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| Transitive Groups of degree 14 | ||||||
| G | Name | |G| | |G| fact. | |Z(G)| | Properties of G | # fields |
|---|---|---|---|---|---|---|
| 14T1 | C(14)=7[x]2 | 14 |
2 · 7
|
14 | cyclic, semiabelian | 131 |
| 14T2 | D14(14)=[7]2 | 14 |
2 · 7
|
1 | solvable, semiabelian | 171 |
| 14T3 | D(7)[x]2 | 28 |
22 · 7
|
2 | solvable, semiabelian | 241 |
| 14T4 | 2[1/2]F42(7) | 42 |
2 · 3 · 7
|
1 | solvable, semiabelian | 125 |
| 14T5 | F21(7)[x]2 | 42 |
2 · 3 · 7
|
2 | solvable, semiabelian | 109 |
| 14T6 | [23]7 | 56 |
23 · 7
|
1 | solvable, semiabelian, even | 125 |
| 14T7 | F42(7)[x]2 | 84 |
22 · 3 · 7
|
2 | solvable, semiabelian | 301 |
| 14T8 | [72]2=7wr2 | 98 |
2 · 72
|
7 | solvable, semiabelian | 193 |
| 14T9 | [24]7 | 112 |
24 · 7
|
2 | solvable, semiabelian | 264 |
| 14T10 | L7(14) | 168 |
23 · 3 · 7
|
1 | not solvable, simple, irreducible, even | 118 |
| 14T11 | [23]F21(7) | 168 |
23 · 3 · 7
|
1 | solvable, semiabelian, even | 137 |
| 14T12 | 1/2[D(7)2]2 | 196 |
22 · 72
|
1 | solvable, semiabelian, even | 123 |
| 14T13 | [1/2.D(7)2]2 | 196 |
22 · 72
|
1 | solvable, semiabelian | 155 |
| 14T14 | [72:3]2 | 294 |
2 · 3 · 72
|
1 | solvable, semiabelian | 136 |
| 14T15 | [72:33]2 | 294 |
2 · 3 · 72
|
1 | solvable, semiabelian | 167 |
| 14T16 | L7:2(14)=[L(7)%]2 | 336 |
24 · 3 · 7
|
1 | not solvable, irreducible | 153 |
| 14T17 | 2L7(14)=[2]L(7) | 336 |
24 · 3 · 7
|
2 | not solvable | 302 |
| 14T18 | [24]F21(7) | 336 |
24 · 3 · 7
|
2 | solvable, semiabelian | 277 |
| 14T19 | L(7)[x]2 | 336 |
24 · 3 · 7
|
2 | not solvable | 343 |
| 14T20 | [D(7)2]2=D(7)wr2 | 392 |
23 · 72
|
1 | solvable, semiabelian | 237 |
| 14T21 | [26]7 | 448 |
26 · 7
|
1 | solvable, semiabelian, even | 427 |
| 14T22 | [1/6-.F42(7)2]22 | 588 |
22 · 3 · 72
|
1 | solvable, semiabelian, even | 3 |
| 14T23 | [1/6+.F42(7)2]22 | 588 |
22 · 3 · 72
|
1 | solvable, semiabelian, even | 43 |
| 14T24 | [72:6]2 | 588 |
22 · 3 · 72
|
1 | solvable, semiabelian | 112 |
| 14T25 | [72:63]2 | 588 |
22 · 3 · 72
|
1 | solvable, semiabelian | 90 |
| 14T26 | 1/2[1/2.F42(7)2]2 | 882 |
2 · 32 · 72
|
1 | solvable, semiabelian | 122 |
| 14T27 | 27[1/2]D(7) | 896 |
27 · 7
|
1 | solvable, semiabelian | 459 |
| 14T28 | [26]D(7) | 896 |
27 · 7
|
1 | solvable, semiabelian, even | 524 |
| 14T29 | [27]7=2wr7 | 896 |
27 · 7
|
2 | solvable, semiabelian | 1051 |
| 14T30 | L(14)=PSL(2,13) | 1092 |
22 · 3 · 7 · 13
|
1 | not solvable, primitive, simple, irreducible, even | 7 |
| 14T31 | [D(7)2:33]2 | 1176 |
23 · 3 · 72
|
1 | solvable, semiabelian | 19 |
| 14T32 | [D(7)2:3]2 | 1176 |
23 · 3 · 72
|
1 | solvable, semiabelian | 173 |
| 14T33 | 23`L7(14) | 1344 |
26 · 3 · 7
|
1 | not solvable, irreducible, even | 185 |
| 14T34 | 23:L7(14)=[23]L(7)=[23]L(3,2) | 1344 |
26 · 3 · 7
|
1 | not solvable, even | 335 |
| 14T35 | [26]F21(7) | 1344 |
26 · 3 · 7
|
1 | solvable, semiabelian, even | 474 |
| 14T36 | 1/2[F42(7)2]2 | 1764 |
22 · 32 · 72
|
1 | solvable, semiabelian, even | 40 |
| 14T37 | [1/2.F42(7)2]2 | 1764 |
22 · 32 · 72
|
1 | solvable, semiabelian | 97 |
| 14T38 | [27]D(7)=2wrD(7) | 1792 |
28 · 7
|
2 | solvable, semiabelian | 1095 |
| 14T39 | L(14):2=PGL(2,13) | 2184 |
23 · 3 · 7 · 13
|
1 | not solvable, primitive, irreducible | 79 |
| 14T40 | 1/2[27]F42(7) | 2688 |
27 · 3 · 7
|
1 | solvable, semiabelian | 497 |
| 14T41 | [26]F42(7) | 2688 |
27 · 3 · 7
|
1 | solvable, semiabelian, even | 513 |
| 14T42 | 24`L7(14) | 2688 |
27 · 3 · 7
|
2 | not solvable | 457 |
| 14T43 | 24:L7(14)=[24]L(7) | 2688 |
27 · 3 · 7
|
2 | not solvable | 747 |
| 14T44 | [27]F21(7)=2wrF21(7) | 2688 |
27 · 3 · 7
|
2 | solvable, semiabelian | 850 |
| 14T45 | [F42(7)2]2=F42(7)wr2 | 3528 |
23 · 32 · 72
|
1 | solvable, semiabelian | 243 |
| 14T46 | 2[1/2]S(7) | 5040 |
24 · 32 · 5 · 7
|
1 | not solvable, irreducible | 190 |
| 14T47 | 2[x]A(7) | 5040 |
24 · 32 · 5 · 7
|
2 | not solvable | 244 |
| 14T48 | [27]F42(7)=2wrF42(7) | 5376 |
28 · 3 · 7
|
2 | solvable, semiabelian | 1130 |
| 14T49 | 2[x]S(7) | 10080 |
25 · 32 · 5 · 7
|
2 | not solvable | 753 |
| 14T50 | [26]L(7) | 10752 |
29 · 3 · 7
|
1 | not solvable, even | 809 |
| 14T51 | [27]L(7)=2wrL(7) | 21504 |
210 · 3 · 7
|
2 | not solvable | 1395 |
| 14T52 | [L(7)2]2=L(7)wr2 | 56448 |
27 · 32 · 72
|
1 | not solvable, irreducible | 281 |
| 14T53 | [26]A(7) | 161280 |
29 · 32 · 5 · 7
|
1 | not solvable, even | 656 |
| 14T54 | 1/2[27]S(7) | 322560 |
210 · 32 · 5 · 7
|
1 | not solvable | 971 |
| 14T55 | [26]S(7) | 322560 |
210 · 32 · 5 · 7
|
1 | not solvable, even | 1283 |
| 14T56 | [27]A(7)=2wrA(7) | 322560 |
210 · 32 · 5 · 7
|
2 | not solvable | 1365 |
| 14T57 | [27]S(7) | 645120 |
211 · 32 · 5 · 7
|
2 | not solvable | 2918 |
| 14T58 | [A(7)2]2=A(7)wr2 | 12700800 |
27 · 34 · 52 · 72
|
1 | not solvable, irreducible | 60 |
| 14T59 | 1/2[S(7)2]2 | 25401600 |
28 · 34 · 52 · 72
|
1 | not solvable, irreducible, even | 32 |
| 14T60 | [1/2.S(7)2]2 | 25401600 |
28 · 34 · 52 · 72
|
1 | not solvable, irreducible | 52 |
| 14T61 | [S(7)2]2=S(7)wr2 | 50803200 |
29 · 34 · 52 · 72
|
1 | not solvable, irreducible | 1372 |
| 14T62 | A(14) | 43589145600 |
210 · 35 · 52 · 72 · 11 · 13
|
1 | not solvable, primitive, simple, irreducible, even | 10 |
| 14T63 | S(14) | 87178291200 |
211 · 35 · 52 · 72 · 11 · 13
|
1 | not solvable, primitive, irreducible | 85 |
9 | 3,14 ms