 47)(37 63 89 46)(38 62 90 45)(39 61 91 44)(40 60 92 43)(41 59 93 56)(42 58 94 55)(99 218 152 169)(100 217 153 182)(101 216 154 181)(102 215 141 180)(103 214 142 179)(104 213 143 178)(105 212 144 177)(106 211 145 176)(107 224 146 175)(108 223 147 174)(109 222 148 173)(110 221 149 172)(111 220 150 171)(112 219 151 170)
(1 107 72 153)(2 108 73 154)(3 109 74 141)(4 110 75 142)(5 111 76 143)(6 112 77 144)(7 99 78 145)(8 100 79 146)(9 101 80 147)(10 102 81 148)(11 103 82 149)(12 104 83 150)(13 105 84 151)(14 106 71 152)(15 35 159 94)(16 36 160 95)(17 37 161 96)(18 38 162 97)(19 39 163 98)(20 40 164 85)(21 41 165 86)(22 42 166 87)(23 29 167 88)(24 30 168 89)(25 31 155 90)(26 32 156 91)(27 33 157 92)(28 34 158 93)(43 137 67 116)(44 138 68 117)(45 139 69 118)(46 140 70 119)(47 127 57 120)(48 128 58 121)(49 129 59 122)(50 130 60 123)(51 131 61 124)(52 132 62 125)(53 133 63 126)(54 134 64 113)(55 135 65 114)(56 136 66 115)(169 198 211 194)(170 199 212 195)(171 200 213 196)(172 201 214 183)(173 202 215 184)(174 203 216 185)(175 204 217 186)(176 205 218 187)(177 206 219 188)(178 207 220 189)(179 208 221 190)(180 209 222 191)(181 210 223 192)(182 197 224 193)
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), (1,89,79,37)(2,88,80,36)(3,87,81,35)(4,86,82,34)(5,85,83,33)(6,98,84,32)(7,97,71,31)(8,96,72,30)(9,95,73,29)(10,94,74,42)(11,93,75,41)(12,92,76,40)(13,91,77,39)(14,90,78,38)(15,141,166,102)(16,154,167,101)(17,153,168,100)(18,152,155,99)(19,151,156,112)(20,150,157,111)(21,149,158,110)(22,148,159,109)(23,147,160,108)(24,146,161,107)(25,145,162,106)(26,144,163,105)(27,143,164,104)(28,142,165,103)(43,207,60,196)(44,206,61,195)(45,205,62,194)(46,204,63,193)(47,203,64,192)(48,202,65,191)(49,201,66,190)(50,200,67,189)(51,199,68,188)(52,198,69,187)(53,197,70,186)(54,210,57,185)(55,209,58,184)(56,208,59,183)(113,181,127,216)(114,180,128,215)(115,179,129,214)(116,178,130,213)(117,177,131,212)(118,176,132,211)(119,175,133,224)(120,174,134,223)(121,173,135,222)(122,172,136,221)(123,171,137,220)(124,170,138,219)(125,169,139,218)(126,182,140,217), (1,30)(2,31)(3,32)(4,33)(5,34)(6,35)(7,36)(8,37)(9,38)(10,39)(11,40)(12,41)(13,42)(14,29)(15,144)(16,145)(17,146)(18,147)(19,148)(20,149)(21,150)(22,151)(23,152)(24,153)(25,154)(26,141)(27,142)(28,143)(43,208)(44,209)(45,210)(46,197)(47,198)(48,199)(49,200)(50,201)(51,202)(52,203)(53,204)(54,205)(55,206)(56,207)(57,194)(58,195)(59,196)(60,183)(61,184)(62,185)(63,186)(64,187)(65,188)(66,189)(67,190)(68,191)(69,192)(70,193)(71,88)(72,89)(73,90)(74,91)(75,92)(76,93)(77,94)(78,95)(79,96)(80,97)(81,98)(82,85)(83,86)(84,87)(99,160)(100,161)(101,162)(102,163)(103,164)(104,165)(105,166)(106,167)(107,168)(108,155)(109,156)(110,157)(111,158)(112,159)(113,176)(114,177)(115,178)(116,179)(117,180)(118,181)(119,182)(120,169)(121,170)(122,171)(123,172)(124,173)(125,174)(126,175)(127,211)(128,212)(129,213)(130,214)(131,215)(132,216)(133,217)(134,218)(135,219)(136,220)(137,221)(138,222)(139,223)(140,224), (1,193,79,204)(2,192,80,203)(3,191,81,202)(4,190,82,201)(5,189,83,200)(6,188,84,199)(7,187,71,198)(8,186,72,197)(9,185,73,210)(10,184,74,209)(11,183,75,208)(12,196,76,207)(13,195,77,206)(14,194,78,205)(15,114,166,128)(16,113,167,127)(17,126,168,140)(18,125,155,139)(19,124,156,138)(20,123,157,137)(21,122,158,136)(22,121,159,135)(23,120,160,134)(24,119,161,133)(25,118,162,132)(26,117,163,131)(27,116,164,130)(28,115,165,129)(29,57,95,54)(30,70,96,53)(31,69,97,52)(32,68,98,51)(33,67,85,50)(34,66,86,49)(35,65,87,48)(36,64,88,47)(37,63,89,46)(38,62,90,45)(39,61,91,44)(40,60,92,43)(41,59,93,56)(42,58,94,55)(99,218,152,169)(100,217,153,182)(101,216,154,181)(102,215,141,180)(103,214,142,179)(104,213,143,178)(105,212,144,177)(106,211,145,176)(107,224,146,175)(108,223,147,174)(109,222,148,173)(110,221,149,172)(111,220,150,171)(112,219,151,170), (1,107,72,153)(2,108,73,154)(3,109,74,141)(4,110,75,142)(5,111,76,143)(6,112,77,144)(7,99,78,145)(8,100,79,146)(9,101,80,147)(10,102,81,148)(11,103,82,149)(12,104,83,150)(13,105,84,151)(14,106,71,152)(15,35,159,94)(16,36,160,95)(17,37,161,96)(18,38,162,97)(19,39,163,98)(20,40,164,85)(21,41,165,86)(22,42,166,87)(23,29,167,88)(24,30,168,89)(25,31,155,90)(26,32,156,91)(27,33,157,92)(28,34,158,93)(43,137,67,116)(44,138,68,117)(45,139,69,118)(46,140,70,119)(47,127,57,120)(48,128,58,121)(49,129,59,122)(50,130,60,123)(51,131,61,124)(52,132,62,125)(53,133,63,126)(54,134,64,113)(55,135,65,114)(56,136,66,115)(169,198,211,194)(170,199,212,195)(171,200,213,196)(172,201,214,183)(173,202,215,184)(174,203,216,185)(175,204,217,186)(176,205,218,187)(177,206,219,188)(178,207,220,189)(179,208,221,190)(180,209,222,191)(181,210,223,192)(182,197,224,193)>;
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), (1,89,79,37)(2,88,80,36)(3,87,81,35)(4,86,82,34)(5,85,83,33)(6,98,84,32)(7,97,71,31)(8,96,72,30)(9,95,73,29)(10,94,74,42)(11,93,75,41)(12,92,76,40)(13,91,77,39)(14,90,78,38)(15,141,166,102)(16,154,167,101)(17,153,168,100)(18,152,155,99)(19,151,156,112)(20,150,157,111)(21,149,158,110)(22,148,159,109)(23,147,160,108)(24,146,161,107)(25,145,162,106)(26,144,163,105)(27,143,164,104)(28,142,165,103)(43,207,60,196)(44,206,61,195)(45,205,62,194)(46,204,63,193)(47,203,64,192)(48,202,65,191)(49,201,66,190)(50,200,67,189)(51,199,68,188)(52,198,69,187)(53,197,70,186)(54,210,57,185)(55,209,58,184)(56,208,59,183)(113,181,127,216)(114,180,128,215)(115,179,129,214)(116,178,130,213)(117,177,131,212)(118,176,132,211)(119,175,133,224)(120,174,134,223)(121,173,135,222)(122,172,136,221)(123,171,137,220)(124,170,138,219)(125,169,139,218)(126,182,140,217), (1,30)(2,31)(3,32)(4,33)(5,34)(6,35)(7,36)(8,37)(9,38)(10,39)(11,40)(12,41)(13,42)(14,29)(15,144)(16,145)(17,146)(18,147)(19,148)(20,149)(21,150)(22,151)(23,152)(24,153)(25,154)(26,141)(27,142)(28,143)(43,208)(44,209)(45,210)(46,197)(47,198)(48,199)(49,200)(50,201)(51,202)(52,203)(53,204)(54,205)(55,206)(56,207)(57,194)(58,195)(59,196)(60,183)(61,184)(62,185)(63,186)(64,187)(65,188)(66,189)(67,190)(68,191)(69,192)(70,193)(71,88)(72,89)(73,90)(74,91)(75,92)(76,93)(77,94)(78,95)(79,96)(80,97)(81,98)(82,85)(83,86)(84,87)(99,160)(100,161)(101,162)(102,163)(103,164)(104,165)(105,166)(106,167)(107,168)(108,155)(109,156)(110,157)(111,158)(112,159)(113,176)(114,177)(115,178)(116,179)(117,180)(118,181)(119,182)(120,169)(121,170)(122,171)(123,172)(124,173)(125,174)(126,175)(127,211)(128,212)(129,213)(130,214)(131,215)(132,216)(133,217)(134,218)(135,219)(136,220)(137,221)(138,222)(139,223)(140,224), (1,193,79,204)(2,192,80,203)(3,191,81,202)(4,190,82,201)(5,189,83,200)(6,188,84,199)(7,187,71,198)(8,186,72,197)(9,185,73,210)(10,184,74,209)(11,183,75,208)(12,196,76,207)(13,195,77,206)(14,194,78,205)(15,114,166,128)(16,113,167,127)(17,126,168,140)(18,125,155,139)(19,124,156,138)(20,123,157,137)(21,122,158,136)(22,121,159,135)(23,120,160,134)(24,119,161,133)(25,118,162,132)(26,117,163,131)(27,116,164,130)(28,115,165,129)(29,57,95,54)(30,70,96,53)(31,69,97,52)(32,68,98,51)(33,67,85,50)(34,66,86,49)(35,65,87,48)(36,64,88,47)(37,63,89,46)(38,62,90,45)(39,61,91,44)(40,60,92,43)(41,59,93,56)(42,58,94,55)(99,218,152,169)(100,217,153,182)(101,216,154,181)(102,215,141,180)(103,214,142,179)(104,213,143,178)(105,212,144,177)(106,211,145,176)(107,224,146,175)(108,223,147,174)(109,222,148,173)(110,221,149,172)(111,220,150,171)(112,219,151,170), (1,107,72,153)(2,108,73,154)(3,109,74,141)(4,110,75,142)(5,111,76,143)(6,112,77,144)(7,99,78,145)(8,100,79,146)(9,101,80,147)(10,102,81,148)(11,103,82,149)(12,104,83,150)(13,105,84,151)(14,106,71,152)(15,35,159,94)(16,36,160,95)(17,37,161,96)(18,38,162,97)(19,39,163,98)(20,40,164,85)(21,41,165,86)(22,42,166,87)(23,29,167,88)(24,30,168,89)(25,31,155,90)(26,32,156,91)(27,33,157,92)(28,34,158,93)(43,137,67,116)(44,138,68,117)(45,139,69,118)(46,140,70,119)(47,127,57,120)(48,128,58,121)(49,129,59,122)(50,130,60,123)(51,131,61,124)(52,132,62,125)(53,133,63,126)(54,134,64,113)(55,135,65,114)(56,136,66,115)(169,198,211,194)(170,199,212,195)(171,200,213,196)(172,201,214,183)(173,202,215,184)(174,203,216,185)(175,204,217,186)(176,205,218,187)(177,206,219,188)(178,207,220,189)(179,208,221,190)(180,209,222,191)(181,210,223,192)(182,197,224,193) );
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)], [(1,89,79,37),(2,88,80,36),(3,87,81,35),(4,86,82,34),(5,85,83,33),(6,98,84,32),(7,97,71,31),(8,96,72,30),(9,95,73,29),(10,94,74,42),(11,93,75,41),(12,92,76,40),(13,91,77,39),(14,90,78,38),(15,141,166,102),(16,154,167,101),(17,153,168,100),(18,152,155,99),(19,151,156,112),(20,150,157,111),(21,149,158,110),(22,148,159,109),(23,147,160,108),(24,146,161,107),(25,145,162,106),(26,144,163,105),(27,143,164,104),(28,142,165,103),(43,207,60,196),(44,206,61,195),(45,205,62,194),(46,204,63,193),(47,203,64,192),(48,202,65,191),(49,201,66,190),(50,200,67,189),(51,199,68,188),(52,198,69,187),(53,197,70,186),(54,210,57,185),(55,209,58,184),(56,208,59,183),(113,181,127,216),(114,180,128,215),(115,179,129,214),(116,178,130,213),(117,177,131,212),(118,176,132,211),(119,175,133,224),(120,174,134,223),(121,173,135,222),(122,172,136,221),(123,171,137,220),(124,170,138,219),(125,169,139,218),(126,182,140,217)], [(1,30),(2,31),(3,32),(4,33),(5,34),(6,35),(7,36),(8,37),(9,38),(10,39),(11,40),(12,41),(13,42),(14,29),(15,144),(16,145),(17,146),(18,147),(19,148),(20,149),(21,150),(22,151),(23,152),(24,153),(25,154),(26,141),(27,142),(28,143),(43,208),(44,209),(45,210),(46,197),(47,198),(48,199),(49,200),(50,201),(51,202),(52,203),(53,204),(54,205),(55,206),(56,207),(57,194),(58,195),(59,196),(60,183),(61,184),(62,185),(63,186),(64,187),(65,188),(66,189),(67,190),(68,191),(69,192),(70,193),(71,88),(72,89),(73,90),(74,91),(75,92),(76,93),(77,94),(78,95),(79,96),(80,97),(81,98),(82,85),(83,86),(84,87),(99,160),(100,161),(101,162),(102,163),(103,164),(104,165),(105,166),(106,167),(107,168),(108,155),(109,156),(110,157),(111,158),(112,159),(113,176),(114,177),(115,178),(116,179),(117,180),(118,181),(119,182),(120,169),(121,170),(122,171),(123,172),(124,173),(125,174),(126,175),(127,211),(128,212),(129,213),(130,214),(131,215),(132,216),(133,217),(134,218),(135,219),(136,220),(137,221),(138,222),(139,223),(140,224)], [(1,193,79,204),(2,192,80,203),(3,191,81,202),(4,190,82,201),(5,189,83,200),(6,188,84,199),(7,187,71,198),(8,186,72,197),(9,185,73,210),(10,184,74,209),(11,183,75,208),(12,196,76,207),(13,195,77,206),(14,194,78,205),(15,114,166,128),(16,113,167,127),(17,126,168,140),(18,125,155,139),(19,124,156,138),(20,123,157,137),(21,122,158,136),(22,121,159,135),(23,120,160,134),(24,119,161,133),(25,118,162,132),(26,117,163,131),(27,116,164,130),(28,115,165,129),(29,57,95,54),(30,70,96,53),(31,69,97,52),(32,68,98,51),(33,67,85,50),(34,66,86,49),(35,65,87,48),(36,64,88,47),(37,63,89,46),(38,62,90,45),(39,61,91,44),(40,60,92,43),(41,59,93,56),(42,58,94,55),(99,218,152,169),(100,217,153,182),(101,216,154,181),(102,215,141,180),(103,214,142,179),(104,213,143,178),(105,212,144,177),(106,211,145,176),(107,224,146,175),(108,223,147,174),(109,222,148,173),(110,221,149,172),(111,220,150,171),(112,219,151,170)], [(1,107,72,153),(2,108,73,154),(3,109,74,141),(4,110,75,142),(5,111,76,143),(6,112,77,144),(7,99,78,145),(8,100,79,146),(9,101,80,147),(10,102,81,148),(11,103,82,149),(12,104,83,150),(13,105,84,151),(14,106,71,152),(15,35,159,94),(16,36,160,95),(17,37,161,96),(18,38,162,97),(19,39,163,98),(20,40,164,85),(21,41,165,86),(22,42,166,87),(23,29,167,88),(24,30,168,89),(25,31,155,90),(26,32,156,91),(27,33,157,92),(28,34,158,93),(43,137,67,116),(44,138,68,117),(45,139,69,118),(46,140,70,119),(47,127,57,120),(48,128,58,121),(49,129,59,122),(50,130,60,123),(51,131,61,124),(52,132,62,125),(53,133,63,126),(54,134,64,113),(55,135,65,114),(56,136,66,115),(169,198,211,194),(170,199,212,195),(171,200,213,196),(172,201,214,183),(173,202,215,184),(174,203,216,185),(175,204,217,186),(176,205,218,187),(177,206,219,188),(178,207,220,189),(179,208,221,190),(180,209,222,191),(181,210,223,192),(182,197,224,193)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | ··· | 4K | 4L | 4M | 4N | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 14P | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28R |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 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 | 14 | 14 | 2 | 2 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 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 | 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 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | D14 | 2- 1+4 | D4⋊2D7 | D4×D7 | D4.10D14 |
| kernel | C14.732- 1+4 | C22⋊Dic14 | D14.D4 | C28⋊Q8 | D7×C4⋊C4 | C2×C4⋊Dic7 | C4×C7⋊D4 | D4×Dic7 | C23.18D14 | C28⋊2D4 | C7×C4⋊D4 | C2×D4⋊2D7 | C7⋊D4 | C4⋊D4 | C28 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C14 | C4 | C22 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 2 | 4 | 3 | 4 | 6 | 3 | 3 | 9 | 1 | 6 | 6 | 6 |
Matrix representation of C14.732- 1+4 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 24 | 25 | 0 | 0 |
| 0 | 0 | 8 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 15 | 18 | 0 | 0 |
| 0 | 0 | 23 | 14 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 14 | 11 | 0 | 0 |
| 0 | 0 | 6 | 15 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 27 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 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 | 0 | 0 | 1 | 2 |
| 0 | 0 | 0 | 0 | 28 | 28 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,24,8,0,0,0,0,25,12,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[0,1,0,0,0,0,28,0,0,0,0,0,0,0,15,23,0,0,0,0,18,14,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,14,6,0,0,0,0,11,15,0,0,0,0,0,0,28,0,0,0,0,0,27,1],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,28,0,0,0,0,2,28] >;
C14.732- 1+4 in GAP, Magma, Sage, TeX
C_{14}._{73}2_-^{1+4} % in TeX
G:=Group("C14.73ES-(2,2)"); // GroupNames label
G:=SmallGroup(448,1064);
// by ID
G=gap.SmallGroup(448,1064);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,387,100,675,185,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=c^2=1,d^2=b^2,e^2=a^7*b^2,b*a*b^-1=d*a*d^-1=a^-1,a*c=c*a,a*e=e*a,c*b*c=b^-1,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=a^7*b^2*d>;
// generators/relations