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| Transitive Groups of degree 8 | ||||||
| G | Name | |G| | |G| fact. | |Z(G)| | Properties of G | # fields |
|---|---|---|---|---|---|---|
| 8T1 | C(8)=8 | 8 |
23
|
8 | cyclic, semiabelian | 352 |
| 8T2 | 4[x]2 | 8 |
23
|
8 | abelian, semiabelian, even | 1487 |
| 8T3 | E(8)=2[x]2[x]2 | 8 |
23
|
8 | abelian, semiabelian, even | 1056 |
| 8T4 | D8(8)=[4]2 | 8 |
23
|
2 | nilpotent, semiabelian, even | 1403 |
| 8T5 | Q8(8) | 8 |
23
|
2 | nilpotent, semiabelian, even | 686 |
| 8T6 | D(8) | 16 |
24
|
2 | nilpotent, semiabelian | 766 |
| 8T7 | 1/2[23]4 | 16 |
24
|
4 | nilpotent, semiabelian | 1109 |
| 8T8 | 2D8(8)=[D(4)]2 | 16 |
24
|
2 | nilpotent, semiabelian | 584 |
| 8T9 | E(8):2=D(4)[x]2 | 16 |
24
|
4 | nilpotent, semiabelian, even | 3844 |
| 8T10 | [22]4 | 16 |
24
|
4 | nilpotent, semiabelian, even | 2719 |
| 8T11 | 1/2[23]E(4)=Q8:2 | 16 |
24
|
4 | nilpotent, semiabelian, even | 2134 |
| 8T12 | 2A4(8)=[2]A(4)=SL(2,3) | 24 |
23 · 3
|
2 | solvable, irreducible, even | 390 |
| 8T13 | E(8):3=A(4)[x]2 | 24 |
23 · 3
|
2 | solvable, semiabelian, even | 1604 |
| 8T14 | S(4)[1/2]2=1/2(S4[x]2) | 24 |
23 · 3
|
1 | solvable, semiabelian, even | 861 |
| 8T15 | [1/4.cD(4)2]2 | 32 |
25
|
2 | nilpotent, semiabelian | 2249 |
| 8T16 | 1/2[24]4 | 32 |
25
|
2 | nilpotent, semiabelian | 2077 |
| 8T17 | [42]2 | 32 |
25
|
4 | nilpotent, semiabelian | 1939 |
| 8T18 | E(8):E4=[22]D(4) | 32 |
25
|
4 | nilpotent, semiabelian, even | 2990 |
| 8T19 | E(8):4=[1/4.eD(4)2]2 | 32 |
25
|
2 | nilpotent, semiabelian, even | 2787 |
| 8T20 | [23]4 | 32 |
25
|
2 | nilpotent, semiabelian, even | 2405 |
| 8T21 | 1/2[24]E(4)=[1/4.dD(4)2]2 | 32 |
25
|
2 | nilpotent, semiabelian | 2323 |
| 8T22 | E(8):D4=[23]22 | 32 |
25
|
2 | nilpotent, semiabelian, even | 2509 |
| 8T23 | 2S4(8)=GL(2,3) | 48 |
24 · 3
|
2 | solvable, irreducible | 801 |
| 8T24 | E(8):D6=S(4)[x]2 | 48 |
24 · 3
|
2 | solvable, semiabelian, even | 3207 |
| 8T25 | E(8):7=F56(8) | 56 |
23 · 7
|
1 | solvable, primitive, semiabelian, even | 175 |
| 8T26 | 1/2[24]eD(4) | 64 |
26
|
2 | nilpotent, semiabelian | 3558 |
| 8T27 | [24]4 | 64 |
26
|
2 | nilpotent, semiabelian | 3787 |
| 8T28 | 1/2[24]dD(4) | 64 |
26
|
2 | nilpotent, semiabelian | 3571 |
| 8T29 | E(8):D8=[23]D(4) | 64 |
26
|
2 | nilpotent, semiabelian, even | 4236 |
| 8T30 | 1/2[24]cD(4) | 64 |
26
|
2 | nilpotent, semiabelian | 2962 |
| 8T31 | [24]E(4) | 64 |
26
|
2 | nilpotent, semiabelian | 3362 |
| 8T32 | [23]A(4) | 96 |
25 · 3
|
2 | solvable, semiabelian, even | 1773 |
| 8T33 | E(8):A4=[1/3.A(4)2]2=E(16):6 | 96 |
25 · 3
|
1 | solvable, semiabelian, even | 713 |
| 8T34 | 1/2[E(4)2:S3]2=E(4)2:D6 | 96 |
25 · 3
|
1 | solvable, semiabelian, even | 629 |
| 8T35 | [24]D(4) | 128 |
27
|
2 | nilpotent, semiabelian | 5807 |
| 8T36 | E(8):F21 | 168 |
23 · 3 · 7
|
1 | solvable, primitive, semiabelian, even | 165 |
| 8T37 | L(8)=PSL(2,7) | 168 |
23 · 3 · 7
|
1 | not solvable, primitive, simple, irreducible, even | 234 |
| 8T38 | [24]A(4) | 192 |
26 · 3
|
2 | solvable, semiabelian | 3049 |
| 8T39 | [23]S(4) | 192 |
26 · 3
|
2 | solvable, semiabelian, even | 3157 |
| 8T40 | 1/2[24]S(4) | 192 |
26 · 3
|
2 | solvable | 2271 |
| 8T41 | E(8):S4=[E(4)2:S3]2=E(4)2:D12 | 192 |
26 · 3
|
1 | solvable, semiabelian, even | 1837 |
| 8T42 | [A(4)2]2 | 288 |
25 · 32
|
1 | solvable, semiabelian, even | 559 |
| 8T43 | L(8):2=PGL(2,7) | 336 |
24 · 3 · 7
|
1 | not solvable, primitive, irreducible | 290 |
| 8T44 | [24]S(4) | 384 |
27 · 3
|
2 | solvable, semiabelian | 4964 |
| 8T45 | [1/2.S(4)2]2 | 576 |
26 · 32
|
1 | solvable, semiabelian, even | 756 |
| 8T46 | 1/2[S(4)2]2 | 576 |
26 · 32
|
1 | solvable, semiabelian | 429 |
| 8T47 | [S(4)2]2 | 1152 |
27 · 32
|
1 | solvable, semiabelian | 3155 |
| 8T48 | E(8):L7=AL(8) | 1344 |
26 · 3 · 7
|
1 | not solvable, primitive, even | 941 |
| 8T49 | A(8) | 20160 |
26 · 32 · 5 · 7
|
1 | not solvable, primitive, simple, irreducible, even | 545 |
| 8T50 | S(8) | 40320 |
27 · 32 · 5 · 7
|
1 | not solvable, primitive, irreducible | 815 |
9 | 2,57 ms