Galois Group: 20T905

• Label: 20T905
• Order: \(327680\)
• n: \(20\)
• Cyclic: No
• Abelian: No
• Solvable: Yes
• Primitive: No
• $p$-group: No

Group action invariants

Degree $n$ :		$20$
Transitive number $t$ :		$905$
Parity:		$-1$
Primitive:		No
Nilpotency class:		$-1$ (not nilpotent)
Generators:		(1,10,8,16,4,2,9,7,15,3)(5,14,12,20,18)(6,13,11,19,17), (1,6,9,13,8,12,15,19,4,18,2,5,10,14,7,11,16,20,3,17), (1,6,11,16)(2,5,12,15)(7,20,8,19)(9,17)(10,18)
$|\Aut(F/K)|$:		$2$

Low degree resolvents

|G/N|	Galois groups for stem field(s)
2:	$C_2$ x 7
4:	$C_2^2$ x 7
8:	$C_2^3$
10:	$D_{5}$
20:	$D_{10}$ x 3
40:	20T8
160:	$(C_2^4 : C_5) : C_2$ x 5
320:	$C_2\times (C_2^4 : D_5)$ x 15
640:	20T141 x 5
2560:	20T240
5120:	20T307 x 3
10240:	20T412
163840:	40T52754

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: None

Degree 5: $D_{5}$

Degree 10: $C_2\times (C_2^4 : D_5)$

Low degree siblings

20T905 x 63, 40T109509 x 32, 40T109778 x 16, 40T109783 x 32, 40T110725 x 64, 40T110868 x 32, 40T110869 x 32, 40T110872 x 32, 40T110873 x 32, 40T110907 x 16, 40T110908 x 16, 40T110909 x 32, 40T110917 x 16, 40T110921 x 32, 40T110922 x 32, 40T111126 x 32, 40T111132 x 64, 40T112018 x 16, 40T112023 x 16, 40T112058 x 32, 40T112059 x 32, 40T112061 x 32, 40T112064 x 32, 40T112169 x 32, 40T112223 x 64, 40T112224 x 64, 40T117318 x 16, 40T117333 x 16, 40T117384 x 32, 40T117401 x 32, 40T117406 x 32, 40T117491 x 32, 40T117541 x 32, 40T117576 x 32, 40T117578 x 32, 40T117579 x 64, 40T117581 x 64, 40T117582 x 64, 40T117583 x 64, 40T117584 x 64, 40T135399 x 32, 40T135401 x 32, 40T135404 x 64, 40T135405 x 64, 40T135406 x 64, 40T135407 x 64, 40T135408 x 64, 40T136489 x 16, 40T136577 x 32, 40T136593 x 32, 40T136788 x 32, 40T136799 x 32, 40T136851 x 32, 40T137108 x 32, 40T137113 x 32, 40T137114 x 32, 40T137130 x 64, 40T137131 x 64, 40T137132 x 64, 40T137133 x 64, 40T137134 x 64, 40T137135 x 64, 40T137138 x 64, 40T137142 x 64, 40T137144 x 64, 40T137146 x 64, 40T137147 x 32

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 512 conjugacy classes of elements. Data not shown.

Group invariants

Order:		$327680=2^{16} \cdot 5$
Cyclic:		No
Abelian:		No
Solvable:		Yes
GAP id:		Data not available

Character table: Data not available.