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## G = C14.1482+ 1+4order 448 = 26·7

### 57th 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 — C2×C14 — C14.1482+ 1+4
 Chief series C1 — C7 — C14 — C2×C14 — C22×D7 — C2×C7⋊D4 — C28⋊2D4 — C14.1482+ 1+4
 Lower central C7 — C2×C14 — C14.1482+ 1+4
 Upper central C1 — C22 — C2×C4○D4

Generators and relations for C14.1482+ 1+4
G = < a,b,c,d,e | a14=b4=c2=e2=1, d2=b2, ab=ba, ac=ca, ad=da, eae=a-1, cbc=b-1, bd=db, be=eb, cd=dc, ece=a7c, ede=a7b2d >

Subgroups: 1460 in 312 conjugacy classes, 113 normal (22 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, C2×C14, C2×C14, C4×D4, C4×Q8, C4⋊D4, C41D4, C2×C4○D4, C2×C4○D4, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C7×Q8, C22×D7, C22×C14, Q86D4, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C2×C4×D7, C2×D28, Q82D7, C2×C7⋊D4, C22×C28, D4×C14, Q8×C14, C7×C4○D4, C4×C7⋊D4, C287D4, C282D4, C28⋊D4, Q8×Dic7, C2×Q82D7, C14×C4○D4, C14.1482+ 1+4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C22×D4, C2×C4○D4, 2+ 1+4, C7⋊D4, C22×D7, Q86D4, C2×C7⋊D4, C23×D7, D7×C4○D4, D48D14, C22×C7⋊D4, C14.1482+ 1+4

Smallest permutation representation of C14.1482+ 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 89 27 102)(2 90 28 103)(3 91 15 104)(4 92 16 105)(5 93 17 106)(6 94 18 107)(7 95 19 108)(8 96 20 109)(9 97 21 110)(10 98 22 111)(11 85 23 112)(12 86 24 99)(13 87 25 100)(14 88 26 101)(29 73 49 63)(30 74 50 64)(31 75 51 65)(32 76 52 66)(33 77 53 67)(34 78 54 68)(35 79 55 69)(36 80 56 70)(37 81 43 57)(38 82 44 58)(39 83 45 59)(40 84 46 60)(41 71 47 61)(42 72 48 62)(113 222 127 205)(114 223 128 206)(115 224 129 207)(116 211 130 208)(117 212 131 209)(118 213 132 210)(119 214 133 197)(120 215 134 198)(121 216 135 199)(122 217 136 200)(123 218 137 201)(124 219 138 202)(125 220 139 203)(126 221 140 204)(141 181 158 183)(142 182 159 184)(143 169 160 185)(144 170 161 186)(145 171 162 187)(146 172 163 188)(147 173 164 189)(148 174 165 190)(149 175 166 191)(150 176 167 192)(151 177 168 193)(152 178 155 194)(153 179 156 195)(154 180 157 196)
(1 125)(2 126)(3 113)(4 114)(5 115)(6 116)(7 117)(8 118)(9 119)(10 120)(11 121)(12 122)(13 123)(14 124)(15 127)(16 128)(17 129)(18 130)(19 131)(20 132)(21 133)(22 134)(23 135)(24 136)(25 137)(26 138)(27 139)(28 140)(29 143)(30 144)(31 145)(32 146)(33 147)(34 148)(35 149)(36 150)(37 151)(38 152)(39 153)(40 154)(41 141)(42 142)(43 168)(44 155)(45 156)(46 157)(47 158)(48 159)(49 160)(50 161)(51 162)(52 163)(53 164)(54 165)(55 166)(56 167)(57 177)(58 178)(59 179)(60 180)(61 181)(62 182)(63 169)(64 170)(65 171)(66 172)(67 173)(68 174)(69 175)(70 176)(71 183)(72 184)(73 185)(74 186)(75 187)(76 188)(77 189)(78 190)(79 191)(80 192)(81 193)(82 194)(83 195)(84 196)(85 199)(86 200)(87 201)(88 202)(89 203)(90 204)(91 205)(92 206)(93 207)(94 208)(95 209)(96 210)(97 197)(98 198)(99 217)(100 218)(101 219)(102 220)(103 221)(104 222)(105 223)(106 224)(107 211)(108 212)(109 213)(110 214)(111 215)(112 216)
(1 47 27 41)(2 48 28 42)(3 49 15 29)(4 50 16 30)(5 51 17 31)(6 52 18 32)(7 53 19 33)(8 54 20 34)(9 55 21 35)(10 56 22 36)(11 43 23 37)(12 44 24 38)(13 45 25 39)(14 46 26 40)(57 112 81 85)(58 99 82 86)(59 100 83 87)(60 101 84 88)(61 102 71 89)(62 103 72 90)(63 104 73 91)(64 105 74 92)(65 106 75 93)(66 107 76 94)(67 108 77 95)(68 109 78 96)(69 110 79 97)(70 111 80 98)(113 160 127 143)(114 161 128 144)(115 162 129 145)(116 163 130 146)(117 164 131 147)(118 165 132 148)(119 166 133 149)(120 167 134 150)(121 168 135 151)(122 155 136 152)(123 156 137 153)(124 157 138 154)(125 158 139 141)(126 159 140 142)(169 222 185 205)(170 223 186 206)(171 224 187 207)(172 211 188 208)(173 212 189 209)(174 213 190 210)(175 214 191 197)(176 215 192 198)(177 216 193 199)(178 217 194 200)(179 218 195 201)(180 219 196 202)(181 220 183 203)(182 221 184 204)
(1 148)(2 147)(3 146)(4 145)(5 144)(6 143)(7 142)(8 141)(9 154)(10 153)(11 152)(12 151)(13 150)(14 149)(15 163)(16 162)(17 161)(18 160)(19 159)(20 158)(21 157)(22 156)(23 155)(24 168)(25 167)(26 166)(27 165)(28 164)(29 123)(30 122)(31 121)(32 120)(33 119)(34 118)(35 117)(36 116)(37 115)(38 114)(39 113)(40 126)(41 125)(42 124)(43 129)(44 128)(45 127)(46 140)(47 139)(48 138)(49 137)(50 136)(51 135)(52 134)(53 133)(54 132)(55 131)(56 130)(57 207)(58 206)(59 205)(60 204)(61 203)(62 202)(63 201)(64 200)(65 199)(66 198)(67 197)(68 210)(69 209)(70 208)(71 220)(72 219)(73 218)(74 217)(75 216)(76 215)(77 214)(78 213)(79 212)(80 211)(81 224)(82 223)(83 222)(84 221)(85 178)(86 177)(87 176)(88 175)(89 174)(90 173)(91 172)(92 171)(93 170)(94 169)(95 182)(96 181)(97 180)(98 179)(99 193)(100 192)(101 191)(102 190)(103 189)(104 188)(105 187)(106 186)(107 185)(108 184)(109 183)(110 196)(111 195)(112 194)```

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

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

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

85 conjugacy classes

 class 1 2A 2B 2C 2D 2E 2F 2G 2H 2I 4A ··· 4H 4I 4J 4K 4L 4M 4N 4O 7A 7B 7C 14A ··· 14I 14J ··· 14AA 28A ··· 28L 28M ··· 28AD order 1 2 2 2 2 2 2 2 2 2 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 4 4 4 28 28 28 2 ··· 2 14 14 14 14 28 28 28 2 2 2 2 ··· 2 4 ··· 4 2 ··· 2 4 ··· 4

85 irreducible representations

 dim 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 4 4 4 type + + + + + + + + + + + + + + + image C1 C2 C2 C2 C2 C2 C2 C2 D4 D7 C4○D4 D14 D14 D14 C7⋊D4 2+ 1+4 D7×C4○D4 D4⋊8D14 kernel C14.1482+ 1+4 C4×C7⋊D4 C28⋊7D4 C28⋊2D4 C28⋊D4 Q8×Dic7 C2×Q8⋊2D7 C14×C4○D4 C7×Q8 C2×C4○D4 Dic7 C22×C4 C2×D4 C2×Q8 Q8 C14 C2 C2 # reps 1 3 3 3 3 1 1 1 4 3 4 9 9 3 24 1 6 6

Matrix representation of C14.1482+ 1+4 in GL4(𝔽29) generated by

 19 19 0 0 10 7 0 0 0 0 28 0 0 0 0 28
,
 28 0 0 0 0 28 0 0 0 0 28 5 0 0 17 1
,
 9 14 0 0 15 20 0 0 0 0 1 24 0 0 0 28
,
 9 14 0 0 15 20 0 0 0 0 12 0 0 0 0 12
,
 1 0 0 0 7 28 0 0 0 0 12 27 0 0 28 17
`G:=sub<GL(4,GF(29))| [19,10,0,0,19,7,0,0,0,0,28,0,0,0,0,28],[28,0,0,0,0,28,0,0,0,0,28,17,0,0,5,1],[9,15,0,0,14,20,0,0,0,0,1,0,0,0,24,28],[9,15,0,0,14,20,0,0,0,0,12,0,0,0,0,12],[1,7,0,0,0,28,0,0,0,0,12,28,0,0,27,17] >;`

C14.1482+ 1+4 in GAP, Magma, Sage, TeX

`C_{14}._{148}2_+^{1+4}`
`% in TeX`

`G:=Group("C14.148ES+(2,2)");`
`// GroupNames label`

`G:=SmallGroup(448,1287);`
`// by ID`

`G=gap.SmallGroup(448,1287);`
`# by ID`

`G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,758,219,1571,80,18822]);`
`// Polycyclic`

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

׿
×
𝔽