G = C14.572+ 1+4 order 448 = 26·7
57th non-split extension by C14 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.572+ 1+4, C14.782- 1+4, C22⋊Q8⋊22D7, C4⋊C4.100D14, (C2×Q8).78D14, D14⋊3Q8⋊24C2, C28⋊7D4.19C2, (C2×C28).65C23, C22⋊C4.65D14, C28.3Q8⋊26C2, Dic7⋊4D4⋊16C2, D14.5D4⋊23C2, (C2×C14).189C24, D14⋊C4.72C22, (C2×D28).31C22, (C22×C4).251D14, C2.59(D4⋊6D14), C22.D28⋊17C2, C4⋊Dic7.221C22, (Q8×C14).118C22, C22.5(Q8⋊2D7), (C2×Dic7).95C23, (C22×D7).80C23, C23.197(C22×D7), C22.210(C23×D7), Dic7⋊C4.119C22, (C22×C14).217C23, (C22×C28).317C22, C7⋊5(C22.33C24), (C4×Dic7).116C22, C2.38(D4.10D14), (C22×Dic7).125C22, C4⋊C4⋊D7⋊24C2, (C7×C22⋊Q8)⋊25C2, (C2×Dic7⋊C4)⋊30C2, C14.117(C2×C4○D4), C2.21(C2×Q8⋊2D7), (C2×C4×D7).105C22, (C2×C14).29(C4○D4), (C7×C4⋊C4).169C22, (C2×C4).186(C22×D7), (C2×C7⋊D4).41C22, (C7×C22⋊C4).44C22, SmallGroup(448,1098)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.572+ 1+4
G = < a,b,c,d,e | a14=b4=c2=1, d2=a7b2, e2=b2, ab=ba, ac=ca, dad-1=a-1, ae=ea, cbc=a7b-1, dbd-1=ebe-1=a7b, cd=dc, ce=ec, ede-1=a7b2d >
Subgroups: 988 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, C22⋊C4, C4⋊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⋊Q8, C22.D4, C42.C2, C42⋊2C2, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×Q8, C22×D7, C22×C14, C22.33C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C7×C22⋊C4, C7×C4⋊C4, C7×C4⋊C4, C2×C4×D7, C2×D28, C22×Dic7, C2×C7⋊D4, C22×C28, Q8×C14, Dic7⋊4D4, C22.D28, C28.3Q8, D14.5D4, C4⋊C4⋊D7, C2×Dic7⋊C4, C28⋊7D4, D14⋊3Q8, C7×C22⋊Q8, C14.572+ 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, Q8⋊2D7, C23×D7, D4⋊6D14, C2×Q8⋊2D7, D4.10D14, C14.572+ 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 51 57 157)(2 52 58 158)(3 53 59 159)(4 54 60 160)(5 55 61 161)(6 56 62 162)(7 43 63 163)(8 44 64 164)(9 45 65 165)(10 46 66 166)(11 47 67 167)(12 48 68 168)(13 49 69 155)(14 50 70 156)(15 105 33 87)(16 106 34 88)(17 107 35 89)(18 108 36 90)(19 109 37 91)(20 110 38 92)(21 111 39 93)(22 112 40 94)(23 99 41 95)(24 100 42 96)(25 101 29 97)(26 102 30 98)(27 103 31 85)(28 104 32 86)(71 223 122 186)(72 224 123 187)(73 211 124 188)(74 212 125 189)(75 213 126 190)(76 214 113 191)(77 215 114 192)(78 216 115 193)(79 217 116 194)(80 218 117 195)(81 219 118 196)(82 220 119 183)(83 221 120 184)(84 222 121 185)(127 202 170 148)(128 203 171 149)(129 204 172 150)(130 205 173 151)(131 206 174 152)(132 207 175 153)(133 208 176 154)(134 209 177 141)(135 210 178 142)(136 197 179 143)(137 198 180 144)(138 199 181 145)(139 200 182 146)(140 201 169 147)
(43 156)(44 157)(45 158)(46 159)(47 160)(48 161)(49 162)(50 163)(51 164)(52 165)(53 166)(54 167)(55 168)(56 155)(71 115)(72 116)(73 117)(74 118)(75 119)(76 120)(77 121)(78 122)(79 123)(80 124)(81 125)(82 126)(83 113)(84 114)(85 110)(86 111)(87 112)(88 99)(89 100)(90 101)(91 102)(92 103)(93 104)(94 105)(95 106)(96 107)(97 108)(98 109)(141 202)(142 203)(143 204)(144 205)(145 206)(146 207)(147 208)(148 209)(149 210)(150 197)(151 198)(152 199)(153 200)(154 201)
(1 176 64 140)(2 175 65 139)(3 174 66 138)(4 173 67 137)(5 172 68 136)(6 171 69 135)(7 170 70 134)(8 169 57 133)(9 182 58 132)(10 181 59 131)(11 180 60 130)(12 179 61 129)(13 178 62 128)(14 177 63 127)(15 221 40 191)(16 220 41 190)(17 219 42 189)(18 218 29 188)(19 217 30 187)(20 216 31 186)(21 215 32 185)(22 214 33 184)(23 213 34 183)(24 212 35 196)(25 211 36 195)(26 224 37 194)(27 223 38 193)(28 222 39 192)(43 141 156 202)(44 154 157 201)(45 153 158 200)(46 152 159 199)(47 151 160 198)(48 150 161 197)(49 149 162 210)(50 148 163 209)(51 147 164 208)(52 146 165 207)(53 145 166 206)(54 144 167 205)(55 143 168 204)(56 142 155 203)(71 103 115 92)(72 102 116 91)(73 101 117 90)(74 100 118 89)(75 99 119 88)(76 112 120 87)(77 111 121 86)(78 110 122 85)(79 109 123 98)(80 108 124 97)(81 107 125 96)(82 106 126 95)(83 105 113 94)(84 104 114 93)
(1 187 57 224)(2 188 58 211)(3 189 59 212)(4 190 60 213)(5 191 61 214)(6 192 62 215)(7 193 63 216)(8 194 64 217)(9 195 65 218)(10 196 66 219)(11 183 67 220)(12 184 68 221)(13 185 69 222)(14 186 70 223)(15 179 33 136)(16 180 34 137)(17 181 35 138)(18 182 36 139)(19 169 37 140)(20 170 38 127)(21 171 39 128)(22 172 40 129)(23 173 41 130)(24 174 42 131)(25 175 29 132)(26 176 30 133)(27 177 31 134)(28 178 32 135)(43 71 163 122)(44 72 164 123)(45 73 165 124)(46 74 166 125)(47 75 167 126)(48 76 168 113)(49 77 155 114)(50 78 156 115)(51 79 157 116)(52 80 158 117)(53 81 159 118)(54 82 160 119)(55 83 161 120)(56 84 162 121)(85 202 103 148)(86 203 104 149)(87 204 105 150)(88 205 106 151)(89 206 107 152)(90 207 108 153)(91 208 109 154)(92 209 110 141)(93 210 111 142)(94 197 112 143)(95 198 99 144)(96 199 100 145)(97 200 101 146)(98 201 102 147)
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), (1,51,57,157)(2,52,58,158)(3,53,59,159)(4,54,60,160)(5,55,61,161)(6,56,62,162)(7,43,63,163)(8,44,64,164)(9,45,65,165)(10,46,66,166)(11,47,67,167)(12,48,68,168)(13,49,69,155)(14,50,70,156)(15,105,33,87)(16,106,34,88)(17,107,35,89)(18,108,36,90)(19,109,37,91)(20,110,38,92)(21,111,39,93)(22,112,40,94)(23,99,41,95)(24,100,42,96)(25,101,29,97)(26,102,30,98)(27,103,31,85)(28,104,32,86)(71,223,122,186)(72,224,123,187)(73,211,124,188)(74,212,125,189)(75,213,126,190)(76,214,113,191)(77,215,114,192)(78,216,115,193)(79,217,116,194)(80,218,117,195)(81,219,118,196)(82,220,119,183)(83,221,120,184)(84,222,121,185)(127,202,170,148)(128,203,171,149)(129,204,172,150)(130,205,173,151)(131,206,174,152)(132,207,175,153)(133,208,176,154)(134,209,177,141)(135,210,178,142)(136,197,179,143)(137,198,180,144)(138,199,181,145)(139,200,182,146)(140,201,169,147), (43,156)(44,157)(45,158)(46,159)(47,160)(48,161)(49,162)(50,163)(51,164)(52,165)(53,166)(54,167)(55,168)(56,155)(71,115)(72,116)(73,117)(74,118)(75,119)(76,120)(77,121)(78,122)(79,123)(80,124)(81,125)(82,126)(83,113)(84,114)(85,110)(86,111)(87,112)(88,99)(89,100)(90,101)(91,102)(92,103)(93,104)(94,105)(95,106)(96,107)(97,108)(98,109)(141,202)(142,203)(143,204)(144,205)(145,206)(146,207)(147,208)(148,209)(149,210)(150,197)(151,198)(152,199)(153,200)(154,201), (1,176,64,140)(2,175,65,139)(3,174,66,138)(4,173,67,137)(5,172,68,136)(6,171,69,135)(7,170,70,134)(8,169,57,133)(9,182,58,132)(10,181,59,131)(11,180,60,130)(12,179,61,129)(13,178,62,128)(14,177,63,127)(15,221,40,191)(16,220,41,190)(17,219,42,189)(18,218,29,188)(19,217,30,187)(20,216,31,186)(21,215,32,185)(22,214,33,184)(23,213,34,183)(24,212,35,196)(25,211,36,195)(26,224,37,194)(27,223,38,193)(28,222,39,192)(43,141,156,202)(44,154,157,201)(45,153,158,200)(46,152,159,199)(47,151,160,198)(48,150,161,197)(49,149,162,210)(50,148,163,209)(51,147,164,208)(52,146,165,207)(53,145,166,206)(54,144,167,205)(55,143,168,204)(56,142,155,203)(71,103,115,92)(72,102,116,91)(73,101,117,90)(74,100,118,89)(75,99,119,88)(76,112,120,87)(77,111,121,86)(78,110,122,85)(79,109,123,98)(80,108,124,97)(81,107,125,96)(82,106,126,95)(83,105,113,94)(84,104,114,93), (1,187,57,224)(2,188,58,211)(3,189,59,212)(4,190,60,213)(5,191,61,214)(6,192,62,215)(7,193,63,216)(8,194,64,217)(9,195,65,218)(10,196,66,219)(11,183,67,220)(12,184,68,221)(13,185,69,222)(14,186,70,223)(15,179,33,136)(16,180,34,137)(17,181,35,138)(18,182,36,139)(19,169,37,140)(20,170,38,127)(21,171,39,128)(22,172,40,129)(23,173,41,130)(24,174,42,131)(25,175,29,132)(26,176,30,133)(27,177,31,134)(28,178,32,135)(43,71,163,122)(44,72,164,123)(45,73,165,124)(46,74,166,125)(47,75,167,126)(48,76,168,113)(49,77,155,114)(50,78,156,115)(51,79,157,116)(52,80,158,117)(53,81,159,118)(54,82,160,119)(55,83,161,120)(56,84,162,121)(85,202,103,148)(86,203,104,149)(87,204,105,150)(88,205,106,151)(89,206,107,152)(90,207,108,153)(91,208,109,154)(92,209,110,141)(93,210,111,142)(94,197,112,143)(95,198,99,144)(96,199,100,145)(97,200,101,146)(98,201,102,147)>;
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), (1,51,57,157)(2,52,58,158)(3,53,59,159)(4,54,60,160)(5,55,61,161)(6,56,62,162)(7,43,63,163)(8,44,64,164)(9,45,65,165)(10,46,66,166)(11,47,67,167)(12,48,68,168)(13,49,69,155)(14,50,70,156)(15,105,33,87)(16,106,34,88)(17,107,35,89)(18,108,36,90)(19,109,37,91)(20,110,38,92)(21,111,39,93)(22,112,40,94)(23,99,41,95)(24,100,42,96)(25,101,29,97)(26,102,30,98)(27,103,31,85)(28,104,32,86)(71,223,122,186)(72,224,123,187)(73,211,124,188)(74,212,125,189)(75,213,126,190)(76,214,113,191)(77,215,114,192)(78,216,115,193)(79,217,116,194)(80,218,117,195)(81,219,118,196)(82,220,119,183)(83,221,120,184)(84,222,121,185)(127,202,170,148)(128,203,171,149)(129,204,172,150)(130,205,173,151)(131,206,174,152)(132,207,175,153)(133,208,176,154)(134,209,177,141)(135,210,178,142)(136,197,179,143)(137,198,180,144)(138,199,181,145)(139,200,182,146)(140,201,169,147), (43,156)(44,157)(45,158)(46,159)(47,160)(48,161)(49,162)(50,163)(51,164)(52,165)(53,166)(54,167)(55,168)(56,155)(71,115)(72,116)(73,117)(74,118)(75,119)(76,120)(77,121)(78,122)(79,123)(80,124)(81,125)(82,126)(83,113)(84,114)(85,110)(86,111)(87,112)(88,99)(89,100)(90,101)(91,102)(92,103)(93,104)(94,105)(95,106)(96,107)(97,108)(98,109)(141,202)(142,203)(143,204)(144,205)(145,206)(146,207)(147,208)(148,209)(149,210)(150,197)(151,198)(152,199)(153,200)(154,201), (1,176,64,140)(2,175,65,139)(3,174,66,138)(4,173,67,137)(5,172,68,136)(6,171,69,135)(7,170,70,134)(8,169,57,133)(9,182,58,132)(10,181,59,131)(11,180,60,130)(12,179,61,129)(13,178,62,128)(14,177,63,127)(15,221,40,191)(16,220,41,190)(17,219,42,189)(18,218,29,188)(19,217,30,187)(20,216,31,186)(21,215,32,185)(22,214,33,184)(23,213,34,183)(24,212,35,196)(25,211,36,195)(26,224,37,194)(27,223,38,193)(28,222,39,192)(43,141,156,202)(44,154,157,201)(45,153,158,200)(46,152,159,199)(47,151,160,198)(48,150,161,197)(49,149,162,210)(50,148,163,209)(51,147,164,208)(52,146,165,207)(53,145,166,206)(54,144,167,205)(55,143,168,204)(56,142,155,203)(71,103,115,92)(72,102,116,91)(73,101,117,90)(74,100,118,89)(75,99,119,88)(76,112,120,87)(77,111,121,86)(78,110,122,85)(79,109,123,98)(80,108,124,97)(81,107,125,96)(82,106,126,95)(83,105,113,94)(84,104,114,93), (1,187,57,224)(2,188,58,211)(3,189,59,212)(4,190,60,213)(5,191,61,214)(6,192,62,215)(7,193,63,216)(8,194,64,217)(9,195,65,218)(10,196,66,219)(11,183,67,220)(12,184,68,221)(13,185,69,222)(14,186,70,223)(15,179,33,136)(16,180,34,137)(17,181,35,138)(18,182,36,139)(19,169,37,140)(20,170,38,127)(21,171,39,128)(22,172,40,129)(23,173,41,130)(24,174,42,131)(25,175,29,132)(26,176,30,133)(27,177,31,134)(28,178,32,135)(43,71,163,122)(44,72,164,123)(45,73,165,124)(46,74,166,125)(47,75,167,126)(48,76,168,113)(49,77,155,114)(50,78,156,115)(51,79,157,116)(52,80,158,117)(53,81,159,118)(54,82,160,119)(55,83,161,120)(56,84,162,121)(85,202,103,148)(86,203,104,149)(87,204,105,150)(88,205,106,151)(89,206,107,152)(90,207,108,153)(91,208,109,154)(92,209,110,141)(93,210,111,142)(94,197,112,143)(95,198,99,144)(96,199,100,145)(97,200,101,146)(98,201,102,147) );
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)], [(1,51,57,157),(2,52,58,158),(3,53,59,159),(4,54,60,160),(5,55,61,161),(6,56,62,162),(7,43,63,163),(8,44,64,164),(9,45,65,165),(10,46,66,166),(11,47,67,167),(12,48,68,168),(13,49,69,155),(14,50,70,156),(15,105,33,87),(16,106,34,88),(17,107,35,89),(18,108,36,90),(19,109,37,91),(20,110,38,92),(21,111,39,93),(22,112,40,94),(23,99,41,95),(24,100,42,96),(25,101,29,97),(26,102,30,98),(27,103,31,85),(28,104,32,86),(71,223,122,186),(72,224,123,187),(73,211,124,188),(74,212,125,189),(75,213,126,190),(76,214,113,191),(77,215,114,192),(78,216,115,193),(79,217,116,194),(80,218,117,195),(81,219,118,196),(82,220,119,183),(83,221,120,184),(84,222,121,185),(127,202,170,148),(128,203,171,149),(129,204,172,150),(130,205,173,151),(131,206,174,152),(132,207,175,153),(133,208,176,154),(134,209,177,141),(135,210,178,142),(136,197,179,143),(137,198,180,144),(138,199,181,145),(139,200,182,146),(140,201,169,147)], [(43,156),(44,157),(45,158),(46,159),(47,160),(48,161),(49,162),(50,163),(51,164),(52,165),(53,166),(54,167),(55,168),(56,155),(71,115),(72,116),(73,117),(74,118),(75,119),(76,120),(77,121),(78,122),(79,123),(80,124),(81,125),(82,126),(83,113),(84,114),(85,110),(86,111),(87,112),(88,99),(89,100),(90,101),(91,102),(92,103),(93,104),(94,105),(95,106),(96,107),(97,108),(98,109),(141,202),(142,203),(143,204),(144,205),(145,206),(146,207),(147,208),(148,209),(149,210),(150,197),(151,198),(152,199),(153,200),(154,201)], [(1,176,64,140),(2,175,65,139),(3,174,66,138),(4,173,67,137),(5,172,68,136),(6,171,69,135),(7,170,70,134),(8,169,57,133),(9,182,58,132),(10,181,59,131),(11,180,60,130),(12,179,61,129),(13,178,62,128),(14,177,63,127),(15,221,40,191),(16,220,41,190),(17,219,42,189),(18,218,29,188),(19,217,30,187),(20,216,31,186),(21,215,32,185),(22,214,33,184),(23,213,34,183),(24,212,35,196),(25,211,36,195),(26,224,37,194),(27,223,38,193),(28,222,39,192),(43,141,156,202),(44,154,157,201),(45,153,158,200),(46,152,159,199),(47,151,160,198),(48,150,161,197),(49,149,162,210),(50,148,163,209),(51,147,164,208),(52,146,165,207),(53,145,166,206),(54,144,167,205),(55,143,168,204),(56,142,155,203),(71,103,115,92),(72,102,116,91),(73,101,117,90),(74,100,118,89),(75,99,119,88),(76,112,120,87),(77,111,121,86),(78,110,122,85),(79,109,123,98),(80,108,124,97),(81,107,125,96),(82,106,126,95),(83,105,113,94),(84,104,114,93)], [(1,187,57,224),(2,188,58,211),(3,189,59,212),(4,190,60,213),(5,191,61,214),(6,192,62,215),(7,193,63,216),(8,194,64,217),(9,195,65,218),(10,196,66,219),(11,183,67,220),(12,184,68,221),(13,185,69,222),(14,186,70,223),(15,179,33,136),(16,180,34,137),(17,181,35,138),(18,182,36,139),(19,169,37,140),(20,170,38,127),(21,171,39,128),(22,172,40,129),(23,173,41,130),(24,174,42,131),(25,175,29,132),(26,176,30,133),(27,177,31,134),(28,178,32,135),(43,71,163,122),(44,72,164,123),(45,73,165,124),(46,74,166,125),(47,75,167,126),(48,76,168,113),(49,77,155,114),(50,78,156,115),(51,79,157,116),(52,80,158,117),(53,81,159,118),(54,82,160,119),(55,83,161,120),(56,84,162,121),(85,202,103,148),(86,203,104,149),(87,204,105,150),(88,205,106,151),(89,206,107,152),(90,207,108,153),(91,208,109,154),(92,209,110,141),(93,210,111,142),(94,197,112,143),(95,198,99,144),(96,199,100,145),(97,200,101,146),(98,201,102,147)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 28 | 28 | 4 | ··· | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | D14 | 2+ 1+4 | 2- 1+4 | Q8⋊2D7 | D4⋊6D14 | D4.10D14 |
| kernel | C14.572+ 1+4 | Dic7⋊4D4 | C22.D28 | C28.3Q8 | D14.5D4 | C4⋊C4⋊D7 | C2×Dic7⋊C4 | C28⋊7D4 | D14⋊3Q8 | C7×C22⋊Q8 | C22⋊Q8 | C2×C14 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×Q8 | C14 | C14 | C22 | C2 | C2 |
| # reps | 1 | 2 | 2 | 2 | 2 | 2 | 1 | 1 | 2 | 1 | 3 | 4 | 6 | 9 | 3 | 3 | 1 | 1 | 6 | 6 | 6 |
Matrix representation of C14.572+ 1+4 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 | 0 |
| 0 | 0 | 7 | 22 | 0 | 0 |
| 0 | 0 | 25 | 0 | 4 | 4 |
| 0 | 0 | 11 | 4 | 25 | 18 |
| 22 | 22 | 0 | 0 | 0 | 0 |
| 3 | 7 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 27 | 13 | 13 |
| 0 | 0 | 12 | 9 | 0 | 28 |
| 0 | 0 | 27 | 0 | 11 | 2 |
| 0 | 0 | 18 | 27 | 11 | 2 |
| 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 | 24 | 18 | 28 | 0 |
| 0 | 0 | 24 | 18 | 0 | 28 |
| 12 | 23 | 0 | 0 | 0 | 0 |
| 19 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 26 | 0 | 0 |
| 0 | 0 | 24 | 19 | 0 | 0 |
| 0 | 0 | 11 | 0 | 26 | 18 |
| 0 | 0 | 7 | 26 | 22 | 3 |
| 1 | 14 | 0 | 0 | 0 | 0 |
| 4 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 20 | 27 | 0 | 0 |
| 0 | 0 | 11 | 9 | 0 | 0 |
| 0 | 0 | 9 | 27 | 11 | 2 |
| 0 | 0 | 2 | 0 | 27 | 18 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,0,7,25,11,0,0,4,22,0,4,0,0,0,0,4,25,0,0,0,0,4,18],[22,3,0,0,0,0,22,7,0,0,0,0,0,0,7,12,27,18,0,0,27,9,0,27,0,0,13,0,11,11,0,0,13,28,2,2],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,24,24,0,0,0,1,18,18,0,0,0,0,28,0,0,0,0,0,0,28],[12,19,0,0,0,0,23,17,0,0,0,0,0,0,10,24,11,7,0,0,26,19,0,26,0,0,0,0,26,22,0,0,0,0,18,3],[1,4,0,0,0,0,14,28,0,0,0,0,0,0,20,11,9,2,0,0,27,9,27,0,0,0,0,0,11,27,0,0,0,0,2,18] >;
C14.572+ 1+4 in GAP, Magma, Sage, TeX
C_{14}._{57}2_+^{1+4} % in TeX
G:=Group("C14.57ES+(2,2)"); // GroupNames label
G:=SmallGroup(448,1098);
// by ID
G=gap.SmallGroup(448,1098);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,387,100,675,409,80,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=c^2=1,d^2=a^7*b^2,e^2=b^2,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,a*e=e*a,c*b*c=a^7*b^-1,d*b*d^-1=e*b*e^-1=a^7*b,c*d=d*c,c*e=e*c,e*d*e^-1=a^7*b^2*d>;
// generators/relations