G = C14.602+ 1+4 order 448 = 26·7
60th non-split extension by C14 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.602+ 1+4, C14.812- 1+4, C28⋊Q8⋊31C2, C4⋊C4.105D14, (C2×D4).97D14, Dic7.Q8⋊26C2, C22⋊C4.26D14, C28.48D4⋊14C2, (C2×C14).195C24, (C2×C28).178C23, C28.17D4.8C2, (C22×C4).256D14, C2.62(D4⋊6D14), C22.D4.3D7, C22⋊Dic14⋊30C2, (D4×C14).133C22, C23.D14⋊29C2, Dic7⋊C4.40C22, C4⋊Dic7.226C22, (C22×C28).86C22, C22.216(C23×D7), C23.128(C22×D7), C23.D7.41C22, (C22×C14).220C23, C7⋊2(C22.57C24), (C2×Dic14).36C22, (C2×Dic7).100C23, (C4×Dic7).122C22, C23.18D14.3C2, C2.42(D4.10D14), (C22×Dic7).128C22, (C2×C4).59(C22×D7), (C7×C4⋊C4).175C22, (C7×C22⋊C4).50C22, (C7×C22.D4).3C2, SmallGroup(448,1104)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.602+ 1+4
G = < a,b,c,d,e | a14=b4=1, c2=a7, d2=e2=a7b2, bab-1=cac-1=eae-1=a-1, ad=da, cbc-1=b-1, bd=db, ebe-1=a7b, dcd-1=a7c, ce=ec, ede-1=a7b2d >
Subgroups: 780 in 196 conjugacy classes, 91 normal (27 characteristic)
C1, C2, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C14, C14, C14, C42, C22⋊C4, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, Dic7, C28, C2×C14, C2×C14, C22⋊Q8, C22.D4, C22.D4, C4.4D4, C42.C2, C42⋊2C2, C4⋊Q8, Dic14, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C2×C28, C7×D4, C22×C14, C22.57C24, C4×Dic7, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C23.D7, C23.D7, C7×C22⋊C4, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C22×Dic7, C22×C28, D4×C14, C22⋊Dic14, C23.D14, C28⋊Q8, Dic7.Q8, C28.48D4, C23.18D14, C28.17D4, C7×C22.D4, C14.602+ 1+4
Quotients: C1, C2, C22, C23, D7, C24, D14, 2+ 1+4, 2- 1+4, C22×D7, C22.57C24, C23×D7, D4⋊6D14, D4.10D14, C14.602+ 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 98 223 161)(2 97 224 160)(3 96 211 159)(4 95 212 158)(5 94 213 157)(6 93 214 156)(7 92 215 155)(8 91 216 168)(9 90 217 167)(10 89 218 166)(11 88 219 165)(12 87 220 164)(13 86 221 163)(14 85 222 162)(15 200 63 184)(16 199 64 183)(17 198 65 196)(18 197 66 195)(19 210 67 194)(20 209 68 193)(21 208 69 192)(22 207 70 191)(23 206 57 190)(24 205 58 189)(25 204 59 188)(26 203 60 187)(27 202 61 186)(28 201 62 185)(29 84 132 46)(30 83 133 45)(31 82 134 44)(32 81 135 43)(33 80 136 56)(34 79 137 55)(35 78 138 54)(36 77 139 53)(37 76 140 52)(38 75 127 51)(39 74 128 50)(40 73 129 49)(41 72 130 48)(42 71 131 47)(99 153 177 115)(100 152 178 114)(101 151 179 113)(102 150 180 126)(103 149 181 125)(104 148 182 124)(105 147 169 123)(106 146 170 122)(107 145 171 121)(108 144 172 120)(109 143 173 119)(110 142 174 118)(111 141 175 117)(112 154 176 116)
(1 103 8 110)(2 102 9 109)(3 101 10 108)(4 100 11 107)(5 99 12 106)(6 112 13 105)(7 111 14 104)(15 132 22 139)(16 131 23 138)(17 130 24 137)(18 129 25 136)(19 128 26 135)(20 127 27 134)(21 140 28 133)(29 70 36 63)(30 69 37 62)(31 68 38 61)(32 67 39 60)(33 66 40 59)(34 65 41 58)(35 64 42 57)(43 194 50 187)(44 193 51 186)(45 192 52 185)(46 191 53 184)(47 190 54 183)(48 189 55 196)(49 188 56 195)(71 206 78 199)(72 205 79 198)(73 204 80 197)(74 203 81 210)(75 202 82 209)(76 201 83 208)(77 200 84 207)(85 124 92 117)(86 123 93 116)(87 122 94 115)(88 121 95 114)(89 120 96 113)(90 119 97 126)(91 118 98 125)(141 162 148 155)(142 161 149 168)(143 160 150 167)(144 159 151 166)(145 158 152 165)(146 157 153 164)(147 156 154 163)(169 214 176 221)(170 213 177 220)(171 212 178 219)(172 211 179 218)(173 224 180 217)(174 223 181 216)(175 222 182 215)
(1 132 216 36)(2 133 217 37)(3 134 218 38)(4 135 219 39)(5 136 220 40)(6 137 221 41)(7 138 222 42)(8 139 223 29)(9 140 224 30)(10 127 211 31)(11 128 212 32)(12 129 213 33)(13 130 214 34)(14 131 215 35)(15 174 70 103)(16 175 57 104)(17 176 58 105)(18 177 59 106)(19 178 60 107)(20 179 61 108)(21 180 62 109)(22 181 63 110)(23 182 64 111)(24 169 65 112)(25 170 66 99)(26 171 67 100)(27 172 68 101)(28 173 69 102)(43 165 74 95)(44 166 75 96)(45 167 76 97)(46 168 77 98)(47 155 78 85)(48 156 79 86)(49 157 80 87)(50 158 81 88)(51 159 82 89)(52 160 83 90)(53 161 84 91)(54 162 71 92)(55 163 72 93)(56 164 73 94)(113 186 144 209)(114 187 145 210)(115 188 146 197)(116 189 147 198)(117 190 148 199)(118 191 149 200)(119 192 150 201)(120 193 151 202)(121 194 152 203)(122 195 153 204)(123 196 154 205)(124 183 141 206)(125 184 142 207)(126 185 143 208)
(1 84 216 53)(2 83 217 52)(3 82 218 51)(4 81 219 50)(5 80 220 49)(6 79 221 48)(7 78 222 47)(8 77 223 46)(9 76 224 45)(10 75 211 44)(11 74 212 43)(12 73 213 56)(13 72 214 55)(14 71 215 54)(15 142 70 125)(16 141 57 124)(17 154 58 123)(18 153 59 122)(19 152 60 121)(20 151 61 120)(21 150 62 119)(22 149 63 118)(23 148 64 117)(24 147 65 116)(25 146 66 115)(26 145 67 114)(27 144 68 113)(28 143 69 126)(29 98 139 168)(30 97 140 167)(31 96 127 166)(32 95 128 165)(33 94 129 164)(34 93 130 163)(35 92 131 162)(36 91 132 161)(37 90 133 160)(38 89 134 159)(39 88 135 158)(40 87 136 157)(41 86 137 156)(42 85 138 155)(99 197 170 188)(100 210 171 187)(101 209 172 186)(102 208 173 185)(103 207 174 184)(104 206 175 183)(105 205 176 196)(106 204 177 195)(107 203 178 194)(108 202 179 193)(109 201 180 192)(110 200 181 191)(111 199 182 190)(112 198 169 189)
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), (1,98,223,161)(2,97,224,160)(3,96,211,159)(4,95,212,158)(5,94,213,157)(6,93,214,156)(7,92,215,155)(8,91,216,168)(9,90,217,167)(10,89,218,166)(11,88,219,165)(12,87,220,164)(13,86,221,163)(14,85,222,162)(15,200,63,184)(16,199,64,183)(17,198,65,196)(18,197,66,195)(19,210,67,194)(20,209,68,193)(21,208,69,192)(22,207,70,191)(23,206,57,190)(24,205,58,189)(25,204,59,188)(26,203,60,187)(27,202,61,186)(28,201,62,185)(29,84,132,46)(30,83,133,45)(31,82,134,44)(32,81,135,43)(33,80,136,56)(34,79,137,55)(35,78,138,54)(36,77,139,53)(37,76,140,52)(38,75,127,51)(39,74,128,50)(40,73,129,49)(41,72,130,48)(42,71,131,47)(99,153,177,115)(100,152,178,114)(101,151,179,113)(102,150,180,126)(103,149,181,125)(104,148,182,124)(105,147,169,123)(106,146,170,122)(107,145,171,121)(108,144,172,120)(109,143,173,119)(110,142,174,118)(111,141,175,117)(112,154,176,116), (1,103,8,110)(2,102,9,109)(3,101,10,108)(4,100,11,107)(5,99,12,106)(6,112,13,105)(7,111,14,104)(15,132,22,139)(16,131,23,138)(17,130,24,137)(18,129,25,136)(19,128,26,135)(20,127,27,134)(21,140,28,133)(29,70,36,63)(30,69,37,62)(31,68,38,61)(32,67,39,60)(33,66,40,59)(34,65,41,58)(35,64,42,57)(43,194,50,187)(44,193,51,186)(45,192,52,185)(46,191,53,184)(47,190,54,183)(48,189,55,196)(49,188,56,195)(71,206,78,199)(72,205,79,198)(73,204,80,197)(74,203,81,210)(75,202,82,209)(76,201,83,208)(77,200,84,207)(85,124,92,117)(86,123,93,116)(87,122,94,115)(88,121,95,114)(89,120,96,113)(90,119,97,126)(91,118,98,125)(141,162,148,155)(142,161,149,168)(143,160,150,167)(144,159,151,166)(145,158,152,165)(146,157,153,164)(147,156,154,163)(169,214,176,221)(170,213,177,220)(171,212,178,219)(172,211,179,218)(173,224,180,217)(174,223,181,216)(175,222,182,215), (1,132,216,36)(2,133,217,37)(3,134,218,38)(4,135,219,39)(5,136,220,40)(6,137,221,41)(7,138,222,42)(8,139,223,29)(9,140,224,30)(10,127,211,31)(11,128,212,32)(12,129,213,33)(13,130,214,34)(14,131,215,35)(15,174,70,103)(16,175,57,104)(17,176,58,105)(18,177,59,106)(19,178,60,107)(20,179,61,108)(21,180,62,109)(22,181,63,110)(23,182,64,111)(24,169,65,112)(25,170,66,99)(26,171,67,100)(27,172,68,101)(28,173,69,102)(43,165,74,95)(44,166,75,96)(45,167,76,97)(46,168,77,98)(47,155,78,85)(48,156,79,86)(49,157,80,87)(50,158,81,88)(51,159,82,89)(52,160,83,90)(53,161,84,91)(54,162,71,92)(55,163,72,93)(56,164,73,94)(113,186,144,209)(114,187,145,210)(115,188,146,197)(116,189,147,198)(117,190,148,199)(118,191,149,200)(119,192,150,201)(120,193,151,202)(121,194,152,203)(122,195,153,204)(123,196,154,205)(124,183,141,206)(125,184,142,207)(126,185,143,208), (1,84,216,53)(2,83,217,52)(3,82,218,51)(4,81,219,50)(5,80,220,49)(6,79,221,48)(7,78,222,47)(8,77,223,46)(9,76,224,45)(10,75,211,44)(11,74,212,43)(12,73,213,56)(13,72,214,55)(14,71,215,54)(15,142,70,125)(16,141,57,124)(17,154,58,123)(18,153,59,122)(19,152,60,121)(20,151,61,120)(21,150,62,119)(22,149,63,118)(23,148,64,117)(24,147,65,116)(25,146,66,115)(26,145,67,114)(27,144,68,113)(28,143,69,126)(29,98,139,168)(30,97,140,167)(31,96,127,166)(32,95,128,165)(33,94,129,164)(34,93,130,163)(35,92,131,162)(36,91,132,161)(37,90,133,160)(38,89,134,159)(39,88,135,158)(40,87,136,157)(41,86,137,156)(42,85,138,155)(99,197,170,188)(100,210,171,187)(101,209,172,186)(102,208,173,185)(103,207,174,184)(104,206,175,183)(105,205,176,196)(106,204,177,195)(107,203,178,194)(108,202,179,193)(109,201,180,192)(110,200,181,191)(111,199,182,190)(112,198,169,189)>;
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), (1,98,223,161)(2,97,224,160)(3,96,211,159)(4,95,212,158)(5,94,213,157)(6,93,214,156)(7,92,215,155)(8,91,216,168)(9,90,217,167)(10,89,218,166)(11,88,219,165)(12,87,220,164)(13,86,221,163)(14,85,222,162)(15,200,63,184)(16,199,64,183)(17,198,65,196)(18,197,66,195)(19,210,67,194)(20,209,68,193)(21,208,69,192)(22,207,70,191)(23,206,57,190)(24,205,58,189)(25,204,59,188)(26,203,60,187)(27,202,61,186)(28,201,62,185)(29,84,132,46)(30,83,133,45)(31,82,134,44)(32,81,135,43)(33,80,136,56)(34,79,137,55)(35,78,138,54)(36,77,139,53)(37,76,140,52)(38,75,127,51)(39,74,128,50)(40,73,129,49)(41,72,130,48)(42,71,131,47)(99,153,177,115)(100,152,178,114)(101,151,179,113)(102,150,180,126)(103,149,181,125)(104,148,182,124)(105,147,169,123)(106,146,170,122)(107,145,171,121)(108,144,172,120)(109,143,173,119)(110,142,174,118)(111,141,175,117)(112,154,176,116), (1,103,8,110)(2,102,9,109)(3,101,10,108)(4,100,11,107)(5,99,12,106)(6,112,13,105)(7,111,14,104)(15,132,22,139)(16,131,23,138)(17,130,24,137)(18,129,25,136)(19,128,26,135)(20,127,27,134)(21,140,28,133)(29,70,36,63)(30,69,37,62)(31,68,38,61)(32,67,39,60)(33,66,40,59)(34,65,41,58)(35,64,42,57)(43,194,50,187)(44,193,51,186)(45,192,52,185)(46,191,53,184)(47,190,54,183)(48,189,55,196)(49,188,56,195)(71,206,78,199)(72,205,79,198)(73,204,80,197)(74,203,81,210)(75,202,82,209)(76,201,83,208)(77,200,84,207)(85,124,92,117)(86,123,93,116)(87,122,94,115)(88,121,95,114)(89,120,96,113)(90,119,97,126)(91,118,98,125)(141,162,148,155)(142,161,149,168)(143,160,150,167)(144,159,151,166)(145,158,152,165)(146,157,153,164)(147,156,154,163)(169,214,176,221)(170,213,177,220)(171,212,178,219)(172,211,179,218)(173,224,180,217)(174,223,181,216)(175,222,182,215), (1,132,216,36)(2,133,217,37)(3,134,218,38)(4,135,219,39)(5,136,220,40)(6,137,221,41)(7,138,222,42)(8,139,223,29)(9,140,224,30)(10,127,211,31)(11,128,212,32)(12,129,213,33)(13,130,214,34)(14,131,215,35)(15,174,70,103)(16,175,57,104)(17,176,58,105)(18,177,59,106)(19,178,60,107)(20,179,61,108)(21,180,62,109)(22,181,63,110)(23,182,64,111)(24,169,65,112)(25,170,66,99)(26,171,67,100)(27,172,68,101)(28,173,69,102)(43,165,74,95)(44,166,75,96)(45,167,76,97)(46,168,77,98)(47,155,78,85)(48,156,79,86)(49,157,80,87)(50,158,81,88)(51,159,82,89)(52,160,83,90)(53,161,84,91)(54,162,71,92)(55,163,72,93)(56,164,73,94)(113,186,144,209)(114,187,145,210)(115,188,146,197)(116,189,147,198)(117,190,148,199)(118,191,149,200)(119,192,150,201)(120,193,151,202)(121,194,152,203)(122,195,153,204)(123,196,154,205)(124,183,141,206)(125,184,142,207)(126,185,143,208), (1,84,216,53)(2,83,217,52)(3,82,218,51)(4,81,219,50)(5,80,220,49)(6,79,221,48)(7,78,222,47)(8,77,223,46)(9,76,224,45)(10,75,211,44)(11,74,212,43)(12,73,213,56)(13,72,214,55)(14,71,215,54)(15,142,70,125)(16,141,57,124)(17,154,58,123)(18,153,59,122)(19,152,60,121)(20,151,61,120)(21,150,62,119)(22,149,63,118)(23,148,64,117)(24,147,65,116)(25,146,66,115)(26,145,67,114)(27,144,68,113)(28,143,69,126)(29,98,139,168)(30,97,140,167)(31,96,127,166)(32,95,128,165)(33,94,129,164)(34,93,130,163)(35,92,131,162)(36,91,132,161)(37,90,133,160)(38,89,134,159)(39,88,135,158)(40,87,136,157)(41,86,137,156)(42,85,138,155)(99,197,170,188)(100,210,171,187)(101,209,172,186)(102,208,173,185)(103,207,174,184)(104,206,175,183)(105,205,176,196)(106,204,177,195)(107,203,178,194)(108,202,179,193)(109,201,180,192)(110,200,181,191)(111,199,182,190)(112,198,169,189) );
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)], [(1,98,223,161),(2,97,224,160),(3,96,211,159),(4,95,212,158),(5,94,213,157),(6,93,214,156),(7,92,215,155),(8,91,216,168),(9,90,217,167),(10,89,218,166),(11,88,219,165),(12,87,220,164),(13,86,221,163),(14,85,222,162),(15,200,63,184),(16,199,64,183),(17,198,65,196),(18,197,66,195),(19,210,67,194),(20,209,68,193),(21,208,69,192),(22,207,70,191),(23,206,57,190),(24,205,58,189),(25,204,59,188),(26,203,60,187),(27,202,61,186),(28,201,62,185),(29,84,132,46),(30,83,133,45),(31,82,134,44),(32,81,135,43),(33,80,136,56),(34,79,137,55),(35,78,138,54),(36,77,139,53),(37,76,140,52),(38,75,127,51),(39,74,128,50),(40,73,129,49),(41,72,130,48),(42,71,131,47),(99,153,177,115),(100,152,178,114),(101,151,179,113),(102,150,180,126),(103,149,181,125),(104,148,182,124),(105,147,169,123),(106,146,170,122),(107,145,171,121),(108,144,172,120),(109,143,173,119),(110,142,174,118),(111,141,175,117),(112,154,176,116)], [(1,103,8,110),(2,102,9,109),(3,101,10,108),(4,100,11,107),(5,99,12,106),(6,112,13,105),(7,111,14,104),(15,132,22,139),(16,131,23,138),(17,130,24,137),(18,129,25,136),(19,128,26,135),(20,127,27,134),(21,140,28,133),(29,70,36,63),(30,69,37,62),(31,68,38,61),(32,67,39,60),(33,66,40,59),(34,65,41,58),(35,64,42,57),(43,194,50,187),(44,193,51,186),(45,192,52,185),(46,191,53,184),(47,190,54,183),(48,189,55,196),(49,188,56,195),(71,206,78,199),(72,205,79,198),(73,204,80,197),(74,203,81,210),(75,202,82,209),(76,201,83,208),(77,200,84,207),(85,124,92,117),(86,123,93,116),(87,122,94,115),(88,121,95,114),(89,120,96,113),(90,119,97,126),(91,118,98,125),(141,162,148,155),(142,161,149,168),(143,160,150,167),(144,159,151,166),(145,158,152,165),(146,157,153,164),(147,156,154,163),(169,214,176,221),(170,213,177,220),(171,212,178,219),(172,211,179,218),(173,224,180,217),(174,223,181,216),(175,222,182,215)], [(1,132,216,36),(2,133,217,37),(3,134,218,38),(4,135,219,39),(5,136,220,40),(6,137,221,41),(7,138,222,42),(8,139,223,29),(9,140,224,30),(10,127,211,31),(11,128,212,32),(12,129,213,33),(13,130,214,34),(14,131,215,35),(15,174,70,103),(16,175,57,104),(17,176,58,105),(18,177,59,106),(19,178,60,107),(20,179,61,108),(21,180,62,109),(22,181,63,110),(23,182,64,111),(24,169,65,112),(25,170,66,99),(26,171,67,100),(27,172,68,101),(28,173,69,102),(43,165,74,95),(44,166,75,96),(45,167,76,97),(46,168,77,98),(47,155,78,85),(48,156,79,86),(49,157,80,87),(50,158,81,88),(51,159,82,89),(52,160,83,90),(53,161,84,91),(54,162,71,92),(55,163,72,93),(56,164,73,94),(113,186,144,209),(114,187,145,210),(115,188,146,197),(116,189,147,198),(117,190,148,199),(118,191,149,200),(119,192,150,201),(120,193,151,202),(121,194,152,203),(122,195,153,204),(123,196,154,205),(124,183,141,206),(125,184,142,207),(126,185,143,208)], [(1,84,216,53),(2,83,217,52),(3,82,218,51),(4,81,219,50),(5,80,220,49),(6,79,221,48),(7,78,222,47),(8,77,223,46),(9,76,224,45),(10,75,211,44),(11,74,212,43),(12,73,213,56),(13,72,214,55),(14,71,215,54),(15,142,70,125),(16,141,57,124),(17,154,58,123),(18,153,59,122),(19,152,60,121),(20,151,61,120),(21,150,62,119),(22,149,63,118),(23,148,64,117),(24,147,65,116),(25,146,66,115),(26,145,67,114),(27,144,68,113),(28,143,69,126),(29,98,139,168),(30,97,140,167),(31,96,127,166),(32,95,128,165),(33,94,129,164),(34,93,130,163),(35,92,131,162),(36,91,132,161),(37,90,133,160),(38,89,134,159),(39,88,135,158),(40,87,136,157),(41,86,137,156),(42,85,138,155),(99,197,170,188),(100,210,171,187),(101,209,172,186),(102,208,173,185),(103,207,174,184),(104,206,175,183),(105,205,176,196),(106,204,177,195),(107,203,178,194),(108,202,179,193),(109,201,180,192),(110,200,181,191),(111,199,182,190),(112,198,169,189)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4E | 4F | ··· | 4M | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 14P | 14Q | 14R | 28A | ··· | 28L | 28M | ··· | 28U |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 4 | ··· | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
61 irreducible representations
| dim | 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 | D7 | D14 | D14 | D14 | D14 | 2+ 1+4 | 2- 1+4 | D4⋊6D14 | D4.10D14 |
| kernel | C14.602+ 1+4 | C22⋊Dic14 | C23.D14 | C28⋊Q8 | Dic7.Q8 | C28.48D4 | C23.18D14 | C28.17D4 | C7×C22.D4 | C22.D4 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C14 | C14 | C2 | C2 |
| # reps | 1 | 2 | 4 | 2 | 2 | 2 | 1 | 1 | 1 | 3 | 9 | 6 | 3 | 3 | 1 | 2 | 6 | 12 |
Matrix representation of C14.602+ 1+4 ►in GL8(𝔽29)
| 6 | 0 | 4 | 0 | 0 | 0 | 0 | 0 |
| 0 | 6 | 0 | 13 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 13 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 | 0 | 13 |
| 9 | 20 | 13 | 22 | 0 | 0 | 0 | 0 |
| 15 | 7 | 14 | 27 | 0 | 0 | 0 | 0 |
| 5 | 24 | 20 | 22 | 0 | 0 | 0 | 0 |
| 10 | 24 | 11 | 22 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 23 | 12 | 24 |
| 0 | 0 | 0 | 0 | 0 | 8 | 26 | 26 |
| 0 | 0 | 0 | 0 | 12 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 12 | 21 | 21 |
| 20 | 0 | 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 7 | 0 | 10 | 0 | 0 | 0 | 0 |
| 24 | 0 | 9 | 0 | 0 | 0 | 0 | 0 |
| 0 | 24 | 0 | 22 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 14 | 1 | 2 |
| 0 | 0 | 0 | 0 | 0 | 20 | 0 | 7 |
| 0 | 0 | 0 | 0 | 28 | 21 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 9 | 0 | 9 |
| 28 | 1 | 21 | 17 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 26 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 7 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 14 | 1 | 2 |
| 0 | 0 | 0 | 0 | 9 | 0 | 28 | 28 |
| 9 | 20 | 1 | 5 | 0 | 0 | 0 | 0 |
| 15 | 7 | 19 | 10 | 0 | 0 | 0 | 0 |
| 5 | 24 | 20 | 22 | 0 | 0 | 0 | 0 |
| 10 | 24 | 11 | 22 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 21 | 3 | 3 |
| 0 | 0 | 0 | 0 | 17 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 17 | 8 | 8 |
G:=sub<GL(8,GF(29))| [6,0,0,0,0,0,0,0,0,6,0,0,0,0,0,0,4,0,5,0,0,0,0,0,0,13,0,5,0,0,0,0,0,0,0,0,9,0,0,0,0,0,0,0,0,9,0,28,0,0,0,0,0,0,13,0,0,0,0,0,0,0,0,13],[9,15,5,10,0,0,0,0,20,7,24,24,0,0,0,0,13,14,20,11,0,0,0,0,22,27,22,22,0,0,0,0,0,0,0,0,0,0,12,17,0,0,0,0,23,8,9,12,0,0,0,0,12,26,0,21,0,0,0,0,24,26,0,21],[20,0,24,0,0,0,0,0,0,7,0,24,0,0,0,0,28,0,9,0,0,0,0,0,0,10,0,22,0,0,0,0,0,0,0,0,0,0,28,0,0,0,0,0,14,20,21,9,0,0,0,0,1,0,0,0,0,0,0,0,2,7,0,9],[28,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,21,0,1,0,0,0,0,0,17,26,28,28,0,0,0,0,0,0,0,0,1,7,0,9,0,0,0,0,8,28,14,0,0,0,0,0,0,0,1,28,0,0,0,0,0,0,2,28],[9,15,5,10,0,0,0,0,20,7,24,24,0,0,0,0,1,19,20,11,0,0,0,0,5,10,22,22,0,0,0,0,0,0,0,0,0,0,17,12,0,0,0,0,0,21,0,17,0,0,0,0,17,3,0,8,0,0,0,0,0,3,0,8] >;
C14.602+ 1+4 in GAP, Magma, Sage, TeX
C_{14}._{60}2_+^{1+4} % in TeX
G:=Group("C14.60ES+(2,2)"); // GroupNames label
G:=SmallGroup(448,1104);
// by ID
G=gap.SmallGroup(448,1104);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,758,219,184,1571,570,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=1,c^2=a^7,d^2=e^2=a^7*b^2,b*a*b^-1=c*a*c^-1=e*a*e^-1=a^-1,a*d=d*a,c*b*c^-1=b^-1,b*d=d*b,e*b*e^-1=a^7*b,d*c*d^-1=a^7*c,c*e=e*c,e*d*e^-1=a^7*b^2*d>;
// generators/relations