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## G = C14.422- 1+4order 448 = 26·7

### 42nd non-split extension by C14 of 2- 1+4 acting via 2- 1+4/C2×Q8=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C14 — C14.422- 1+4
 Chief series C1 — C7 — C14 — C2×C14 — C2×Dic7 — C4×Dic7 — Q8×Dic7 — C14.422- 1+4
 Lower central C7 — C14 — C14.422- 1+4
 Upper central C1 — C22 — C22×Q8

Generators and relations for C14.422- 1+4
G = < a,b,c,d,e | a14=b4=1, c2=a7, d2=a7b2, e2=b2, ab=ba, cac-1=dad-1=a-1, ae=ea, cbc-1=b-1, bd=db, be=eb, cd=dc, ce=ec, ede-1=b2d >

Subgroups: 692 in 266 conjugacy classes, 191 normal (11 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, Q8, C23, C14, C14, C14, C42, C22⋊C4, C4⋊C4, C22×C4, C2×Q8, Dic7, C28, C2×C14, C2×C14, C2×C14, C42⋊C2, C4×Q8, C22×Q8, C2×Dic7, C2×C28, C7×Q8, C22×C14, C23.32C23, C4×Dic7, C4⋊Dic7, C23.D7, C22×C28, Q8×C14, C23.21D14, Q8×Dic7, Q8×C2×C14, C14.422- 1+4
Quotients: C1, C2, C4, C22, C2×C4, C23, D7, C22×C4, C24, Dic7, D14, C23×C4, 2- 1+4, C2×Dic7, C22×D7, C23.32C23, C22×Dic7, C23×D7, Q8.10D14, C23×Dic7, C14.422- 1+4

Smallest permutation representation of C14.422- 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)
(1 198 223 139)(2 199 224 140)(3 200 211 127)(4 201 212 128)(5 202 213 129)(6 203 214 130)(7 204 215 131)(8 205 216 132)(9 206 217 133)(10 207 218 134)(11 208 219 135)(12 209 220 136)(13 210 221 137)(14 197 222 138)(15 79 113 184)(16 80 114 185)(17 81 115 186)(18 82 116 187)(19 83 117 188)(20 84 118 189)(21 71 119 190)(22 72 120 191)(23 73 121 192)(24 74 122 193)(25 75 123 194)(26 76 124 195)(27 77 125 196)(28 78 126 183)(29 176 142 57)(30 177 143 58)(31 178 144 59)(32 179 145 60)(33 180 146 61)(34 181 147 62)(35 182 148 63)(36 169 149 64)(37 170 150 65)(38 171 151 66)(39 172 152 67)(40 173 153 68)(41 174 154 69)(42 175 141 70)(43 160 99 88)(44 161 100 89)(45 162 101 90)(46 163 102 91)(47 164 103 92)(48 165 104 93)(49 166 105 94)(50 167 106 95)(51 168 107 96)(52 155 108 97)(53 156 109 98)(54 157 110 85)(55 158 111 86)(56 159 112 87)
(1 62 8 69)(2 61 9 68)(3 60 10 67)(4 59 11 66)(5 58 12 65)(6 57 13 64)(7 70 14 63)(15 52 22 45)(16 51 23 44)(17 50 24 43)(18 49 25 56)(19 48 26 55)(20 47 27 54)(21 46 28 53)(29 137 36 130)(30 136 37 129)(31 135 38 128)(32 134 39 127)(33 133 40 140)(34 132 41 139)(35 131 42 138)(71 91 78 98)(72 90 79 97)(73 89 80 96)(74 88 81 95)(75 87 82 94)(76 86 83 93)(77 85 84 92)(99 115 106 122)(100 114 107 121)(101 113 108 120)(102 126 109 119)(103 125 110 118)(104 124 111 117)(105 123 112 116)(141 197 148 204)(142 210 149 203)(143 209 150 202)(144 208 151 201)(145 207 152 200)(146 206 153 199)(147 205 154 198)(155 191 162 184)(156 190 163 183)(157 189 164 196)(158 188 165 195)(159 187 166 194)(160 186 167 193)(161 185 168 192)(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)
(1 167 216 88)(2 166 217 87)(3 165 218 86)(4 164 219 85)(5 163 220 98)(6 162 221 97)(7 161 222 96)(8 160 223 95)(9 159 224 94)(10 158 211 93)(11 157 212 92)(12 156 213 91)(13 155 214 90)(14 168 215 89)(15 149 120 29)(16 148 121 42)(17 147 122 41)(18 146 123 40)(19 145 124 39)(20 144 125 38)(21 143 126 37)(22 142 113 36)(23 141 114 35)(24 154 115 34)(25 153 116 33)(26 152 117 32)(27 151 118 31)(28 150 119 30)(43 198 106 132)(44 197 107 131)(45 210 108 130)(46 209 109 129)(47 208 110 128)(48 207 111 127)(49 206 112 140)(50 205 99 139)(51 204 100 138)(52 203 101 137)(53 202 102 136)(54 201 103 135)(55 200 104 134)(56 199 105 133)(57 184 169 72)(58 183 170 71)(59 196 171 84)(60 195 172 83)(61 194 173 82)(62 193 174 81)(63 192 175 80)(64 191 176 79)(65 190 177 78)(66 189 178 77)(67 188 179 76)(68 187 180 75)(69 186 181 74)(70 185 182 73)
(1 198 223 139)(2 199 224 140)(3 200 211 127)(4 201 212 128)(5 202 213 129)(6 203 214 130)(7 204 215 131)(8 205 216 132)(9 206 217 133)(10 207 218 134)(11 208 219 135)(12 209 220 136)(13 210 221 137)(14 197 222 138)(15 79 113 184)(16 80 114 185)(17 81 115 186)(18 82 116 187)(19 83 117 188)(20 84 118 189)(21 71 119 190)(22 72 120 191)(23 73 121 192)(24 74 122 193)(25 75 123 194)(26 76 124 195)(27 77 125 196)(28 78 126 183)(29 57 142 176)(30 58 143 177)(31 59 144 178)(32 60 145 179)(33 61 146 180)(34 62 147 181)(35 63 148 182)(36 64 149 169)(37 65 150 170)(38 66 151 171)(39 67 152 172)(40 68 153 173)(41 69 154 174)(42 70 141 175)(43 88 99 160)(44 89 100 161)(45 90 101 162)(46 91 102 163)(47 92 103 164)(48 93 104 165)(49 94 105 166)(50 95 106 167)(51 96 107 168)(52 97 108 155)(53 98 109 156)(54 85 110 157)(55 86 111 158)(56 87 112 159)

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), (1,198,223,139)(2,199,224,140)(3,200,211,127)(4,201,212,128)(5,202,213,129)(6,203,214,130)(7,204,215,131)(8,205,216,132)(9,206,217,133)(10,207,218,134)(11,208,219,135)(12,209,220,136)(13,210,221,137)(14,197,222,138)(15,79,113,184)(16,80,114,185)(17,81,115,186)(18,82,116,187)(19,83,117,188)(20,84,118,189)(21,71,119,190)(22,72,120,191)(23,73,121,192)(24,74,122,193)(25,75,123,194)(26,76,124,195)(27,77,125,196)(28,78,126,183)(29,176,142,57)(30,177,143,58)(31,178,144,59)(32,179,145,60)(33,180,146,61)(34,181,147,62)(35,182,148,63)(36,169,149,64)(37,170,150,65)(38,171,151,66)(39,172,152,67)(40,173,153,68)(41,174,154,69)(42,175,141,70)(43,160,99,88)(44,161,100,89)(45,162,101,90)(46,163,102,91)(47,164,103,92)(48,165,104,93)(49,166,105,94)(50,167,106,95)(51,168,107,96)(52,155,108,97)(53,156,109,98)(54,157,110,85)(55,158,111,86)(56,159,112,87), (1,62,8,69)(2,61,9,68)(3,60,10,67)(4,59,11,66)(5,58,12,65)(6,57,13,64)(7,70,14,63)(15,52,22,45)(16,51,23,44)(17,50,24,43)(18,49,25,56)(19,48,26,55)(20,47,27,54)(21,46,28,53)(29,137,36,130)(30,136,37,129)(31,135,38,128)(32,134,39,127)(33,133,40,140)(34,132,41,139)(35,131,42,138)(71,91,78,98)(72,90,79,97)(73,89,80,96)(74,88,81,95)(75,87,82,94)(76,86,83,93)(77,85,84,92)(99,115,106,122)(100,114,107,121)(101,113,108,120)(102,126,109,119)(103,125,110,118)(104,124,111,117)(105,123,112,116)(141,197,148,204)(142,210,149,203)(143,209,150,202)(144,208,151,201)(145,207,152,200)(146,206,153,199)(147,205,154,198)(155,191,162,184)(156,190,163,183)(157,189,164,196)(158,188,165,195)(159,187,166,194)(160,186,167,193)(161,185,168,192)(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), (1,167,216,88)(2,166,217,87)(3,165,218,86)(4,164,219,85)(5,163,220,98)(6,162,221,97)(7,161,222,96)(8,160,223,95)(9,159,224,94)(10,158,211,93)(11,157,212,92)(12,156,213,91)(13,155,214,90)(14,168,215,89)(15,149,120,29)(16,148,121,42)(17,147,122,41)(18,146,123,40)(19,145,124,39)(20,144,125,38)(21,143,126,37)(22,142,113,36)(23,141,114,35)(24,154,115,34)(25,153,116,33)(26,152,117,32)(27,151,118,31)(28,150,119,30)(43,198,106,132)(44,197,107,131)(45,210,108,130)(46,209,109,129)(47,208,110,128)(48,207,111,127)(49,206,112,140)(50,205,99,139)(51,204,100,138)(52,203,101,137)(53,202,102,136)(54,201,103,135)(55,200,104,134)(56,199,105,133)(57,184,169,72)(58,183,170,71)(59,196,171,84)(60,195,172,83)(61,194,173,82)(62,193,174,81)(63,192,175,80)(64,191,176,79)(65,190,177,78)(66,189,178,77)(67,188,179,76)(68,187,180,75)(69,186,181,74)(70,185,182,73), (1,198,223,139)(2,199,224,140)(3,200,211,127)(4,201,212,128)(5,202,213,129)(6,203,214,130)(7,204,215,131)(8,205,216,132)(9,206,217,133)(10,207,218,134)(11,208,219,135)(12,209,220,136)(13,210,221,137)(14,197,222,138)(15,79,113,184)(16,80,114,185)(17,81,115,186)(18,82,116,187)(19,83,117,188)(20,84,118,189)(21,71,119,190)(22,72,120,191)(23,73,121,192)(24,74,122,193)(25,75,123,194)(26,76,124,195)(27,77,125,196)(28,78,126,183)(29,57,142,176)(30,58,143,177)(31,59,144,178)(32,60,145,179)(33,61,146,180)(34,62,147,181)(35,63,148,182)(36,64,149,169)(37,65,150,170)(38,66,151,171)(39,67,152,172)(40,68,153,173)(41,69,154,174)(42,70,141,175)(43,88,99,160)(44,89,100,161)(45,90,101,162)(46,91,102,163)(47,92,103,164)(48,93,104,165)(49,94,105,166)(50,95,106,167)(51,96,107,168)(52,97,108,155)(53,98,109,156)(54,85,110,157)(55,86,111,158)(56,87,112,159)>;

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), (1,198,223,139)(2,199,224,140)(3,200,211,127)(4,201,212,128)(5,202,213,129)(6,203,214,130)(7,204,215,131)(8,205,216,132)(9,206,217,133)(10,207,218,134)(11,208,219,135)(12,209,220,136)(13,210,221,137)(14,197,222,138)(15,79,113,184)(16,80,114,185)(17,81,115,186)(18,82,116,187)(19,83,117,188)(20,84,118,189)(21,71,119,190)(22,72,120,191)(23,73,121,192)(24,74,122,193)(25,75,123,194)(26,76,124,195)(27,77,125,196)(28,78,126,183)(29,176,142,57)(30,177,143,58)(31,178,144,59)(32,179,145,60)(33,180,146,61)(34,181,147,62)(35,182,148,63)(36,169,149,64)(37,170,150,65)(38,171,151,66)(39,172,152,67)(40,173,153,68)(41,174,154,69)(42,175,141,70)(43,160,99,88)(44,161,100,89)(45,162,101,90)(46,163,102,91)(47,164,103,92)(48,165,104,93)(49,166,105,94)(50,167,106,95)(51,168,107,96)(52,155,108,97)(53,156,109,98)(54,157,110,85)(55,158,111,86)(56,159,112,87), (1,62,8,69)(2,61,9,68)(3,60,10,67)(4,59,11,66)(5,58,12,65)(6,57,13,64)(7,70,14,63)(15,52,22,45)(16,51,23,44)(17,50,24,43)(18,49,25,56)(19,48,26,55)(20,47,27,54)(21,46,28,53)(29,137,36,130)(30,136,37,129)(31,135,38,128)(32,134,39,127)(33,133,40,140)(34,132,41,139)(35,131,42,138)(71,91,78,98)(72,90,79,97)(73,89,80,96)(74,88,81,95)(75,87,82,94)(76,86,83,93)(77,85,84,92)(99,115,106,122)(100,114,107,121)(101,113,108,120)(102,126,109,119)(103,125,110,118)(104,124,111,117)(105,123,112,116)(141,197,148,204)(142,210,149,203)(143,209,150,202)(144,208,151,201)(145,207,152,200)(146,206,153,199)(147,205,154,198)(155,191,162,184)(156,190,163,183)(157,189,164,196)(158,188,165,195)(159,187,166,194)(160,186,167,193)(161,185,168,192)(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), (1,167,216,88)(2,166,217,87)(3,165,218,86)(4,164,219,85)(5,163,220,98)(6,162,221,97)(7,161,222,96)(8,160,223,95)(9,159,224,94)(10,158,211,93)(11,157,212,92)(12,156,213,91)(13,155,214,90)(14,168,215,89)(15,149,120,29)(16,148,121,42)(17,147,122,41)(18,146,123,40)(19,145,124,39)(20,144,125,38)(21,143,126,37)(22,142,113,36)(23,141,114,35)(24,154,115,34)(25,153,116,33)(26,152,117,32)(27,151,118,31)(28,150,119,30)(43,198,106,132)(44,197,107,131)(45,210,108,130)(46,209,109,129)(47,208,110,128)(48,207,111,127)(49,206,112,140)(50,205,99,139)(51,204,100,138)(52,203,101,137)(53,202,102,136)(54,201,103,135)(55,200,104,134)(56,199,105,133)(57,184,169,72)(58,183,170,71)(59,196,171,84)(60,195,172,83)(61,194,173,82)(62,193,174,81)(63,192,175,80)(64,191,176,79)(65,190,177,78)(66,189,178,77)(67,188,179,76)(68,187,180,75)(69,186,181,74)(70,185,182,73), (1,198,223,139)(2,199,224,140)(3,200,211,127)(4,201,212,128)(5,202,213,129)(6,203,214,130)(7,204,215,131)(8,205,216,132)(9,206,217,133)(10,207,218,134)(11,208,219,135)(12,209,220,136)(13,210,221,137)(14,197,222,138)(15,79,113,184)(16,80,114,185)(17,81,115,186)(18,82,116,187)(19,83,117,188)(20,84,118,189)(21,71,119,190)(22,72,120,191)(23,73,121,192)(24,74,122,193)(25,75,123,194)(26,76,124,195)(27,77,125,196)(28,78,126,183)(29,57,142,176)(30,58,143,177)(31,59,144,178)(32,60,145,179)(33,61,146,180)(34,62,147,181)(35,63,148,182)(36,64,149,169)(37,65,150,170)(38,66,151,171)(39,67,152,172)(40,68,153,173)(41,69,154,174)(42,70,141,175)(43,88,99,160)(44,89,100,161)(45,90,101,162)(46,91,102,163)(47,92,103,164)(48,93,104,165)(49,94,105,166)(50,95,106,167)(51,96,107,168)(52,97,108,155)(53,98,109,156)(54,85,110,157)(55,86,111,158)(56,87,112,159) );

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)], [(1,198,223,139),(2,199,224,140),(3,200,211,127),(4,201,212,128),(5,202,213,129),(6,203,214,130),(7,204,215,131),(8,205,216,132),(9,206,217,133),(10,207,218,134),(11,208,219,135),(12,209,220,136),(13,210,221,137),(14,197,222,138),(15,79,113,184),(16,80,114,185),(17,81,115,186),(18,82,116,187),(19,83,117,188),(20,84,118,189),(21,71,119,190),(22,72,120,191),(23,73,121,192),(24,74,122,193),(25,75,123,194),(26,76,124,195),(27,77,125,196),(28,78,126,183),(29,176,142,57),(30,177,143,58),(31,178,144,59),(32,179,145,60),(33,180,146,61),(34,181,147,62),(35,182,148,63),(36,169,149,64),(37,170,150,65),(38,171,151,66),(39,172,152,67),(40,173,153,68),(41,174,154,69),(42,175,141,70),(43,160,99,88),(44,161,100,89),(45,162,101,90),(46,163,102,91),(47,164,103,92),(48,165,104,93),(49,166,105,94),(50,167,106,95),(51,168,107,96),(52,155,108,97),(53,156,109,98),(54,157,110,85),(55,158,111,86),(56,159,112,87)], [(1,62,8,69),(2,61,9,68),(3,60,10,67),(4,59,11,66),(5,58,12,65),(6,57,13,64),(7,70,14,63),(15,52,22,45),(16,51,23,44),(17,50,24,43),(18,49,25,56),(19,48,26,55),(20,47,27,54),(21,46,28,53),(29,137,36,130),(30,136,37,129),(31,135,38,128),(32,134,39,127),(33,133,40,140),(34,132,41,139),(35,131,42,138),(71,91,78,98),(72,90,79,97),(73,89,80,96),(74,88,81,95),(75,87,82,94),(76,86,83,93),(77,85,84,92),(99,115,106,122),(100,114,107,121),(101,113,108,120),(102,126,109,119),(103,125,110,118),(104,124,111,117),(105,123,112,116),(141,197,148,204),(142,210,149,203),(143,209,150,202),(144,208,151,201),(145,207,152,200),(146,206,153,199),(147,205,154,198),(155,191,162,184),(156,190,163,183),(157,189,164,196),(158,188,165,195),(159,187,166,194),(160,186,167,193),(161,185,168,192),(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)], [(1,167,216,88),(2,166,217,87),(3,165,218,86),(4,164,219,85),(5,163,220,98),(6,162,221,97),(7,161,222,96),(8,160,223,95),(9,159,224,94),(10,158,211,93),(11,157,212,92),(12,156,213,91),(13,155,214,90),(14,168,215,89),(15,149,120,29),(16,148,121,42),(17,147,122,41),(18,146,123,40),(19,145,124,39),(20,144,125,38),(21,143,126,37),(22,142,113,36),(23,141,114,35),(24,154,115,34),(25,153,116,33),(26,152,117,32),(27,151,118,31),(28,150,119,30),(43,198,106,132),(44,197,107,131),(45,210,108,130),(46,209,109,129),(47,208,110,128),(48,207,111,127),(49,206,112,140),(50,205,99,139),(51,204,100,138),(52,203,101,137),(53,202,102,136),(54,201,103,135),(55,200,104,134),(56,199,105,133),(57,184,169,72),(58,183,170,71),(59,196,171,84),(60,195,172,83),(61,194,173,82),(62,193,174,81),(63,192,175,80),(64,191,176,79),(65,190,177,78),(66,189,178,77),(67,188,179,76),(68,187,180,75),(69,186,181,74),(70,185,182,73)], [(1,198,223,139),(2,199,224,140),(3,200,211,127),(4,201,212,128),(5,202,213,129),(6,203,214,130),(7,204,215,131),(8,205,216,132),(9,206,217,133),(10,207,218,134),(11,208,219,135),(12,209,220,136),(13,210,221,137),(14,197,222,138),(15,79,113,184),(16,80,114,185),(17,81,115,186),(18,82,116,187),(19,83,117,188),(20,84,118,189),(21,71,119,190),(22,72,120,191),(23,73,121,192),(24,74,122,193),(25,75,123,194),(26,76,124,195),(27,77,125,196),(28,78,126,183),(29,57,142,176),(30,58,143,177),(31,59,144,178),(32,60,145,179),(33,61,146,180),(34,62,147,181),(35,63,148,182),(36,64,149,169),(37,65,150,170),(38,66,151,171),(39,67,152,172),(40,68,153,173),(41,69,154,174),(42,70,141,175),(43,88,99,160),(44,89,100,161),(45,90,101,162),(46,91,102,163),(47,92,103,164),(48,93,104,165),(49,94,105,166),(50,95,106,167),(51,96,107,168),(52,97,108,155),(53,98,109,156),(54,85,110,157),(55,86,111,158),(56,87,112,159)]])

94 conjugacy classes

 class 1 2A 2B 2C 2D 2E 4A ··· 4L 4M ··· 4AB 7A 7B 7C 14A ··· 14U 28A ··· 28AJ order 1 2 2 2 2 2 4 ··· 4 4 ··· 4 7 7 7 14 ··· 14 28 ··· 28 size 1 1 1 1 2 2 2 ··· 2 14 ··· 14 2 2 2 2 ··· 2 4 ··· 4

94 irreducible representations

 dim 1 1 1 1 1 2 2 2 2 4 4 type + + + + + + - + - image C1 C2 C2 C2 C4 D7 D14 Dic7 D14 2- 1+4 Q8.10D14 kernel C14.422- 1+4 C23.21D14 Q8×Dic7 Q8×C2×C14 Q8×C14 C22×Q8 C22×C4 C2×Q8 C2×Q8 C14 C2 # reps 1 6 8 1 16 3 9 24 12 2 12

Matrix representation of C14.422- 1+4 in GL6(𝔽29)

 0 19 0 0 0 0 3 26 0 0 0 0 0 0 22 0 0 0 0 0 0 22 0 0 0 0 0 20 4 0 0 0 28 1 0 4
,
 28 0 0 0 0 0 0 28 0 0 0 0 0 0 0 1 0 0 0 0 28 0 0 0 0 0 3 26 28 16 0 0 0 25 18 1
,
 27 10 0 0 0 0 14 2 0 0 0 0 0 0 16 4 11 27 0 0 0 9 18 0 0 0 0 18 20 0 0 0 27 4 2 13
,
 27 10 0 0 0 0 14 2 0 0 0 0 0 0 0 8 16 0 0 0 11 10 13 24 0 0 0 24 8 17 0 0 22 7 24 11
,
 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 28 0 0 0 0 0 27 3 1 13 0 0 16 20 11 28

G:=sub<GL(6,GF(29))| [0,3,0,0,0,0,19,26,0,0,0,0,0,0,22,0,0,28,0,0,0,22,20,1,0,0,0,0,4,0,0,0,0,0,0,4],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,0,28,3,0,0,0,1,0,26,25,0,0,0,0,28,18,0,0,0,0,16,1],[27,14,0,0,0,0,10,2,0,0,0,0,0,0,16,0,0,27,0,0,4,9,18,4,0,0,11,18,20,2,0,0,27,0,0,13],[27,14,0,0,0,0,10,2,0,0,0,0,0,0,0,11,0,22,0,0,8,10,24,7,0,0,16,13,8,24,0,0,0,24,17,11],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,28,27,16,0,0,1,0,3,20,0,0,0,0,1,11,0,0,0,0,13,28] >;

C14.422- 1+4 in GAP, Magma, Sage, TeX

C_{14}._{42}2_-^{1+4}
% in TeX

G:=Group("C14.42ES-(2,2)");
// GroupNames label

G:=SmallGroup(448,1265);
// by ID

G=gap.SmallGroup(448,1265);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,232,387,184,1123,18822]);
// Polycyclic

G:=Group<a,b,c,d,e|a^14=b^4=1,c^2=a^7,d^2=a^7*b^2,e^2=b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,a*e=e*a,c*b*c^-1=b^-1,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=b^2*d>;
// generators/relations

׿
×
𝔽