G = C14.442- 1+4 order 448 = 26·7
44th non-split extension by C14 of 2- 1+4 acting via 2- 1+4/C2×Q8=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.442- 1+4, (C22×Q8)⋊8D7, (C2×C28).216D4, C28.261(C2×D4), D14⋊3Q8⋊41C2, (C2×Q8).188D14, Dic7⋊Q8⋊30C2, C28.23D4⋊29C2, (C2×C28).648C23, (C2×C14).308C24, D14⋊C4.77C22, (C22×C4).278D14, C14.156(C22×D4), (C2×D28).279C22, Dic7⋊C4.90C22, C4⋊Dic7.390C22, (Q8×C14).235C22, C22.319(C23×D7), C23.239(C22×D7), C23.21D14⋊34C2, C23.23D14⋊29C2, (C22×C14).426C23, (C22×C28).440C22, C7⋊6(C23.38C23), (C4×Dic7).171C22, (C2×Dic7).159C23, (C22×D7).134C23, C23.D7.132C22, C2.44(Q8.10D14), (C2×Dic14).308C22, (Q8×C2×C14)⋊7C2, C4.99(C2×C7⋊D4), (C2×C4○D28).25C2, (C2×C14).590(C2×D4), (C2×C4).94(C7⋊D4), (C2×C4×D7).165C22, C22.37(C2×C7⋊D4), C2.29(C22×C7⋊D4), (C2×C4).634(C22×D7), (C2×C7⋊D4).138C22, SmallGroup(448,1269)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.442- 1+4
G = < a,b,c,d,e | a14=b4=1, c2=a7, d2=e2=a7b2, bab-1=cac-1=a-1, ad=da, ae=ea, cbc-1=a7b-1, dbd-1=ebe-1=a7b, dcd-1=ece-1=a7c, ede-1=a7b2d >
Subgroups: 1076 in 270 conjugacy classes, 111 normal (21 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C14, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×D4, C2×Q8, C2×Q8, C4○D4, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C14, C42⋊C2, C22⋊Q8, C22.D4, C4.4D4, C4⋊Q8, C22×Q8, C2×C4○D4, Dic14, C4×D7, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×Q8, C22×D7, C22×C14, C23.38C23, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C2×Dic14, C2×C4×D7, C2×D28, C4○D28, C2×C7⋊D4, C22×C28, C22×C28, Q8×C14, Q8×C14, C23.21D14, C23.23D14, Dic7⋊Q8, D14⋊3Q8, C28.23D4, C2×C4○D28, Q8×C2×C14, C14.442- 1+4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C24, D14, C22×D4, 2- 1+4, C7⋊D4, C22×D7, C23.38C23, C2×C7⋊D4, C23×D7, Q8.10D14, C22×C7⋊D4, C14.442- 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 90 71 45)(2 89 72 44)(3 88 73 43)(4 87 74 56)(5 86 75 55)(6 85 76 54)(7 98 77 53)(8 97 78 52)(9 96 79 51)(10 95 80 50)(11 94 81 49)(12 93 82 48)(13 92 83 47)(14 91 84 46)(15 204 126 68)(16 203 113 67)(17 202 114 66)(18 201 115 65)(19 200 116 64)(20 199 117 63)(21 198 118 62)(22 197 119 61)(23 210 120 60)(24 209 121 59)(25 208 122 58)(26 207 123 57)(27 206 124 70)(28 205 125 69)(29 175 193 132)(30 174 194 131)(31 173 195 130)(32 172 196 129)(33 171 183 128)(34 170 184 127)(35 169 185 140)(36 182 186 139)(37 181 187 138)(38 180 188 137)(39 179 189 136)(40 178 190 135)(41 177 191 134)(42 176 192 133)(99 148 220 156)(100 147 221 155)(101 146 222 168)(102 145 223 167)(103 144 224 166)(104 143 211 165)(105 142 212 164)(106 141 213 163)(107 154 214 162)(108 153 215 161)(109 152 216 160)(110 151 217 159)(111 150 218 158)(112 149 219 157)
(1 52 8 45)(2 51 9 44)(3 50 10 43)(4 49 11 56)(5 48 12 55)(6 47 13 54)(7 46 14 53)(15 61 22 68)(16 60 23 67)(17 59 24 66)(18 58 25 65)(19 57 26 64)(20 70 27 63)(21 69 28 62)(29 175 36 182)(30 174 37 181)(31 173 38 180)(32 172 39 179)(33 171 40 178)(34 170 41 177)(35 169 42 176)(71 97 78 90)(72 96 79 89)(73 95 80 88)(74 94 81 87)(75 93 82 86)(76 92 83 85)(77 91 84 98)(99 163 106 156)(100 162 107 155)(101 161 108 168)(102 160 109 167)(103 159 110 166)(104 158 111 165)(105 157 112 164)(113 210 120 203)(114 209 121 202)(115 208 122 201)(116 207 123 200)(117 206 124 199)(118 205 125 198)(119 204 126 197)(127 191 134 184)(128 190 135 183)(129 189 136 196)(130 188 137 195)(131 187 138 194)(132 186 139 193)(133 185 140 192)(141 213 148 220)(142 212 149 219)(143 211 150 218)(144 224 151 217)(145 223 152 216)(146 222 153 215)(147 221 154 214)
(1 171 78 135)(2 172 79 136)(3 173 80 137)(4 174 81 138)(5 175 82 139)(6 176 83 140)(7 177 84 127)(8 178 71 128)(9 179 72 129)(10 180 73 130)(11 181 74 131)(12 182 75 132)(13 169 76 133)(14 170 77 134)(15 105 119 219)(16 106 120 220)(17 107 121 221)(18 108 122 222)(19 109 123 223)(20 110 124 224)(21 111 125 211)(22 112 126 212)(23 99 113 213)(24 100 114 214)(25 101 115 215)(26 102 116 216)(27 103 117 217)(28 104 118 218)(29 86 186 48)(30 87 187 49)(31 88 188 50)(32 89 189 51)(33 90 190 52)(34 91 191 53)(35 92 192 54)(36 93 193 55)(37 94 194 56)(38 95 195 43)(39 96 196 44)(40 97 183 45)(41 98 184 46)(42 85 185 47)(57 160 200 145)(58 161 201 146)(59 162 202 147)(60 163 203 148)(61 164 204 149)(62 165 205 150)(63 166 206 151)(64 167 207 152)(65 168 208 153)(66 155 209 154)(67 156 210 141)(68 157 197 142)(69 158 198 143)(70 159 199 144)
(1 218 78 104)(2 219 79 105)(3 220 80 106)(4 221 81 107)(5 222 82 108)(6 223 83 109)(7 224 84 110)(8 211 71 111)(9 212 72 112)(10 213 73 99)(11 214 74 100)(12 215 75 101)(13 216 76 102)(14 217 77 103)(15 172 119 136)(16 173 120 137)(17 174 121 138)(18 175 122 139)(19 176 123 140)(20 177 124 127)(21 178 125 128)(22 179 126 129)(23 180 113 130)(24 181 114 131)(25 182 115 132)(26 169 116 133)(27 170 117 134)(28 171 118 135)(29 201 186 58)(30 202 187 59)(31 203 188 60)(32 204 189 61)(33 205 190 62)(34 206 191 63)(35 207 192 64)(36 208 193 65)(37 209 194 66)(38 210 195 67)(39 197 196 68)(40 198 183 69)(41 199 184 70)(42 200 185 57)(43 141 95 156)(44 142 96 157)(45 143 97 158)(46 144 98 159)(47 145 85 160)(48 146 86 161)(49 147 87 162)(50 148 88 163)(51 149 89 164)(52 150 90 165)(53 151 91 166)(54 152 92 167)(55 153 93 168)(56 154 94 155)
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), (1,90,71,45)(2,89,72,44)(3,88,73,43)(4,87,74,56)(5,86,75,55)(6,85,76,54)(7,98,77,53)(8,97,78,52)(9,96,79,51)(10,95,80,50)(11,94,81,49)(12,93,82,48)(13,92,83,47)(14,91,84,46)(15,204,126,68)(16,203,113,67)(17,202,114,66)(18,201,115,65)(19,200,116,64)(20,199,117,63)(21,198,118,62)(22,197,119,61)(23,210,120,60)(24,209,121,59)(25,208,122,58)(26,207,123,57)(27,206,124,70)(28,205,125,69)(29,175,193,132)(30,174,194,131)(31,173,195,130)(32,172,196,129)(33,171,183,128)(34,170,184,127)(35,169,185,140)(36,182,186,139)(37,181,187,138)(38,180,188,137)(39,179,189,136)(40,178,190,135)(41,177,191,134)(42,176,192,133)(99,148,220,156)(100,147,221,155)(101,146,222,168)(102,145,223,167)(103,144,224,166)(104,143,211,165)(105,142,212,164)(106,141,213,163)(107,154,214,162)(108,153,215,161)(109,152,216,160)(110,151,217,159)(111,150,218,158)(112,149,219,157), (1,52,8,45)(2,51,9,44)(3,50,10,43)(4,49,11,56)(5,48,12,55)(6,47,13,54)(7,46,14,53)(15,61,22,68)(16,60,23,67)(17,59,24,66)(18,58,25,65)(19,57,26,64)(20,70,27,63)(21,69,28,62)(29,175,36,182)(30,174,37,181)(31,173,38,180)(32,172,39,179)(33,171,40,178)(34,170,41,177)(35,169,42,176)(71,97,78,90)(72,96,79,89)(73,95,80,88)(74,94,81,87)(75,93,82,86)(76,92,83,85)(77,91,84,98)(99,163,106,156)(100,162,107,155)(101,161,108,168)(102,160,109,167)(103,159,110,166)(104,158,111,165)(105,157,112,164)(113,210,120,203)(114,209,121,202)(115,208,122,201)(116,207,123,200)(117,206,124,199)(118,205,125,198)(119,204,126,197)(127,191,134,184)(128,190,135,183)(129,189,136,196)(130,188,137,195)(131,187,138,194)(132,186,139,193)(133,185,140,192)(141,213,148,220)(142,212,149,219)(143,211,150,218)(144,224,151,217)(145,223,152,216)(146,222,153,215)(147,221,154,214), (1,171,78,135)(2,172,79,136)(3,173,80,137)(4,174,81,138)(5,175,82,139)(6,176,83,140)(7,177,84,127)(8,178,71,128)(9,179,72,129)(10,180,73,130)(11,181,74,131)(12,182,75,132)(13,169,76,133)(14,170,77,134)(15,105,119,219)(16,106,120,220)(17,107,121,221)(18,108,122,222)(19,109,123,223)(20,110,124,224)(21,111,125,211)(22,112,126,212)(23,99,113,213)(24,100,114,214)(25,101,115,215)(26,102,116,216)(27,103,117,217)(28,104,118,218)(29,86,186,48)(30,87,187,49)(31,88,188,50)(32,89,189,51)(33,90,190,52)(34,91,191,53)(35,92,192,54)(36,93,193,55)(37,94,194,56)(38,95,195,43)(39,96,196,44)(40,97,183,45)(41,98,184,46)(42,85,185,47)(57,160,200,145)(58,161,201,146)(59,162,202,147)(60,163,203,148)(61,164,204,149)(62,165,205,150)(63,166,206,151)(64,167,207,152)(65,168,208,153)(66,155,209,154)(67,156,210,141)(68,157,197,142)(69,158,198,143)(70,159,199,144), (1,218,78,104)(2,219,79,105)(3,220,80,106)(4,221,81,107)(5,222,82,108)(6,223,83,109)(7,224,84,110)(8,211,71,111)(9,212,72,112)(10,213,73,99)(11,214,74,100)(12,215,75,101)(13,216,76,102)(14,217,77,103)(15,172,119,136)(16,173,120,137)(17,174,121,138)(18,175,122,139)(19,176,123,140)(20,177,124,127)(21,178,125,128)(22,179,126,129)(23,180,113,130)(24,181,114,131)(25,182,115,132)(26,169,116,133)(27,170,117,134)(28,171,118,135)(29,201,186,58)(30,202,187,59)(31,203,188,60)(32,204,189,61)(33,205,190,62)(34,206,191,63)(35,207,192,64)(36,208,193,65)(37,209,194,66)(38,210,195,67)(39,197,196,68)(40,198,183,69)(41,199,184,70)(42,200,185,57)(43,141,95,156)(44,142,96,157)(45,143,97,158)(46,144,98,159)(47,145,85,160)(48,146,86,161)(49,147,87,162)(50,148,88,163)(51,149,89,164)(52,150,90,165)(53,151,91,166)(54,152,92,167)(55,153,93,168)(56,154,94,155)>;
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), (1,90,71,45)(2,89,72,44)(3,88,73,43)(4,87,74,56)(5,86,75,55)(6,85,76,54)(7,98,77,53)(8,97,78,52)(9,96,79,51)(10,95,80,50)(11,94,81,49)(12,93,82,48)(13,92,83,47)(14,91,84,46)(15,204,126,68)(16,203,113,67)(17,202,114,66)(18,201,115,65)(19,200,116,64)(20,199,117,63)(21,198,118,62)(22,197,119,61)(23,210,120,60)(24,209,121,59)(25,208,122,58)(26,207,123,57)(27,206,124,70)(28,205,125,69)(29,175,193,132)(30,174,194,131)(31,173,195,130)(32,172,196,129)(33,171,183,128)(34,170,184,127)(35,169,185,140)(36,182,186,139)(37,181,187,138)(38,180,188,137)(39,179,189,136)(40,178,190,135)(41,177,191,134)(42,176,192,133)(99,148,220,156)(100,147,221,155)(101,146,222,168)(102,145,223,167)(103,144,224,166)(104,143,211,165)(105,142,212,164)(106,141,213,163)(107,154,214,162)(108,153,215,161)(109,152,216,160)(110,151,217,159)(111,150,218,158)(112,149,219,157), (1,52,8,45)(2,51,9,44)(3,50,10,43)(4,49,11,56)(5,48,12,55)(6,47,13,54)(7,46,14,53)(15,61,22,68)(16,60,23,67)(17,59,24,66)(18,58,25,65)(19,57,26,64)(20,70,27,63)(21,69,28,62)(29,175,36,182)(30,174,37,181)(31,173,38,180)(32,172,39,179)(33,171,40,178)(34,170,41,177)(35,169,42,176)(71,97,78,90)(72,96,79,89)(73,95,80,88)(74,94,81,87)(75,93,82,86)(76,92,83,85)(77,91,84,98)(99,163,106,156)(100,162,107,155)(101,161,108,168)(102,160,109,167)(103,159,110,166)(104,158,111,165)(105,157,112,164)(113,210,120,203)(114,209,121,202)(115,208,122,201)(116,207,123,200)(117,206,124,199)(118,205,125,198)(119,204,126,197)(127,191,134,184)(128,190,135,183)(129,189,136,196)(130,188,137,195)(131,187,138,194)(132,186,139,193)(133,185,140,192)(141,213,148,220)(142,212,149,219)(143,211,150,218)(144,224,151,217)(145,223,152,216)(146,222,153,215)(147,221,154,214), (1,171,78,135)(2,172,79,136)(3,173,80,137)(4,174,81,138)(5,175,82,139)(6,176,83,140)(7,177,84,127)(8,178,71,128)(9,179,72,129)(10,180,73,130)(11,181,74,131)(12,182,75,132)(13,169,76,133)(14,170,77,134)(15,105,119,219)(16,106,120,220)(17,107,121,221)(18,108,122,222)(19,109,123,223)(20,110,124,224)(21,111,125,211)(22,112,126,212)(23,99,113,213)(24,100,114,214)(25,101,115,215)(26,102,116,216)(27,103,117,217)(28,104,118,218)(29,86,186,48)(30,87,187,49)(31,88,188,50)(32,89,189,51)(33,90,190,52)(34,91,191,53)(35,92,192,54)(36,93,193,55)(37,94,194,56)(38,95,195,43)(39,96,196,44)(40,97,183,45)(41,98,184,46)(42,85,185,47)(57,160,200,145)(58,161,201,146)(59,162,202,147)(60,163,203,148)(61,164,204,149)(62,165,205,150)(63,166,206,151)(64,167,207,152)(65,168,208,153)(66,155,209,154)(67,156,210,141)(68,157,197,142)(69,158,198,143)(70,159,199,144), (1,218,78,104)(2,219,79,105)(3,220,80,106)(4,221,81,107)(5,222,82,108)(6,223,83,109)(7,224,84,110)(8,211,71,111)(9,212,72,112)(10,213,73,99)(11,214,74,100)(12,215,75,101)(13,216,76,102)(14,217,77,103)(15,172,119,136)(16,173,120,137)(17,174,121,138)(18,175,122,139)(19,176,123,140)(20,177,124,127)(21,178,125,128)(22,179,126,129)(23,180,113,130)(24,181,114,131)(25,182,115,132)(26,169,116,133)(27,170,117,134)(28,171,118,135)(29,201,186,58)(30,202,187,59)(31,203,188,60)(32,204,189,61)(33,205,190,62)(34,206,191,63)(35,207,192,64)(36,208,193,65)(37,209,194,66)(38,210,195,67)(39,197,196,68)(40,198,183,69)(41,199,184,70)(42,200,185,57)(43,141,95,156)(44,142,96,157)(45,143,97,158)(46,144,98,159)(47,145,85,160)(48,146,86,161)(49,147,87,162)(50,148,88,163)(51,149,89,164)(52,150,90,165)(53,151,91,166)(54,152,92,167)(55,153,93,168)(56,154,94,155) );
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)], [(1,90,71,45),(2,89,72,44),(3,88,73,43),(4,87,74,56),(5,86,75,55),(6,85,76,54),(7,98,77,53),(8,97,78,52),(9,96,79,51),(10,95,80,50),(11,94,81,49),(12,93,82,48),(13,92,83,47),(14,91,84,46),(15,204,126,68),(16,203,113,67),(17,202,114,66),(18,201,115,65),(19,200,116,64),(20,199,117,63),(21,198,118,62),(22,197,119,61),(23,210,120,60),(24,209,121,59),(25,208,122,58),(26,207,123,57),(27,206,124,70),(28,205,125,69),(29,175,193,132),(30,174,194,131),(31,173,195,130),(32,172,196,129),(33,171,183,128),(34,170,184,127),(35,169,185,140),(36,182,186,139),(37,181,187,138),(38,180,188,137),(39,179,189,136),(40,178,190,135),(41,177,191,134),(42,176,192,133),(99,148,220,156),(100,147,221,155),(101,146,222,168),(102,145,223,167),(103,144,224,166),(104,143,211,165),(105,142,212,164),(106,141,213,163),(107,154,214,162),(108,153,215,161),(109,152,216,160),(110,151,217,159),(111,150,218,158),(112,149,219,157)], [(1,52,8,45),(2,51,9,44),(3,50,10,43),(4,49,11,56),(5,48,12,55),(6,47,13,54),(7,46,14,53),(15,61,22,68),(16,60,23,67),(17,59,24,66),(18,58,25,65),(19,57,26,64),(20,70,27,63),(21,69,28,62),(29,175,36,182),(30,174,37,181),(31,173,38,180),(32,172,39,179),(33,171,40,178),(34,170,41,177),(35,169,42,176),(71,97,78,90),(72,96,79,89),(73,95,80,88),(74,94,81,87),(75,93,82,86),(76,92,83,85),(77,91,84,98),(99,163,106,156),(100,162,107,155),(101,161,108,168),(102,160,109,167),(103,159,110,166),(104,158,111,165),(105,157,112,164),(113,210,120,203),(114,209,121,202),(115,208,122,201),(116,207,123,200),(117,206,124,199),(118,205,125,198),(119,204,126,197),(127,191,134,184),(128,190,135,183),(129,189,136,196),(130,188,137,195),(131,187,138,194),(132,186,139,193),(133,185,140,192),(141,213,148,220),(142,212,149,219),(143,211,150,218),(144,224,151,217),(145,223,152,216),(146,222,153,215),(147,221,154,214)], [(1,171,78,135),(2,172,79,136),(3,173,80,137),(4,174,81,138),(5,175,82,139),(6,176,83,140),(7,177,84,127),(8,178,71,128),(9,179,72,129),(10,180,73,130),(11,181,74,131),(12,182,75,132),(13,169,76,133),(14,170,77,134),(15,105,119,219),(16,106,120,220),(17,107,121,221),(18,108,122,222),(19,109,123,223),(20,110,124,224),(21,111,125,211),(22,112,126,212),(23,99,113,213),(24,100,114,214),(25,101,115,215),(26,102,116,216),(27,103,117,217),(28,104,118,218),(29,86,186,48),(30,87,187,49),(31,88,188,50),(32,89,189,51),(33,90,190,52),(34,91,191,53),(35,92,192,54),(36,93,193,55),(37,94,194,56),(38,95,195,43),(39,96,196,44),(40,97,183,45),(41,98,184,46),(42,85,185,47),(57,160,200,145),(58,161,201,146),(59,162,202,147),(60,163,203,148),(61,164,204,149),(62,165,205,150),(63,166,206,151),(64,167,207,152),(65,168,208,153),(66,155,209,154),(67,156,210,141),(68,157,197,142),(69,158,198,143),(70,159,199,144)], [(1,218,78,104),(2,219,79,105),(3,220,80,106),(4,221,81,107),(5,222,82,108),(6,223,83,109),(7,224,84,110),(8,211,71,111),(9,212,72,112),(10,213,73,99),(11,214,74,100),(12,215,75,101),(13,216,76,102),(14,217,77,103),(15,172,119,136),(16,173,120,137),(17,174,121,138),(18,175,122,139),(19,176,123,140),(20,177,124,127),(21,178,125,128),(22,179,126,129),(23,180,113,130),(24,181,114,131),(25,182,115,132),(26,169,116,133),(27,170,117,134),(28,171,118,135),(29,201,186,58),(30,202,187,59),(31,203,188,60),(32,204,189,61),(33,205,190,62),(34,206,191,63),(35,207,192,64),(36,208,193,65),(37,209,194,66),(38,210,195,67),(39,197,196,68),(40,198,183,69),(41,199,184,70),(42,200,185,57),(43,141,95,156),(44,142,96,157),(45,143,97,158),(46,144,98,159),(47,145,85,160),(48,146,86,161),(49,147,87,162),(50,148,88,163),(51,149,89,164),(52,150,90,165),(53,151,91,166),(54,152,92,167),(55,153,93,168),(56,154,94,155)]])
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 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | D14 | D14 | C7⋊D4 | 2- 1+4 | Q8.10D14 |
| kernel | C14.442- 1+4 | C23.21D14 | C23.23D14 | Dic7⋊Q8 | D14⋊3Q8 | C28.23D4 | C2×C4○D28 | Q8×C2×C14 | C2×C28 | C22×Q8 | C22×C4 | C2×Q8 | C2×C4 | C14 | C2 |
| # reps | 1 | 1 | 4 | 2 | 4 | 2 | 1 | 1 | 4 | 3 | 9 | 12 | 24 | 2 | 12 |
Matrix representation of C14.442- 1+4 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 13 | 0 | 0 | 0 |
| 0 | 0 | 0 | 13 | 0 | 0 |
| 0 | 0 | 23 | 0 | 9 | 0 |
| 0 | 0 | 24 | 0 | 0 | 9 |
| 12 | 16 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 0 | 9 | 27 |
| 0 | 0 | 8 | 0 | 11 | 28 |
| 0 | 0 | 18 | 18 | 1 | 3 |
| 0 | 0 | 25 | 23 | 25 | 17 |
| 17 | 13 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 0 | 9 | 27 |
| 0 | 0 | 8 | 0 | 11 | 28 |
| 0 | 0 | 7 | 11 | 1 | 3 |
| 0 | 0 | 20 | 6 | 25 | 17 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 16 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 23 | 28 | 0 | 0 |
| 0 | 0 | 8 | 6 | 0 | 0 |
| 0 | 0 | 27 | 16 | 5 | 20 |
| 0 | 0 | 8 | 23 | 19 | 24 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 13 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 2 | 0 | 0 |
| 0 | 0 | 28 | 1 | 0 | 0 |
| 0 | 0 | 28 | 26 | 23 | 11 |
| 0 | 0 | 7 | 12 | 23 | 6 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,13,0,23,24,0,0,0,13,0,0,0,0,0,0,9,0,0,0,0,0,0,9],[12,0,0,0,0,0,16,17,0,0,0,0,0,0,11,8,18,25,0,0,0,0,18,23,0,0,9,11,1,25,0,0,27,28,3,17],[17,0,0,0,0,0,13,12,0,0,0,0,0,0,11,8,7,20,0,0,0,0,11,6,0,0,9,11,1,25,0,0,27,28,3,17],[28,16,0,0,0,0,0,1,0,0,0,0,0,0,23,8,27,8,0,0,28,6,16,23,0,0,0,0,5,19,0,0,0,0,20,24],[1,13,0,0,0,0,0,28,0,0,0,0,0,0,28,28,28,7,0,0,2,1,26,12,0,0,0,0,23,23,0,0,0,0,11,6] >;
C14.442- 1+4 in GAP, Magma, Sage, TeX
C_{14}._{44}2_-^{1+4} % in TeX
G:=Group("C14.44ES-(2,2)"); // GroupNames label
G:=SmallGroup(448,1269);
// by ID
G=gap.SmallGroup(448,1269);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,675,570,136,18822]);
// 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=a^-1,a*d=d*a,a*e=e*a,c*b*c^-1=a^7*b^-1,d*b*d^-1=e*b*e^-1=a^7*b,d*c*d^-1=e*c*e^-1=a^7*c,e*d*e^-1=a^7*b^2*d>;
// generators/relations