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G = C14.1062- 1+4order 448 = 26·7

61st non-split extension by C14 of 2- 1+4 acting via 2- 1+4/C4○D4=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C14 — C14.1062- 1+4
 Chief series C1 — C7 — C14 — C2×C14 — C2×Dic7 — C22×Dic7 — D4×Dic7 — C14.1062- 1+4
 Lower central C7 — C14 — C14.1062- 1+4
 Upper central C1 — C22 — C2×C4○D4

Generators and relations for C14.1062- 1+4
G = < a,b,c,d,e | a14=b4=c2=1, d2=b2, e2=a7, ab=ba, ac=ca, ad=da, eae-1=a-1, cbc=b-1, bd=db, be=eb, cd=dc, ce=ec, ede-1=b2d >

Subgroups: 916 in 294 conjugacy classes, 191 normal (18 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C14, C14, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic7, C28, C2×C14, C2×C14, C2×C14, C2×C4⋊C4, C42⋊C2, C4×D4, C4×Q8, C2×C4○D4, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×D4, C7×Q8, C22×C14, C23.33C23, C4×Dic7, C4⋊Dic7, C4⋊Dic7, C23.D7, C22×Dic7, C22×C28, D4×C14, Q8×C14, C7×C4○D4, C2×C4⋊Dic7, C23.21D14, D4×Dic7, Q8×Dic7, C14×C4○D4, C14.1062- 1+4
Quotients: C1, C2, C4, C22, C2×C4, C23, D7, C22×C4, C24, Dic7, D14, C23×C4, 2+ 1+4, 2- 1+4, C2×Dic7, C22×D7, C23.33C23, C22×Dic7, C23×D7, D48D14, D4.10D14, C23×Dic7, C14.1062- 1+4

Smallest permutation representation of C14.1062- 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)
(1 184 40 210)(2 185 41 197)(3 186 42 198)(4 187 29 199)(5 188 30 200)(6 189 31 201)(7 190 32 202)(8 191 33 203)(9 192 34 204)(10 193 35 205)(11 194 36 206)(12 195 37 207)(13 196 38 208)(14 183 39 209)(15 45 130 83)(16 46 131 84)(17 47 132 71)(18 48 133 72)(19 49 134 73)(20 50 135 74)(21 51 136 75)(22 52 137 76)(23 53 138 77)(24 54 139 78)(25 55 140 79)(26 56 127 80)(27 43 128 81)(28 44 129 82)(57 155 87 112)(58 156 88 99)(59 157 89 100)(60 158 90 101)(61 159 91 102)(62 160 92 103)(63 161 93 104)(64 162 94 105)(65 163 95 106)(66 164 96 107)(67 165 97 108)(68 166 98 109)(69 167 85 110)(70 168 86 111)(113 211 154 182)(114 212 141 169)(115 213 142 170)(116 214 143 171)(117 215 144 172)(118 216 145 173)(119 217 146 174)(120 218 147 175)(121 219 148 176)(122 220 149 177)(123 221 150 178)(124 222 151 179)(125 223 152 180)(126 224 153 181)
(15 130)(16 131)(17 132)(18 133)(19 134)(20 135)(21 136)(22 137)(23 138)(24 139)(25 140)(26 127)(27 128)(28 129)(57 87)(58 88)(59 89)(60 90)(61 91)(62 92)(63 93)(64 94)(65 95)(66 96)(67 97)(68 98)(69 85)(70 86)(169 212)(170 213)(171 214)(172 215)(173 216)(174 217)(175 218)(176 219)(177 220)(178 221)(179 222)(180 223)(181 224)(182 211)(183 209)(184 210)(185 197)(186 198)(187 199)(188 200)(189 201)(190 202)(191 203)(192 204)(193 205)(194 206)(195 207)(196 208)
(1 76 40 52)(2 77 41 53)(3 78 42 54)(4 79 29 55)(5 80 30 56)(6 81 31 43)(7 82 32 44)(8 83 33 45)(9 84 34 46)(10 71 35 47)(11 72 36 48)(12 73 37 49)(13 74 38 50)(14 75 39 51)(15 203 130 191)(16 204 131 192)(17 205 132 193)(18 206 133 194)(19 207 134 195)(20 208 135 196)(21 209 136 183)(22 210 137 184)(23 197 138 185)(24 198 139 186)(25 199 140 187)(26 200 127 188)(27 201 128 189)(28 202 129 190)(57 222 87 179)(58 223 88 180)(59 224 89 181)(60 211 90 182)(61 212 91 169)(62 213 92 170)(63 214 93 171)(64 215 94 172)(65 216 95 173)(66 217 96 174)(67 218 97 175)(68 219 98 176)(69 220 85 177)(70 221 86 178)(99 125 156 152)(100 126 157 153)(101 113 158 154)(102 114 159 141)(103 115 160 142)(104 116 161 143)(105 117 162 144)(106 118 163 145)(107 119 164 146)(108 120 165 147)(109 121 166 148)(110 122 167 149)(111 123 168 150)(112 124 155 151)
(1 148 8 141)(2 147 9 154)(3 146 10 153)(4 145 11 152)(5 144 12 151)(6 143 13 150)(7 142 14 149)(15 91 22 98)(16 90 23 97)(17 89 24 96)(18 88 25 95)(19 87 26 94)(20 86 27 93)(21 85 28 92)(29 118 36 125)(30 117 37 124)(31 116 38 123)(32 115 39 122)(33 114 40 121)(34 113 41 120)(35 126 42 119)(43 104 50 111)(44 103 51 110)(45 102 52 109)(46 101 53 108)(47 100 54 107)(48 99 55 106)(49 112 56 105)(57 127 64 134)(58 140 65 133)(59 139 66 132)(60 138 67 131)(61 137 68 130)(62 136 69 129)(63 135 70 128)(71 157 78 164)(72 156 79 163)(73 155 80 162)(74 168 81 161)(75 167 82 160)(76 166 83 159)(77 165 84 158)(169 184 176 191)(170 183 177 190)(171 196 178 189)(172 195 179 188)(173 194 180 187)(174 193 181 186)(175 192 182 185)(197 218 204 211)(198 217 205 224)(199 216 206 223)(200 215 207 222)(201 214 208 221)(202 213 209 220)(203 212 210 219)```

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

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

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

94 conjugacy classes

 class 1 2A 2B 2C 2D ··· 2I 4A ··· 4H 4I ··· 4X 7A 7B 7C 14A ··· 14I 14J ··· 14AA 28A ··· 28L 28M ··· 28AD order 1 2 2 2 2 ··· 2 4 ··· 4 4 ··· 4 7 7 7 14 ··· 14 14 ··· 14 28 ··· 28 28 ··· 28 size 1 1 1 1 2 ··· 2 2 ··· 2 14 ··· 14 2 2 2 2 ··· 2 4 ··· 4 2 ··· 2 4 ··· 4

94 irreducible representations

 dim 1 1 1 1 1 1 1 2 2 2 2 2 4 4 4 4 type + + + + + + + + + + - + - + - image C1 C2 C2 C2 C2 C2 C4 D7 D14 D14 D14 Dic7 2+ 1+4 2- 1+4 D4⋊8D14 D4.10D14 kernel C14.1062- 1+4 C2×C4⋊Dic7 C23.21D14 D4×Dic7 Q8×Dic7 C14×C4○D4 C7×C4○D4 C2×C4○D4 C22×C4 C2×D4 C2×Q8 C4○D4 C14 C14 C2 C2 # reps 1 3 3 6 2 1 16 3 9 9 3 24 1 1 6 6

Matrix representation of C14.1062- 1+4 in GL6(𝔽29)

 4 4 0 0 0 0 25 18 0 0 0 0 0 0 8 8 0 0 0 0 21 3 0 0 0 0 0 0 9 8 0 0 0 0 13 2
,
 28 0 0 0 0 0 0 28 0 0 0 0 0 0 2 18 8 21 0 0 11 27 17 14 0 0 0 0 3 11 0 0 0 0 7 26
,
 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 0 14 28 0 0 0 15 4 0 28
,
 1 0 0 0 0 0 0 1 0 0 0 0 0 0 27 11 0 0 0 0 18 2 0 0 0 0 0 0 3 11 0 0 0 0 7 26
,
 2 11 0 0 0 0 18 27 0 0 0 0 0 0 5 16 0 0 0 0 2 24 0 0 0 0 28 17 21 2 0 0 25 17 11 8

`G:=sub<GL(6,GF(29))| [4,25,0,0,0,0,4,18,0,0,0,0,0,0,8,21,0,0,0,0,8,3,0,0,0,0,0,0,9,13,0,0,0,0,8,2],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,2,11,0,0,0,0,18,27,0,0,0,0,8,17,3,7,0,0,21,14,11,26],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,15,0,0,0,1,14,4,0,0,0,0,28,0,0,0,0,0,0,28],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,27,18,0,0,0,0,11,2,0,0,0,0,0,0,3,7,0,0,0,0,11,26],[2,18,0,0,0,0,11,27,0,0,0,0,0,0,5,2,28,25,0,0,16,24,17,17,0,0,0,0,21,11,0,0,0,0,2,8] >;`

C14.1062- 1+4 in GAP, Magma, Sage, TeX

`C_{14}._{106}2_-^{1+4}`
`% in TeX`

`G:=Group("C14.106ES-(2,2)");`
`// GroupNames label`

`G:=SmallGroup(448,1280);`
`// by ID`

`G=gap.SmallGroup(448,1280);`
`# by ID`

`G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,387,1123,136,18822]);`
`// Polycyclic`

`G:=Group<a,b,c,d,e|a^14=b^4=c^2=1,d^2=b^2,e^2=a^7,a*b=b*a,a*c=c*a,a*d=d*a,e*a*e^-1=a^-1,c*b*c=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`

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