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Transitive Groups of degree 10

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Transitive Groups of degree 10
G Δ Name |G| |G| fact. |Z(G)| Properties of G # fields
10T16 1/2[25]D(5) 160
25 · 5
1 solvable, semiabelian 524
10T25 1/2[25]F(5) 320
26 · 5
1 solvable, semiabelian 355
10T38 1/2[25]S(5) 1920
27 · 3 · 5
1 not solvable 599
10T9 [1/2.D(5)2]2 100
22 · 52
1 solvable, semiabelian 255
10T10 1/2[D(5)2]2 100
22 · 52
1 solvable, semiabelian 201
10T4 1/2[F(5)]2 20
22 · 5
1 solvable, semiabelian 226
10T27 [1/2.F(5)2]2 400
24 · 52
1 solvable, semiabelian 542
10T28 1/2[F(5)2]2 400
24 · 52
1 solvable, semiabelian, even 288
10T42 1/2[S(5)2]2 14400
26 · 32 · 52
1 not solvable, irreducible, even 198
10T41 [1/2.S(5)2]2=[A(5):2]2 14400
26 · 32 · 52
1 not solvable, irreducible 625
10T12 1/2[S(5)]2=S5(10a) 120
23 · 3 · 5
1 not solvable, irreducible 559
10T8 [24]5 80
24 · 5
1 solvable, semiabelian, even 510
10T34 [24]A(5) 960
26 · 3 · 5
1 not solvable, even 444
10T15 [24]D(5) 160
25 · 5
1 solvable, semiabelian, even 902
10T24 [24]F(5) 320
26 · 5
1 solvable, semiabelian, even 394
10T37 [24]S(5) 1920
27 · 3 · 5
1 not solvable, even 793
10T14 [25]5 160
25 · 5
2 solvable, semiabelian 824
10T36 [25]A(5) 1920
27 · 3 · 5
2 not solvable 1379
10T23 [25]D(5) 320
26 · 5
2 solvable, semiabelian 1387
10T29 [25]F(5) 640
27 · 5
2 solvable, semiabelian 1454
10T39 [25]S(5) 3840
28 · 3 · 5
2 not solvable 1798
10T6 [52]2 50
2 · 52
5 solvable, semiabelian 207
10T17 [52:4]2 200
23 · 52
1 solvable, semiabelian 236
10T19 [52:42]2 200
23 · 52
1 solvable, semiabelian 344
10T18 [52:4]22 200
23 · 52
1 solvable, semiabelian, even 189
10T20 [52:42]22 200
23 · 52
1 solvable, semiabelian 227
10T44 A(10) 1814400
27 · 34 · 52 · 7
1 not solvable, primitive, simple, irreducible, even 224
10T7 A5(10) 60
22 · 3 · 5
1 not solvable, primitive, simple, irreducible, even 377
10T40 [A(5)2]2 7200
25 · 32 · 52
1 not solvable, irreducible 544
10T11 A(5)[x]2 120
23 · 3 · 5
2 not solvable 419
10T1 C(10)=5[x]2 10
2 · 5
10 cyclic, semiabelian 260
10T3 D10(10)=[D(5)]2 20
22 · 5
2 solvable, semiabelian 542
10T2 D(10)=5:2 10
2 · 5
1 solvable, semiabelian 169
10T21 [D(5)2]2 200
23 · 52
1 solvable, semiabelian 485
10T33 [F(5)2]2 800
25 · 52
1 solvable, semiabelian 411
10T5 F(5)[x]2 40
23 · 5
2 solvable, semiabelian 456
10T35 L(10).22=P|L(2,9) 1440
25 · 32 · 5
1 not solvable, primitive, irreducible 369
10T30 L(10):2=PGL(2,9) 720
24 · 32 · 5
1 not solvable, primitive, irreducible 92
10T26 L(10)=PSL(2,9) 360
23 · 32 · 5
1 not solvable, primitive, simple, irreducible, even 74
10T31 M(10)=L(10)'2 720
24 · 32 · 5
1 not solvable, primitive, irreducible, even 15
10T45 S(10) 3628800
28 · 34 · 52 · 7
1 not solvable, primitive, irreducible 588
10T13 S5(10d) 120
23 · 3 · 5
1 not solvable, primitive, irreducible 451
10T43 [S(5)2]2 28800
27 · 32 · 52
1 not solvable, irreducible 1103
10T22 S(5)[x]2 240
24 · 3 · 5
2 not solvable 720
10T32 S6(10)=L(10):2 720
24 · 32 · 5
1 not solvable, primitive, irreducible 231

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