G = C14.62- 1+4 order 448 = 26·7
6th non-split extension by C14 of 2- 1+4 acting via 2- 1+4/C2×Q8=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.62- 1+4, C14.122+ 1+4, C4⋊C4.265D14, D14⋊Q8⋊3C2, C28⋊7D4.6C2, Dic7.Q8⋊3C2, D14.5D4⋊3C2, C28.48D4⋊5C2, (C2×C14).59C24, (C2×C28).139C23, D14⋊C4.62C22, (C2×D28).22C22, (C22×C4).184D14, C4⋊Dic7.30C22, C2.15(D4⋊6D14), C22.93(C23×D7), C22.24(C4○D28), Dic7⋊C4.73C22, (C2×Dic7).20C23, (C22×D7).17C23, C23.230(C22×D7), C23.D7.89C22, C23.23D14⋊26C2, (C22×C28).361C22, (C22×C14).408C23, C2.9(Q8.10D14), C7⋊1(C22.33C24), (C4×Dic7).193C22, (C2×Dic14).22C22, (C2×C4⋊C4)⋊24D7, (C14×C4⋊C4)⋊21C2, C4⋊C4⋊D7⋊3C2, (C4×C7⋊D4)⋊36C2, C2.28(C2×C4○D28), C14.26(C2×C4○D4), (C2×C4×D7).192C22, (C7×C4⋊C4).300C22, (C2×C4).147(C22×D7), (C2×C7⋊D4).96C22, (C2×C14).109(C4○D4), SmallGroup(448,968)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.62- 1+4
G = < a,b,c,d,e | a14=b4=c2=1, d2=b2, e2=a7b2, bab-1=cac=a-1, ad=da, ae=ea, cbc=b-1, dbd-1=a7b, be=eb, dcd-1=a7c, ce=ec, ede-1=b2d >
Subgroups: 964 in 218 conjugacy classes, 95 normal (31 characteristic)
C1, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, Dic7, C28, D14, C2×C14, C2×C14, C2×C14, C2×C4⋊C4, C4×D4, C4⋊D4, C22⋊Q8, C22.D4, C42.C2, C42⋊2C2, Dic14, C4×D7, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C22×D7, C22×C14, C22.33C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C2×C7⋊D4, C22×C28, Dic7.Q8, D14.5D4, D14⋊Q8, C4⋊C4⋊D7, C28.48D4, C4×C7⋊D4, C23.23D14, C28⋊7D4, C14×C4⋊C4, C14.62- 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, C4○D28, C23×D7, C2×C4○D28, D4⋊6D14, Q8.10D14, C14.62- 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)
(1 106 34 133)(2 105 35 132)(3 104 36 131)(4 103 37 130)(5 102 38 129)(6 101 39 128)(7 100 40 127)(8 99 41 140)(9 112 42 139)(10 111 29 138)(11 110 30 137)(12 109 31 136)(13 108 32 135)(14 107 33 134)(15 141 196 92)(16 154 183 91)(17 153 184 90)(18 152 185 89)(19 151 186 88)(20 150 187 87)(21 149 188 86)(22 148 189 85)(23 147 190 98)(24 146 191 97)(25 145 192 96)(26 144 193 95)(27 143 194 94)(28 142 195 93)(43 219 65 73)(44 218 66 72)(45 217 67 71)(46 216 68 84)(47 215 69 83)(48 214 70 82)(49 213 57 81)(50 212 58 80)(51 211 59 79)(52 224 60 78)(53 223 61 77)(54 222 62 76)(55 221 63 75)(56 220 64 74)(113 204 178 165)(114 203 179 164)(115 202 180 163)(116 201 181 162)(117 200 182 161)(118 199 169 160)(119 198 170 159)(120 197 171 158)(121 210 172 157)(122 209 173 156)(123 208 174 155)(124 207 175 168)(125 206 176 167)(126 205 177 166)
(1 140)(2 139)(3 138)(4 137)(5 136)(6 135)(7 134)(8 133)(9 132)(10 131)(11 130)(12 129)(13 128)(14 127)(15 85)(16 98)(17 97)(18 96)(19 95)(20 94)(21 93)(22 92)(23 91)(24 90)(25 89)(26 88)(27 87)(28 86)(29 104)(30 103)(31 102)(32 101)(33 100)(34 99)(35 112)(36 111)(37 110)(38 109)(39 108)(40 107)(41 106)(42 105)(43 80)(44 79)(45 78)(46 77)(47 76)(48 75)(49 74)(50 73)(51 72)(52 71)(53 84)(54 83)(55 82)(56 81)(57 220)(58 219)(59 218)(60 217)(61 216)(62 215)(63 214)(64 213)(65 212)(66 211)(67 224)(68 223)(69 222)(70 221)(113 197)(114 210)(115 209)(116 208)(117 207)(118 206)(119 205)(120 204)(121 203)(122 202)(123 201)(124 200)(125 199)(126 198)(141 189)(142 188)(143 187)(144 186)(145 185)(146 184)(147 183)(148 196)(149 195)(150 194)(151 193)(152 192)(153 191)(154 190)(155 181)(156 180)(157 179)(158 178)(159 177)(160 176)(161 175)(162 174)(163 173)(164 172)(165 171)(166 170)(167 169)(168 182)
(1 21 34 188)(2 22 35 189)(3 23 36 190)(4 24 37 191)(5 25 38 192)(6 26 39 193)(7 27 40 194)(8 28 41 195)(9 15 42 196)(10 16 29 183)(11 17 30 184)(12 18 31 185)(13 19 32 186)(14 20 33 187)(43 156 65 209)(44 157 66 210)(45 158 67 197)(46 159 68 198)(47 160 69 199)(48 161 70 200)(49 162 57 201)(50 163 58 202)(51 164 59 203)(52 165 60 204)(53 166 61 205)(54 167 62 206)(55 168 63 207)(56 155 64 208)(71 178 217 113)(72 179 218 114)(73 180 219 115)(74 181 220 116)(75 182 221 117)(76 169 222 118)(77 170 223 119)(78 171 224 120)(79 172 211 121)(80 173 212 122)(81 174 213 123)(82 175 214 124)(83 176 215 125)(84 177 216 126)(85 112 148 139)(86 99 149 140)(87 100 150 127)(88 101 151 128)(89 102 152 129)(90 103 153 130)(91 104 154 131)(92 105 141 132)(93 106 142 133)(94 107 143 134)(95 108 144 135)(96 109 145 136)(97 110 146 137)(98 111 147 138)
(1 61 41 46)(2 62 42 47)(3 63 29 48)(4 64 30 49)(5 65 31 50)(6 66 32 51)(7 67 33 52)(8 68 34 53)(9 69 35 54)(10 70 36 55)(11 57 37 56)(12 58 38 43)(13 59 39 44)(14 60 40 45)(15 160 189 206)(16 161 190 207)(17 162 191 208)(18 163 192 209)(19 164 193 210)(20 165 194 197)(21 166 195 198)(22 167 196 199)(23 168 183 200)(24 155 184 201)(25 156 185 202)(26 157 186 203)(27 158 187 204)(28 159 188 205)(71 134 224 100)(72 135 211 101)(73 136 212 102)(74 137 213 103)(75 138 214 104)(76 139 215 105)(77 140 216 106)(78 127 217 107)(79 128 218 108)(80 129 219 109)(81 130 220 110)(82 131 221 111)(83 132 222 112)(84 133 223 99)(85 176 141 118)(86 177 142 119)(87 178 143 120)(88 179 144 121)(89 180 145 122)(90 181 146 123)(91 182 147 124)(92 169 148 125)(93 170 149 126)(94 171 150 113)(95 172 151 114)(96 173 152 115)(97 174 153 116)(98 175 154 117)
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), (1,106,34,133)(2,105,35,132)(3,104,36,131)(4,103,37,130)(5,102,38,129)(6,101,39,128)(7,100,40,127)(8,99,41,140)(9,112,42,139)(10,111,29,138)(11,110,30,137)(12,109,31,136)(13,108,32,135)(14,107,33,134)(15,141,196,92)(16,154,183,91)(17,153,184,90)(18,152,185,89)(19,151,186,88)(20,150,187,87)(21,149,188,86)(22,148,189,85)(23,147,190,98)(24,146,191,97)(25,145,192,96)(26,144,193,95)(27,143,194,94)(28,142,195,93)(43,219,65,73)(44,218,66,72)(45,217,67,71)(46,216,68,84)(47,215,69,83)(48,214,70,82)(49,213,57,81)(50,212,58,80)(51,211,59,79)(52,224,60,78)(53,223,61,77)(54,222,62,76)(55,221,63,75)(56,220,64,74)(113,204,178,165)(114,203,179,164)(115,202,180,163)(116,201,181,162)(117,200,182,161)(118,199,169,160)(119,198,170,159)(120,197,171,158)(121,210,172,157)(122,209,173,156)(123,208,174,155)(124,207,175,168)(125,206,176,167)(126,205,177,166), (1,140)(2,139)(3,138)(4,137)(5,136)(6,135)(7,134)(8,133)(9,132)(10,131)(11,130)(12,129)(13,128)(14,127)(15,85)(16,98)(17,97)(18,96)(19,95)(20,94)(21,93)(22,92)(23,91)(24,90)(25,89)(26,88)(27,87)(28,86)(29,104)(30,103)(31,102)(32,101)(33,100)(34,99)(35,112)(36,111)(37,110)(38,109)(39,108)(40,107)(41,106)(42,105)(43,80)(44,79)(45,78)(46,77)(47,76)(48,75)(49,74)(50,73)(51,72)(52,71)(53,84)(54,83)(55,82)(56,81)(57,220)(58,219)(59,218)(60,217)(61,216)(62,215)(63,214)(64,213)(65,212)(66,211)(67,224)(68,223)(69,222)(70,221)(113,197)(114,210)(115,209)(116,208)(117,207)(118,206)(119,205)(120,204)(121,203)(122,202)(123,201)(124,200)(125,199)(126,198)(141,189)(142,188)(143,187)(144,186)(145,185)(146,184)(147,183)(148,196)(149,195)(150,194)(151,193)(152,192)(153,191)(154,190)(155,181)(156,180)(157,179)(158,178)(159,177)(160,176)(161,175)(162,174)(163,173)(164,172)(165,171)(166,170)(167,169)(168,182), (1,21,34,188)(2,22,35,189)(3,23,36,190)(4,24,37,191)(5,25,38,192)(6,26,39,193)(7,27,40,194)(8,28,41,195)(9,15,42,196)(10,16,29,183)(11,17,30,184)(12,18,31,185)(13,19,32,186)(14,20,33,187)(43,156,65,209)(44,157,66,210)(45,158,67,197)(46,159,68,198)(47,160,69,199)(48,161,70,200)(49,162,57,201)(50,163,58,202)(51,164,59,203)(52,165,60,204)(53,166,61,205)(54,167,62,206)(55,168,63,207)(56,155,64,208)(71,178,217,113)(72,179,218,114)(73,180,219,115)(74,181,220,116)(75,182,221,117)(76,169,222,118)(77,170,223,119)(78,171,224,120)(79,172,211,121)(80,173,212,122)(81,174,213,123)(82,175,214,124)(83,176,215,125)(84,177,216,126)(85,112,148,139)(86,99,149,140)(87,100,150,127)(88,101,151,128)(89,102,152,129)(90,103,153,130)(91,104,154,131)(92,105,141,132)(93,106,142,133)(94,107,143,134)(95,108,144,135)(96,109,145,136)(97,110,146,137)(98,111,147,138), (1,61,41,46)(2,62,42,47)(3,63,29,48)(4,64,30,49)(5,65,31,50)(6,66,32,51)(7,67,33,52)(8,68,34,53)(9,69,35,54)(10,70,36,55)(11,57,37,56)(12,58,38,43)(13,59,39,44)(14,60,40,45)(15,160,189,206)(16,161,190,207)(17,162,191,208)(18,163,192,209)(19,164,193,210)(20,165,194,197)(21,166,195,198)(22,167,196,199)(23,168,183,200)(24,155,184,201)(25,156,185,202)(26,157,186,203)(27,158,187,204)(28,159,188,205)(71,134,224,100)(72,135,211,101)(73,136,212,102)(74,137,213,103)(75,138,214,104)(76,139,215,105)(77,140,216,106)(78,127,217,107)(79,128,218,108)(80,129,219,109)(81,130,220,110)(82,131,221,111)(83,132,222,112)(84,133,223,99)(85,176,141,118)(86,177,142,119)(87,178,143,120)(88,179,144,121)(89,180,145,122)(90,181,146,123)(91,182,147,124)(92,169,148,125)(93,170,149,126)(94,171,150,113)(95,172,151,114)(96,173,152,115)(97,174,153,116)(98,175,154,117)>;
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), (1,106,34,133)(2,105,35,132)(3,104,36,131)(4,103,37,130)(5,102,38,129)(6,101,39,128)(7,100,40,127)(8,99,41,140)(9,112,42,139)(10,111,29,138)(11,110,30,137)(12,109,31,136)(13,108,32,135)(14,107,33,134)(15,141,196,92)(16,154,183,91)(17,153,184,90)(18,152,185,89)(19,151,186,88)(20,150,187,87)(21,149,188,86)(22,148,189,85)(23,147,190,98)(24,146,191,97)(25,145,192,96)(26,144,193,95)(27,143,194,94)(28,142,195,93)(43,219,65,73)(44,218,66,72)(45,217,67,71)(46,216,68,84)(47,215,69,83)(48,214,70,82)(49,213,57,81)(50,212,58,80)(51,211,59,79)(52,224,60,78)(53,223,61,77)(54,222,62,76)(55,221,63,75)(56,220,64,74)(113,204,178,165)(114,203,179,164)(115,202,180,163)(116,201,181,162)(117,200,182,161)(118,199,169,160)(119,198,170,159)(120,197,171,158)(121,210,172,157)(122,209,173,156)(123,208,174,155)(124,207,175,168)(125,206,176,167)(126,205,177,166), (1,140)(2,139)(3,138)(4,137)(5,136)(6,135)(7,134)(8,133)(9,132)(10,131)(11,130)(12,129)(13,128)(14,127)(15,85)(16,98)(17,97)(18,96)(19,95)(20,94)(21,93)(22,92)(23,91)(24,90)(25,89)(26,88)(27,87)(28,86)(29,104)(30,103)(31,102)(32,101)(33,100)(34,99)(35,112)(36,111)(37,110)(38,109)(39,108)(40,107)(41,106)(42,105)(43,80)(44,79)(45,78)(46,77)(47,76)(48,75)(49,74)(50,73)(51,72)(52,71)(53,84)(54,83)(55,82)(56,81)(57,220)(58,219)(59,218)(60,217)(61,216)(62,215)(63,214)(64,213)(65,212)(66,211)(67,224)(68,223)(69,222)(70,221)(113,197)(114,210)(115,209)(116,208)(117,207)(118,206)(119,205)(120,204)(121,203)(122,202)(123,201)(124,200)(125,199)(126,198)(141,189)(142,188)(143,187)(144,186)(145,185)(146,184)(147,183)(148,196)(149,195)(150,194)(151,193)(152,192)(153,191)(154,190)(155,181)(156,180)(157,179)(158,178)(159,177)(160,176)(161,175)(162,174)(163,173)(164,172)(165,171)(166,170)(167,169)(168,182), (1,21,34,188)(2,22,35,189)(3,23,36,190)(4,24,37,191)(5,25,38,192)(6,26,39,193)(7,27,40,194)(8,28,41,195)(9,15,42,196)(10,16,29,183)(11,17,30,184)(12,18,31,185)(13,19,32,186)(14,20,33,187)(43,156,65,209)(44,157,66,210)(45,158,67,197)(46,159,68,198)(47,160,69,199)(48,161,70,200)(49,162,57,201)(50,163,58,202)(51,164,59,203)(52,165,60,204)(53,166,61,205)(54,167,62,206)(55,168,63,207)(56,155,64,208)(71,178,217,113)(72,179,218,114)(73,180,219,115)(74,181,220,116)(75,182,221,117)(76,169,222,118)(77,170,223,119)(78,171,224,120)(79,172,211,121)(80,173,212,122)(81,174,213,123)(82,175,214,124)(83,176,215,125)(84,177,216,126)(85,112,148,139)(86,99,149,140)(87,100,150,127)(88,101,151,128)(89,102,152,129)(90,103,153,130)(91,104,154,131)(92,105,141,132)(93,106,142,133)(94,107,143,134)(95,108,144,135)(96,109,145,136)(97,110,146,137)(98,111,147,138), (1,61,41,46)(2,62,42,47)(3,63,29,48)(4,64,30,49)(5,65,31,50)(6,66,32,51)(7,67,33,52)(8,68,34,53)(9,69,35,54)(10,70,36,55)(11,57,37,56)(12,58,38,43)(13,59,39,44)(14,60,40,45)(15,160,189,206)(16,161,190,207)(17,162,191,208)(18,163,192,209)(19,164,193,210)(20,165,194,197)(21,166,195,198)(22,167,196,199)(23,168,183,200)(24,155,184,201)(25,156,185,202)(26,157,186,203)(27,158,187,204)(28,159,188,205)(71,134,224,100)(72,135,211,101)(73,136,212,102)(74,137,213,103)(75,138,214,104)(76,139,215,105)(77,140,216,106)(78,127,217,107)(79,128,218,108)(80,129,219,109)(81,130,220,110)(82,131,221,111)(83,132,222,112)(84,133,223,99)(85,176,141,118)(86,177,142,119)(87,178,143,120)(88,179,144,121)(89,180,145,122)(90,181,146,123)(91,182,147,124)(92,169,148,125)(93,170,149,126)(94,171,150,113)(95,172,151,114)(96,173,152,115)(97,174,153,116)(98,175,154,117) );
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)], [(1,106,34,133),(2,105,35,132),(3,104,36,131),(4,103,37,130),(5,102,38,129),(6,101,39,128),(7,100,40,127),(8,99,41,140),(9,112,42,139),(10,111,29,138),(11,110,30,137),(12,109,31,136),(13,108,32,135),(14,107,33,134),(15,141,196,92),(16,154,183,91),(17,153,184,90),(18,152,185,89),(19,151,186,88),(20,150,187,87),(21,149,188,86),(22,148,189,85),(23,147,190,98),(24,146,191,97),(25,145,192,96),(26,144,193,95),(27,143,194,94),(28,142,195,93),(43,219,65,73),(44,218,66,72),(45,217,67,71),(46,216,68,84),(47,215,69,83),(48,214,70,82),(49,213,57,81),(50,212,58,80),(51,211,59,79),(52,224,60,78),(53,223,61,77),(54,222,62,76),(55,221,63,75),(56,220,64,74),(113,204,178,165),(114,203,179,164),(115,202,180,163),(116,201,181,162),(117,200,182,161),(118,199,169,160),(119,198,170,159),(120,197,171,158),(121,210,172,157),(122,209,173,156),(123,208,174,155),(124,207,175,168),(125,206,176,167),(126,205,177,166)], [(1,140),(2,139),(3,138),(4,137),(5,136),(6,135),(7,134),(8,133),(9,132),(10,131),(11,130),(12,129),(13,128),(14,127),(15,85),(16,98),(17,97),(18,96),(19,95),(20,94),(21,93),(22,92),(23,91),(24,90),(25,89),(26,88),(27,87),(28,86),(29,104),(30,103),(31,102),(32,101),(33,100),(34,99),(35,112),(36,111),(37,110),(38,109),(39,108),(40,107),(41,106),(42,105),(43,80),(44,79),(45,78),(46,77),(47,76),(48,75),(49,74),(50,73),(51,72),(52,71),(53,84),(54,83),(55,82),(56,81),(57,220),(58,219),(59,218),(60,217),(61,216),(62,215),(63,214),(64,213),(65,212),(66,211),(67,224),(68,223),(69,222),(70,221),(113,197),(114,210),(115,209),(116,208),(117,207),(118,206),(119,205),(120,204),(121,203),(122,202),(123,201),(124,200),(125,199),(126,198),(141,189),(142,188),(143,187),(144,186),(145,185),(146,184),(147,183),(148,196),(149,195),(150,194),(151,193),(152,192),(153,191),(154,190),(155,181),(156,180),(157,179),(158,178),(159,177),(160,176),(161,175),(162,174),(163,173),(164,172),(165,171),(166,170),(167,169),(168,182)], [(1,21,34,188),(2,22,35,189),(3,23,36,190),(4,24,37,191),(5,25,38,192),(6,26,39,193),(7,27,40,194),(8,28,41,195),(9,15,42,196),(10,16,29,183),(11,17,30,184),(12,18,31,185),(13,19,32,186),(14,20,33,187),(43,156,65,209),(44,157,66,210),(45,158,67,197),(46,159,68,198),(47,160,69,199),(48,161,70,200),(49,162,57,201),(50,163,58,202),(51,164,59,203),(52,165,60,204),(53,166,61,205),(54,167,62,206),(55,168,63,207),(56,155,64,208),(71,178,217,113),(72,179,218,114),(73,180,219,115),(74,181,220,116),(75,182,221,117),(76,169,222,118),(77,170,223,119),(78,171,224,120),(79,172,211,121),(80,173,212,122),(81,174,213,123),(82,175,214,124),(83,176,215,125),(84,177,216,126),(85,112,148,139),(86,99,149,140),(87,100,150,127),(88,101,151,128),(89,102,152,129),(90,103,153,130),(91,104,154,131),(92,105,141,132),(93,106,142,133),(94,107,143,134),(95,108,144,135),(96,109,145,136),(97,110,146,137),(98,111,147,138)], [(1,61,41,46),(2,62,42,47),(3,63,29,48),(4,64,30,49),(5,65,31,50),(6,66,32,51),(7,67,33,52),(8,68,34,53),(9,69,35,54),(10,70,36,55),(11,57,37,56),(12,58,38,43),(13,59,39,44),(14,60,40,45),(15,160,189,206),(16,161,190,207),(17,162,191,208),(18,163,192,209),(19,164,193,210),(20,165,194,197),(21,166,195,198),(22,167,196,199),(23,168,183,200),(24,155,184,201),(25,156,185,202),(26,157,186,203),(27,158,187,204),(28,159,188,205),(71,134,224,100),(72,135,211,101),(73,136,212,102),(74,137,213,103),(75,138,214,104),(76,139,215,105),(77,140,216,106),(78,127,217,107),(79,128,218,108),(80,129,219,109),(81,130,220,110),(82,131,221,111),(83,132,222,112),(84,133,223,99),(85,176,141,118),(86,177,142,119),(87,178,143,120),(88,179,144,121),(89,180,145,122),(90,181,146,123),(91,182,147,124),(92,169,148,125),(93,170,149,126),(94,171,150,113),(95,172,151,114),(96,173,152,115),(97,174,153,116),(98,175,154,117)]])
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4N | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | C4○D28 | 2+ 1+4 | 2- 1+4 | D4⋊6D14 | Q8.10D14 |
| kernel | C14.62- 1+4 | Dic7.Q8 | D14.5D4 | D14⋊Q8 | C4⋊C4⋊D7 | C28.48D4 | C4×C7⋊D4 | C23.23D14 | C28⋊7D4 | C14×C4⋊C4 | C2×C4⋊C4 | C2×C14 | C4⋊C4 | C22×C4 | C22 | C14 | C14 | C2 | C2 |
| # reps | 1 | 2 | 2 | 2 | 2 | 1 | 2 | 2 | 1 | 1 | 3 | 4 | 12 | 9 | 24 | 1 | 1 | 6 | 6 |
Matrix representation of C14.62- 1+4 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 23 | 0 | 0 | 0 |
| 0 | 0 | 0 | 23 | 0 | 0 |
| 0 | 0 | 0 | 0 | 24 | 0 |
| 0 | 0 | 0 | 0 | 0 | 24 |
| 3 | 28 | 0 | 0 | 0 | 0 |
| 8 | 26 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 3 | 28 | 0 | 0 | 0 | 0 |
| 8 | 26 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 6 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 20 | 11 | 0 | 0 |
| 0 | 0 | 11 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 11 |
| 0 | 0 | 0 | 0 | 11 | 9 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,23,0,0,0,0,0,0,23,0,0,0,0,0,0,24,0,0,0,0,0,0,24],[3,8,0,0,0,0,28,26,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,1,0,0,0,0,0,0,1,0,0],[3,8,0,0,0,0,28,26,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,1,0,0],[1,6,0,0,0,0,0,28,0,0,0,0,0,0,0,28,0,0,0,0,1,0,0,0,0,0,0,0,0,28,0,0,0,0,1,0],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,20,11,0,0,0,0,11,9,0,0,0,0,0,0,20,11,0,0,0,0,11,9] >;
C14.62- 1+4 in GAP, Magma, Sage, TeX
C_{14}._62_-^{1+4} % in TeX
G:=Group("C14.6ES-(2,2)"); // GroupNames label
G:=SmallGroup(448,968);
// by ID
G=gap.SmallGroup(448,968);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,100,675,297,136,18822]);
// 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=c*a*c=a^-1,a*d=d*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=b^2*d>;
// generators/relations