<< degree 9 | overview | degree 11 >>

Transitive Groups of degree 10

Jump to group T

Smallest Discs display

Transitive Groups of degree 10
Δ G Name |G| |G| fact. |Z(G)| Properties of G # fields
10T1 C(10)=5[x]2 10
2 · 5
10 cyclic, semiabelian 260
10T2 D(10)=5:2 10
2 · 5
1 solvable, semiabelian 169
10T3 D10(10)=[D(5)]2 20
22 · 5
2 solvable, semiabelian 533
10T4 1/2[F(5)]2 20
22 · 5
1 solvable, semiabelian 226
10T5 F(5)[x]2 40
23 · 5
2 solvable, semiabelian 452
10T6 [52]2 50
2 · 52
5 solvable, semiabelian 207
10T7 A5(10) 60
22 · 3 · 5
1 not solvable, primitive, simple, irreducible, even 377
10T8 [24]5 80
24 · 5
1 solvable, semiabelian, even 510
10T9 [1/2.D(5)2]2 100
22 · 52
1 solvable, semiabelian 234
10T10 1/2[D(5)2]2 100
22 · 52
1 solvable, semiabelian 196
10T11 A(5)[x]2 120
23 · 3 · 5
2 not solvable 419
10T12 1/2[S(5)]2=S5(10a) 120
23 · 3 · 5
1 not solvable, irreducible 550
10T13 S5(10d) 120
23 · 3 · 5
1 not solvable, primitive, irreducible 451
10T14 [25]5 160
25 · 5
2 solvable, semiabelian 824
10T15 [24]D(5) 160
25 · 5
1 solvable, semiabelian, even 902
10T16 1/2[25]D(5) 160
25 · 5
1 solvable, semiabelian 521
10T17 [52:4]2 200
23 · 52
1 solvable, semiabelian 225
10T18 [52:4]22 200
23 · 52
1 solvable, semiabelian, even 147
10T19 [52:42]2 200
23 · 52
1 solvable, semiabelian 331
10T20 [52:42]22 200
23 · 52
1 solvable, semiabelian 203
10T21 [D(5)2]2 200
23 · 52
1 solvable, semiabelian 485
10T22 S(5)[x]2 240
24 · 3 · 5
2 not solvable 720
10T23 [25]D(5) 320
26 · 5
2 solvable, semiabelian 1387
10T24 [24]F(5) 320
26 · 5
1 solvable, semiabelian, even 394
10T25 1/2[25]F(5) 320
26 · 5
1 solvable, semiabelian 351
10T26 L(10)=PSL(2,9) 360
23 · 32 · 5
1 not solvable, primitive, simple, irreducible, even 62
10T27 [1/2.F(5)2]2 400
24 · 52
1 solvable, semiabelian 531
10T28 1/2[F(5)2]2 400
24 · 52
1 solvable, semiabelian, even 229
10T29 [25]F(5) 640
27 · 5
2 solvable, semiabelian 1445
10T30 L(10):2=PGL(2,9) 720
24 · 32 · 5
1 not solvable, primitive, irreducible 88
10T31 M(10)=L(10)'2 720
24 · 32 · 5
1 not solvable, primitive, irreducible, even 15
10T32 S6(10)=L(10):2 720
24 · 32 · 5
1 not solvable, primitive, irreducible 221
10T33 [F(5)2]2 800
25 · 52
1 solvable, semiabelian 336
10T34 [24]A(5) 960
26 · 3 · 5
1 not solvable, even 444
10T35 L(10).22=P|L(2,9) 1440
25 · 32 · 5
1 not solvable, primitive, irreducible 360
10T36 [25]A(5) 1920
27 · 3 · 5
2 not solvable 1378
10T37 [24]S(5) 1920
27 · 3 · 5
1 not solvable, even 792
10T38 1/2[25]S(5) 1920
27 · 3 · 5
1 not solvable 585
10T39 [25]S(5) 3840
28 · 3 · 5
2 not solvable 1796
10T40 [A(5)2]2 7200
25 · 32 · 52
1 not solvable, irreducible 544
10T41 [1/2.S(5)2]2=[A(5):2]2 14400
26 · 32 · 52
1 not solvable, irreducible 624
10T42 1/2[S(5)2]2 14400
26 · 32 · 52
1 not solvable, irreducible, even 196
10T43 [S(5)2]2 28800
27 · 32 · 52
1 not solvable, irreducible 1103
10T44 A(10) 1814400
27 · 34 · 52 · 7
1 not solvable, primitive, simple, irreducible, even 224
10T45 S(10) 3628800
28 · 34 · 52 · 7
1 not solvable, primitive, irreducible 587

9   |   3,95 ms