<< degree 7 | overview | degree 9 >>

Transitive Groups of degree 8

Jump to group T

Smallest Discs display

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 755
8T7 1/2[23]4 16
24
4 nilpotent, semiabelian 1103
8T8 2D8(8)=[D(4)]2 16
24
2 nilpotent, semiabelian 579
8T9 E(8):2=D(4)[x]2 16
24
4 nilpotent, semiabelian, even 3844
8T10 [22]4 16
24
4 nilpotent, semiabelian, even 2713
8T11 1/2[23]E(4)=Q8:2 16
24
4 nilpotent, semiabelian, even 2131
8T12 2A4(8)=[2]A(4)=SL(2,3) 24
23 · 3
2 solvable, irreducible, even 382
8T13 E(8):3=A(4)[x]2 24
23 · 3
2 solvable, semiabelian, even 1595
8T14 S(4)[1/2]2=1/2(S4[x]2) 24
23 · 3
1 solvable, semiabelian, even 838
8T15 [1/4.cD(4)2]2 32
25
2 nilpotent, semiabelian 2246
8T16 1/2[24]4 32
25
2 nilpotent, semiabelian 2067
8T17 [42]2 32
25
4 nilpotent, semiabelian 1937
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 2786
8T20 [23]4 32
25
2 nilpotent, semiabelian, even 2398
8T21 1/2[24]E(4)=[1/4.dD(4)2]2 32
25
2 nilpotent, semiabelian 2320
8T22 E(8):D4=[23]22 32
25
2 nilpotent, semiabelian, even 2508
8T23 2S4(8)=GL(2,3) 48
24 · 3
2 solvable, irreducible 799
8T24 E(8):D6=S(4)[x]2 48
24 · 3
2 solvable, semiabelian, even 3179
8T25 E(8):7=F56(8) 56
23 · 7
1 solvable, primitive, semiabelian, even 148
8T26 1/2[24]eD(4) 64
26
2 nilpotent, semiabelian 3552
8T27 [24]4 64
26
2 nilpotent, semiabelian 3762
8T28 1/2[24]dD(4) 64
26
2 nilpotent, semiabelian 3561
8T29 E(8):D8=[23]D(4) 64
26
2 nilpotent, semiabelian, even 4227
8T30 1/2[24]cD(4) 64
26
2 nilpotent, semiabelian 2957
8T31 [24]E(4) 64
26
2 nilpotent, semiabelian 3342
8T32 [23]A(4) 96
25 · 3
2 solvable, even 1759
8T33 E(8):A4=[1/3.A(4)2]2=E(4):6 96
25 · 3
1 solvable, semiabelian, even 683
8T34 1/2[E(4)2:S3]2=E(4)2:D6 96
25 · 3
1 solvable, semiabelian, even 596
8T35 [24]D(4) 128
27
2 nilpotent, semiabelian 5750
8T36 E(8):F21 168
23 · 3 · 7
1 solvable, primitive, semiabelian, even 143
8T37 L(8)=PSL(2,7) 168
23 · 3 · 7
1 not solvable, primitive, simple, irreducible, even 205
8T38 [24]A(4) 192
26 · 3
2 solvable 3048
8T39 [23]S(4) 192
26 · 3
2 solvable, semiabelian, even 3127
8T40 1/2[24]S(4) 192
26 · 3
2 solvable 2265
8T41 E(8):S4=[E(4)2:S3]2=E(4)2:D12 192
26 · 3
1 solvable, semiabelian, even 1759
8T42 [A(4)2]2 288
25 · 32
1 solvable, semiabelian, even 518
8T43 L(8):2=PGL(2,7) 336
24 · 3 · 7
1 not solvable, primitive, irreducible 246
8T44 [24]S(4) 384
27 · 3
2 solvable 4913
8T45 [1/2.S(4)2]2 576
26 · 32
1 solvable, semiabelian, even 675
8T46 1/2[S(4)2]2 576
26 · 32
1 solvable, semiabelian 386
8T47 [S(4)2]2 1152
27 · 32
1 solvable, semiabelian 3037
8T48 E(8):L7=AL(8) 1344
26 · 3 · 7
1 not solvable, primitive, even 856
8T49 A(8) 20160
26 · 32 · 5 · 7
1 not solvable, primitive, simple, irreducible, even 447
8T50 S(8) 40320
27 · 32 · 5 · 7
1 not solvable, primitive, irreducible 815

9   |   4,59 ms