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## G = C14.102+ 1+4order 448 = 26·7

### 10th non-split extension by C14 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C14 — C14.102+ 1+4
 Chief series C1 — C7 — C14 — C2×C14 — C22×D7 — C2×C4×D7 — D7×C4⋊C4 — C14.102+ 1+4
 Lower central C7 — C2×C14 — C14.102+ 1+4
 Upper central C1 — C22 — C2×C4⋊C4

Generators and relations for C14.102+ 1+4
G = < a,b,c,d,e | a14=b4=c2=1, d2=b2, e2=a7, bab-1=a-1, ac=ca, ad=da, ae=ea, cbc=a7b-1, dbd-1=a7b, be=eb, cd=dc, ce=ec, ede-1=b2d >

Subgroups: 932 in 228 conjugacy classes, 107 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×D4, C2×Q8, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C14, C2×C4⋊C4, C2×C4⋊C4, C4×D4, C4×Q8, C22⋊Q8, C42.C2, C4⋊Q8, Dic14, C4×D7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C22×D7, C22×C14, D43Q8, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, D14⋊C4, C23.D7, C23.D7, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C2×C4×D7, C2×C4×D7, C2×C7⋊D4, C22×C28, C22×C28, Dic73Q8, C28⋊Q8, Dic7.Q8, D7×C4⋊C4, D14⋊Q8, D142Q8, C28.48D4, C28.48D4, C4×C7⋊D4, C4×C7⋊D4, C14×C4⋊C4, C14.102+ 1+4
Quotients: C1, C2, C22, Q8, C23, D7, C2×Q8, C4○D4, C24, D14, C22×Q8, C2×C4○D4, 2+ 1+4, C22×D7, D43Q8, C4○D28, Q8×D7, C23×D7, C2×C4○D28, D46D14, C2×Q8×D7, C14.102+ 1+4

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

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

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

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

85 conjugacy classes

 class 1 2A 2B 2C 2D 2E 2F 2G 4A ··· 4F 4G 4H 4I 4J 4K 4L ··· 4Q 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 7 7 7 14 ··· 14 28 ··· 28 size 1 1 1 1 2 2 14 14 2 ··· 2 4 4 4 14 14 28 ··· 28 2 2 2 2 ··· 2 4 ··· 4

85 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 4 4 4 type + + + + + + + + + + - + + + + - image C1 C2 C2 C2 C2 C2 C2 C2 C2 C2 Q8 D7 C4○D4 D14 D14 C4○D28 2+ 1+4 Q8×D7 D4⋊6D14 kernel C14.102+ 1+4 Dic7⋊3Q8 C28⋊Q8 Dic7.Q8 D7×C4⋊C4 D14⋊Q8 D14⋊2Q8 C28.48D4 C4×C7⋊D4 C14×C4⋊C4 C7⋊D4 C2×C4⋊C4 C28 C4⋊C4 C22×C4 C4 C14 C22 C2 # reps 1 1 1 2 1 2 1 3 3 1 4 3 4 12 9 24 1 6 6

Matrix representation of C14.102+ 1+4 in GL6(𝔽29)

 0 21 0 0 0 0 11 18 0 0 0 0 0 0 28 0 0 0 0 0 0 28 0 0 0 0 0 0 28 0 0 0 0 0 0 28
,
 4 28 0 0 0 0 15 25 0 0 0 0 0 0 28 22 0 0 0 0 0 1 0 0 0 0 0 0 17 0 0 0 0 0 0 12
,
 1 0 0 0 0 0 0 1 0 0 0 0 0 0 12 26 0 0 0 0 9 17 0 0 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 12 26 0 0 0 0 9 17 0 0 0 0 0 0 0 12 0 0 0 0 12 0
,
 28 0 0 0 0 0 0 28 0 0 0 0 0 0 17 0 0 0 0 0 0 17 0 0 0 0 0 0 12 0 0 0 0 0 0 17

`G:=sub<GL(6,GF(29))| [0,11,0,0,0,0,21,18,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[4,15,0,0,0,0,28,25,0,0,0,0,0,0,28,0,0,0,0,0,22,1,0,0,0,0,0,0,17,0,0,0,0,0,0,12],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,9,0,0,0,0,26,17,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,9,0,0,0,0,26,17,0,0,0,0,0,0,0,12,0,0,0,0,12,0],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,0,0,0,0,12,0,0,0,0,0,0,17] >;`

C14.102+ 1+4 in GAP, Magma, Sage, TeX

`C_{14}._{10}2_+^{1+4}`
`% in TeX`

`G:=Group("C14.10ES+(2,2)");`
`// GroupNames label`

`G:=SmallGroup(448,964);`
`// by ID`

`G=gap.SmallGroup(448,964);`
`# by ID`

`G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,387,100,1571,18822]);`
`// Polycyclic`

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

׿
×
𝔽