G = C14.1072- 1+4 order 448 = 26·7
62nd non-split extension by C14 of 2- 1+4 acting via 2- 1+4/C4○D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.1072- 1+4, (C7×Q8)⋊18D4, Q8⋊9(C7⋊D4), C7⋊7(Q8⋊5D4), C28⋊2D4⋊42C2, (Q8×Dic7)⋊29C2, C28.267(C2×D4), D14⋊16(C4○D4), (C2×D4).236D14, (C2×Q8).210D14, C28.48D4⋊40C2, C28.17D4⋊31C2, (C2×C14).317C24, (C2×C28).561C23, C14.167(C22×D4), (C22×C4).287D14, D14⋊C4.164C22, (D4×C14).276C22, C4⋊Dic7.260C22, (Q8×C14).243C22, C23.138(C22×D7), C22.326(C23×D7), C23.D7.76C22, Dic7⋊C4.101C22, (C22×C14).243C23, (C22×C28).296C22, (C2×Dic7).164C23, (C4×Dic7).176C22, (C22×D7).244C23, C2.70(D4.10D14), (C2×Dic14).204C22, (C2×Q8×D7)⋊19C2, (C2×C4○D4)⋊9D7, (C14×C4○D4)⋊9C2, (C4×C7⋊D4)⋊30C2, C4.73(C2×C7⋊D4), C2.105(D7×C4○D4), C14.217(C2×C4○D4), (C2×C4×D7).169C22, C2.40(C22×C7⋊D4), (C2×C4).640(C22×D7), (C2×C7⋊D4).141C22, SmallGroup(448,1284)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.1072- 1+4
G = < a,b,c,d,e | a14=b4=c2=1, d2=e2=a7b2, bab-1=dad-1=a-1, ac=ca, ae=ea, cbc=b-1, dbd-1=a7b, be=eb, dcd-1=a7c, ce=ec, ede-1=a7b2d >
Subgroups: 1140 in 290 conjugacy classes, 113 normal (22 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, Q8, C23, C23, D7, C14, C14, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, C4○D4, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C4.4D4, C22×Q8, C2×C4○D4, Dic14, C4×D7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C7×Q8, C22×D7, C22×C14, Q8⋊5D4, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C2×Dic14, C2×C4×D7, Q8×D7, C2×C7⋊D4, C22×C28, D4×C14, Q8×C14, C7×C4○D4, C28.48D4, C4×C7⋊D4, C28.17D4, C28⋊2D4, Q8×Dic7, C2×Q8×D7, C14×C4○D4, C14.1072- 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⋊5D4, C2×C7⋊D4, C23×D7, D7×C4○D4, D4.10D14, C22×C7⋊D4, C14.1072- 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)
(1 210 172 70)(2 209 173 69)(3 208 174 68)(4 207 175 67)(5 206 176 66)(6 205 177 65)(7 204 178 64)(8 203 179 63)(9 202 180 62)(10 201 181 61)(11 200 182 60)(12 199 169 59)(13 198 170 58)(14 197 171 57)(15 135 156 49)(16 134 157 48)(17 133 158 47)(18 132 159 46)(19 131 160 45)(20 130 161 44)(21 129 162 43)(22 128 163 56)(23 127 164 55)(24 140 165 54)(25 139 166 53)(26 138 167 52)(27 137 168 51)(28 136 155 50)(29 73 109 88)(30 72 110 87)(31 71 111 86)(32 84 112 85)(33 83 99 98)(34 82 100 97)(35 81 101 96)(36 80 102 95)(37 79 103 94)(38 78 104 93)(39 77 105 92)(40 76 106 91)(41 75 107 90)(42 74 108 89)(113 211 185 144)(114 224 186 143)(115 223 187 142)(116 222 188 141)(117 221 189 154)(118 220 190 153)(119 219 191 152)(120 218 192 151)(121 217 193 150)(122 216 194 149)(123 215 195 148)(124 214 196 147)(125 213 183 146)(126 212 184 145)
(1 210)(2 197)(3 198)(4 199)(5 200)(6 201)(7 202)(8 203)(9 204)(10 205)(11 206)(12 207)(13 208)(14 209)(15 43)(16 44)(17 45)(18 46)(19 47)(20 48)(21 49)(22 50)(23 51)(24 52)(25 53)(26 54)(27 55)(28 56)(29 75)(30 76)(31 77)(32 78)(33 79)(34 80)(35 81)(36 82)(37 83)(38 84)(39 71)(40 72)(41 73)(42 74)(57 173)(58 174)(59 175)(60 176)(61 177)(62 178)(63 179)(64 180)(65 181)(66 182)(67 169)(68 170)(69 171)(70 172)(85 104)(86 105)(87 106)(88 107)(89 108)(90 109)(91 110)(92 111)(93 112)(94 99)(95 100)(96 101)(97 102)(98 103)(113 213)(114 214)(115 215)(116 216)(117 217)(118 218)(119 219)(120 220)(121 221)(122 222)(123 223)(124 224)(125 211)(126 212)(127 168)(128 155)(129 156)(130 157)(131 158)(132 159)(133 160)(134 161)(135 162)(136 163)(137 164)(138 165)(139 166)(140 167)(141 194)(142 195)(143 196)(144 183)(145 184)(146 185)(147 186)(148 187)(149 188)(150 189)(151 190)(152 191)(153 192)(154 193)
(1 42 179 101)(2 41 180 100)(3 40 181 99)(4 39 182 112)(5 38 169 111)(6 37 170 110)(7 36 171 109)(8 35 172 108)(9 34 173 107)(10 33 174 106)(11 32 175 105)(12 31 176 104)(13 30 177 103)(14 29 178 102)(15 141 163 215)(16 154 164 214)(17 153 165 213)(18 152 166 212)(19 151 167 211)(20 150 168 224)(21 149 155 223)(22 148 156 222)(23 147 157 221)(24 146 158 220)(25 145 159 219)(26 144 160 218)(27 143 161 217)(28 142 162 216)(43 187 136 122)(44 186 137 121)(45 185 138 120)(46 184 139 119)(47 183 140 118)(48 196 127 117)(49 195 128 116)(50 194 129 115)(51 193 130 114)(52 192 131 113)(53 191 132 126)(54 190 133 125)(55 189 134 124)(56 188 135 123)(57 95 204 73)(58 94 205 72)(59 93 206 71)(60 92 207 84)(61 91 208 83)(62 90 209 82)(63 89 210 81)(64 88 197 80)(65 87 198 79)(66 86 199 78)(67 85 200 77)(68 98 201 76)(69 97 202 75)(70 96 203 74)
(1 53 179 132)(2 54 180 133)(3 55 181 134)(4 56 182 135)(5 43 169 136)(6 44 170 137)(7 45 171 138)(8 46 172 139)(9 47 173 140)(10 48 174 127)(11 49 175 128)(12 50 176 129)(13 51 177 130)(14 52 178 131)(15 67 163 200)(16 68 164 201)(17 69 165 202)(18 70 166 203)(19 57 167 204)(20 58 168 205)(21 59 155 206)(22 60 156 207)(23 61 157 208)(24 62 158 209)(25 63 159 210)(26 64 160 197)(27 65 161 198)(28 66 162 199)(29 113 102 192)(30 114 103 193)(31 115 104 194)(32 116 105 195)(33 117 106 196)(34 118 107 183)(35 119 108 184)(36 120 109 185)(37 121 110 186)(38 122 111 187)(39 123 112 188)(40 124 99 189)(41 125 100 190)(42 126 101 191)(71 223 93 149)(72 224 94 150)(73 211 95 151)(74 212 96 152)(75 213 97 153)(76 214 98 154)(77 215 85 141)(78 216 86 142)(79 217 87 143)(80 218 88 144)(81 219 89 145)(82 220 90 146)(83 221 91 147)(84 222 92 148)
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), (1,210,172,70)(2,209,173,69)(3,208,174,68)(4,207,175,67)(5,206,176,66)(6,205,177,65)(7,204,178,64)(8,203,179,63)(9,202,180,62)(10,201,181,61)(11,200,182,60)(12,199,169,59)(13,198,170,58)(14,197,171,57)(15,135,156,49)(16,134,157,48)(17,133,158,47)(18,132,159,46)(19,131,160,45)(20,130,161,44)(21,129,162,43)(22,128,163,56)(23,127,164,55)(24,140,165,54)(25,139,166,53)(26,138,167,52)(27,137,168,51)(28,136,155,50)(29,73,109,88)(30,72,110,87)(31,71,111,86)(32,84,112,85)(33,83,99,98)(34,82,100,97)(35,81,101,96)(36,80,102,95)(37,79,103,94)(38,78,104,93)(39,77,105,92)(40,76,106,91)(41,75,107,90)(42,74,108,89)(113,211,185,144)(114,224,186,143)(115,223,187,142)(116,222,188,141)(117,221,189,154)(118,220,190,153)(119,219,191,152)(120,218,192,151)(121,217,193,150)(122,216,194,149)(123,215,195,148)(124,214,196,147)(125,213,183,146)(126,212,184,145), (1,210)(2,197)(3,198)(4,199)(5,200)(6,201)(7,202)(8,203)(9,204)(10,205)(11,206)(12,207)(13,208)(14,209)(15,43)(16,44)(17,45)(18,46)(19,47)(20,48)(21,49)(22,50)(23,51)(24,52)(25,53)(26,54)(27,55)(28,56)(29,75)(30,76)(31,77)(32,78)(33,79)(34,80)(35,81)(36,82)(37,83)(38,84)(39,71)(40,72)(41,73)(42,74)(57,173)(58,174)(59,175)(60,176)(61,177)(62,178)(63,179)(64,180)(65,181)(66,182)(67,169)(68,170)(69,171)(70,172)(85,104)(86,105)(87,106)(88,107)(89,108)(90,109)(91,110)(92,111)(93,112)(94,99)(95,100)(96,101)(97,102)(98,103)(113,213)(114,214)(115,215)(116,216)(117,217)(118,218)(119,219)(120,220)(121,221)(122,222)(123,223)(124,224)(125,211)(126,212)(127,168)(128,155)(129,156)(130,157)(131,158)(132,159)(133,160)(134,161)(135,162)(136,163)(137,164)(138,165)(139,166)(140,167)(141,194)(142,195)(143,196)(144,183)(145,184)(146,185)(147,186)(148,187)(149,188)(150,189)(151,190)(152,191)(153,192)(154,193), (1,42,179,101)(2,41,180,100)(3,40,181,99)(4,39,182,112)(5,38,169,111)(6,37,170,110)(7,36,171,109)(8,35,172,108)(9,34,173,107)(10,33,174,106)(11,32,175,105)(12,31,176,104)(13,30,177,103)(14,29,178,102)(15,141,163,215)(16,154,164,214)(17,153,165,213)(18,152,166,212)(19,151,167,211)(20,150,168,224)(21,149,155,223)(22,148,156,222)(23,147,157,221)(24,146,158,220)(25,145,159,219)(26,144,160,218)(27,143,161,217)(28,142,162,216)(43,187,136,122)(44,186,137,121)(45,185,138,120)(46,184,139,119)(47,183,140,118)(48,196,127,117)(49,195,128,116)(50,194,129,115)(51,193,130,114)(52,192,131,113)(53,191,132,126)(54,190,133,125)(55,189,134,124)(56,188,135,123)(57,95,204,73)(58,94,205,72)(59,93,206,71)(60,92,207,84)(61,91,208,83)(62,90,209,82)(63,89,210,81)(64,88,197,80)(65,87,198,79)(66,86,199,78)(67,85,200,77)(68,98,201,76)(69,97,202,75)(70,96,203,74), (1,53,179,132)(2,54,180,133)(3,55,181,134)(4,56,182,135)(5,43,169,136)(6,44,170,137)(7,45,171,138)(8,46,172,139)(9,47,173,140)(10,48,174,127)(11,49,175,128)(12,50,176,129)(13,51,177,130)(14,52,178,131)(15,67,163,200)(16,68,164,201)(17,69,165,202)(18,70,166,203)(19,57,167,204)(20,58,168,205)(21,59,155,206)(22,60,156,207)(23,61,157,208)(24,62,158,209)(25,63,159,210)(26,64,160,197)(27,65,161,198)(28,66,162,199)(29,113,102,192)(30,114,103,193)(31,115,104,194)(32,116,105,195)(33,117,106,196)(34,118,107,183)(35,119,108,184)(36,120,109,185)(37,121,110,186)(38,122,111,187)(39,123,112,188)(40,124,99,189)(41,125,100,190)(42,126,101,191)(71,223,93,149)(72,224,94,150)(73,211,95,151)(74,212,96,152)(75,213,97,153)(76,214,98,154)(77,215,85,141)(78,216,86,142)(79,217,87,143)(80,218,88,144)(81,219,89,145)(82,220,90,146)(83,221,91,147)(84,222,92,148)>;
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), (1,210,172,70)(2,209,173,69)(3,208,174,68)(4,207,175,67)(5,206,176,66)(6,205,177,65)(7,204,178,64)(8,203,179,63)(9,202,180,62)(10,201,181,61)(11,200,182,60)(12,199,169,59)(13,198,170,58)(14,197,171,57)(15,135,156,49)(16,134,157,48)(17,133,158,47)(18,132,159,46)(19,131,160,45)(20,130,161,44)(21,129,162,43)(22,128,163,56)(23,127,164,55)(24,140,165,54)(25,139,166,53)(26,138,167,52)(27,137,168,51)(28,136,155,50)(29,73,109,88)(30,72,110,87)(31,71,111,86)(32,84,112,85)(33,83,99,98)(34,82,100,97)(35,81,101,96)(36,80,102,95)(37,79,103,94)(38,78,104,93)(39,77,105,92)(40,76,106,91)(41,75,107,90)(42,74,108,89)(113,211,185,144)(114,224,186,143)(115,223,187,142)(116,222,188,141)(117,221,189,154)(118,220,190,153)(119,219,191,152)(120,218,192,151)(121,217,193,150)(122,216,194,149)(123,215,195,148)(124,214,196,147)(125,213,183,146)(126,212,184,145), (1,210)(2,197)(3,198)(4,199)(5,200)(6,201)(7,202)(8,203)(9,204)(10,205)(11,206)(12,207)(13,208)(14,209)(15,43)(16,44)(17,45)(18,46)(19,47)(20,48)(21,49)(22,50)(23,51)(24,52)(25,53)(26,54)(27,55)(28,56)(29,75)(30,76)(31,77)(32,78)(33,79)(34,80)(35,81)(36,82)(37,83)(38,84)(39,71)(40,72)(41,73)(42,74)(57,173)(58,174)(59,175)(60,176)(61,177)(62,178)(63,179)(64,180)(65,181)(66,182)(67,169)(68,170)(69,171)(70,172)(85,104)(86,105)(87,106)(88,107)(89,108)(90,109)(91,110)(92,111)(93,112)(94,99)(95,100)(96,101)(97,102)(98,103)(113,213)(114,214)(115,215)(116,216)(117,217)(118,218)(119,219)(120,220)(121,221)(122,222)(123,223)(124,224)(125,211)(126,212)(127,168)(128,155)(129,156)(130,157)(131,158)(132,159)(133,160)(134,161)(135,162)(136,163)(137,164)(138,165)(139,166)(140,167)(141,194)(142,195)(143,196)(144,183)(145,184)(146,185)(147,186)(148,187)(149,188)(150,189)(151,190)(152,191)(153,192)(154,193), (1,42,179,101)(2,41,180,100)(3,40,181,99)(4,39,182,112)(5,38,169,111)(6,37,170,110)(7,36,171,109)(8,35,172,108)(9,34,173,107)(10,33,174,106)(11,32,175,105)(12,31,176,104)(13,30,177,103)(14,29,178,102)(15,141,163,215)(16,154,164,214)(17,153,165,213)(18,152,166,212)(19,151,167,211)(20,150,168,224)(21,149,155,223)(22,148,156,222)(23,147,157,221)(24,146,158,220)(25,145,159,219)(26,144,160,218)(27,143,161,217)(28,142,162,216)(43,187,136,122)(44,186,137,121)(45,185,138,120)(46,184,139,119)(47,183,140,118)(48,196,127,117)(49,195,128,116)(50,194,129,115)(51,193,130,114)(52,192,131,113)(53,191,132,126)(54,190,133,125)(55,189,134,124)(56,188,135,123)(57,95,204,73)(58,94,205,72)(59,93,206,71)(60,92,207,84)(61,91,208,83)(62,90,209,82)(63,89,210,81)(64,88,197,80)(65,87,198,79)(66,86,199,78)(67,85,200,77)(68,98,201,76)(69,97,202,75)(70,96,203,74), (1,53,179,132)(2,54,180,133)(3,55,181,134)(4,56,182,135)(5,43,169,136)(6,44,170,137)(7,45,171,138)(8,46,172,139)(9,47,173,140)(10,48,174,127)(11,49,175,128)(12,50,176,129)(13,51,177,130)(14,52,178,131)(15,67,163,200)(16,68,164,201)(17,69,165,202)(18,70,166,203)(19,57,167,204)(20,58,168,205)(21,59,155,206)(22,60,156,207)(23,61,157,208)(24,62,158,209)(25,63,159,210)(26,64,160,197)(27,65,161,198)(28,66,162,199)(29,113,102,192)(30,114,103,193)(31,115,104,194)(32,116,105,195)(33,117,106,196)(34,118,107,183)(35,119,108,184)(36,120,109,185)(37,121,110,186)(38,122,111,187)(39,123,112,188)(40,124,99,189)(41,125,100,190)(42,126,101,191)(71,223,93,149)(72,224,94,150)(73,211,95,151)(74,212,96,152)(75,213,97,153)(76,214,98,154)(77,215,85,141)(78,216,86,142)(79,217,87,143)(80,218,88,144)(81,219,89,145)(82,220,90,146)(83,221,91,147)(84,222,92,148) );
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)], [(1,210,172,70),(2,209,173,69),(3,208,174,68),(4,207,175,67),(5,206,176,66),(6,205,177,65),(7,204,178,64),(8,203,179,63),(9,202,180,62),(10,201,181,61),(11,200,182,60),(12,199,169,59),(13,198,170,58),(14,197,171,57),(15,135,156,49),(16,134,157,48),(17,133,158,47),(18,132,159,46),(19,131,160,45),(20,130,161,44),(21,129,162,43),(22,128,163,56),(23,127,164,55),(24,140,165,54),(25,139,166,53),(26,138,167,52),(27,137,168,51),(28,136,155,50),(29,73,109,88),(30,72,110,87),(31,71,111,86),(32,84,112,85),(33,83,99,98),(34,82,100,97),(35,81,101,96),(36,80,102,95),(37,79,103,94),(38,78,104,93),(39,77,105,92),(40,76,106,91),(41,75,107,90),(42,74,108,89),(113,211,185,144),(114,224,186,143),(115,223,187,142),(116,222,188,141),(117,221,189,154),(118,220,190,153),(119,219,191,152),(120,218,192,151),(121,217,193,150),(122,216,194,149),(123,215,195,148),(124,214,196,147),(125,213,183,146),(126,212,184,145)], [(1,210),(2,197),(3,198),(4,199),(5,200),(6,201),(7,202),(8,203),(9,204),(10,205),(11,206),(12,207),(13,208),(14,209),(15,43),(16,44),(17,45),(18,46),(19,47),(20,48),(21,49),(22,50),(23,51),(24,52),(25,53),(26,54),(27,55),(28,56),(29,75),(30,76),(31,77),(32,78),(33,79),(34,80),(35,81),(36,82),(37,83),(38,84),(39,71),(40,72),(41,73),(42,74),(57,173),(58,174),(59,175),(60,176),(61,177),(62,178),(63,179),(64,180),(65,181),(66,182),(67,169),(68,170),(69,171),(70,172),(85,104),(86,105),(87,106),(88,107),(89,108),(90,109),(91,110),(92,111),(93,112),(94,99),(95,100),(96,101),(97,102),(98,103),(113,213),(114,214),(115,215),(116,216),(117,217),(118,218),(119,219),(120,220),(121,221),(122,222),(123,223),(124,224),(125,211),(126,212),(127,168),(128,155),(129,156),(130,157),(131,158),(132,159),(133,160),(134,161),(135,162),(136,163),(137,164),(138,165),(139,166),(140,167),(141,194),(142,195),(143,196),(144,183),(145,184),(146,185),(147,186),(148,187),(149,188),(150,189),(151,190),(152,191),(153,192),(154,193)], [(1,42,179,101),(2,41,180,100),(3,40,181,99),(4,39,182,112),(5,38,169,111),(6,37,170,110),(7,36,171,109),(8,35,172,108),(9,34,173,107),(10,33,174,106),(11,32,175,105),(12,31,176,104),(13,30,177,103),(14,29,178,102),(15,141,163,215),(16,154,164,214),(17,153,165,213),(18,152,166,212),(19,151,167,211),(20,150,168,224),(21,149,155,223),(22,148,156,222),(23,147,157,221),(24,146,158,220),(25,145,159,219),(26,144,160,218),(27,143,161,217),(28,142,162,216),(43,187,136,122),(44,186,137,121),(45,185,138,120),(46,184,139,119),(47,183,140,118),(48,196,127,117),(49,195,128,116),(50,194,129,115),(51,193,130,114),(52,192,131,113),(53,191,132,126),(54,190,133,125),(55,189,134,124),(56,188,135,123),(57,95,204,73),(58,94,205,72),(59,93,206,71),(60,92,207,84),(61,91,208,83),(62,90,209,82),(63,89,210,81),(64,88,197,80),(65,87,198,79),(66,86,199,78),(67,85,200,77),(68,98,201,76),(69,97,202,75),(70,96,203,74)], [(1,53,179,132),(2,54,180,133),(3,55,181,134),(4,56,182,135),(5,43,169,136),(6,44,170,137),(7,45,171,138),(8,46,172,139),(9,47,173,140),(10,48,174,127),(11,49,175,128),(12,50,176,129),(13,51,177,130),(14,52,178,131),(15,67,163,200),(16,68,164,201),(17,69,165,202),(18,70,166,203),(19,57,167,204),(20,58,168,205),(21,59,155,206),(22,60,156,207),(23,61,157,208),(24,62,158,209),(25,63,159,210),(26,64,160,197),(27,65,161,198),(28,66,162,199),(29,113,102,192),(30,114,103,193),(31,115,104,194),(32,116,105,195),(33,117,106,196),(34,118,107,183),(35,119,108,184),(36,120,109,185),(37,121,110,186),(38,122,111,187),(39,123,112,188),(40,124,99,189),(41,125,100,190),(42,126,101,191),(71,223,93,149),(72,224,94,150),(73,211,95,151),(74,212,96,152),(75,213,97,153),(76,214,98,154),(77,215,85,141),(78,216,86,142),(79,217,87,143),(80,218,88,144),(81,219,89,145),(82,220,90,146),(83,221,91,147),(84,222,92,148)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | ··· | 4H | 4I | 4J | 4K | ··· | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14AA | 28A | ··· | 28L | 28M | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 14 | 14 | 2 | ··· | 2 | 14 | 14 | 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 | D4.10D14 |
| kernel | C14.1072- 1+4 | C28.48D4 | C4×C7⋊D4 | C28.17D4 | C28⋊2D4 | Q8×Dic7 | C2×Q8×D7 | C14×C4○D4 | C7×Q8 | C2×C4○D4 | D14 | 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 C14.1072- 1+4 ►in GL4(𝔽29) generated by
| 8 | 8 | 0 | 0 |
| 21 | 3 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 28 |
| 5 | 16 | 0 | 0 |
| 2 | 24 | 0 | 0 |
| 0 | 0 | 26 | 20 |
| 0 | 0 | 17 | 3 |
| 5 | 16 | 0 | 0 |
| 13 | 24 | 0 | 0 |
| 0 | 0 | 26 | 20 |
| 0 | 0 | 17 | 3 |
| 28 | 0 | 0 | 0 |
| 26 | 1 | 0 | 0 |
| 0 | 0 | 28 | 28 |
| 0 | 0 | 2 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 22 | 8 |
| 0 | 0 | 1 | 7 |
G:=sub<GL(4,GF(29))| [8,21,0,0,8,3,0,0,0,0,28,0,0,0,0,28],[5,2,0,0,16,24,0,0,0,0,26,17,0,0,20,3],[5,13,0,0,16,24,0,0,0,0,26,17,0,0,20,3],[28,26,0,0,0,1,0,0,0,0,28,2,0,0,28,1],[1,0,0,0,0,1,0,0,0,0,22,1,0,0,8,7] >;
C14.1072- 1+4 in GAP, Magma, Sage, TeX
C_{14}._{107}2_-^{1+4} % in TeX
G:=Group("C14.107ES-(2,2)"); // GroupNames label
G:=SmallGroup(448,1284);
// by ID
G=gap.SmallGroup(448,1284);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,387,184,675,136,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=c^2=1,d^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,d*b*d^-1=a^7*b,b*e=e*b,d*c*d^-1=a^7*c,c*e=e*c,e*d*e^-1=a^7*b^2*d>;
// generators/relations