Galois Group: 20T853

• Label: 20T853
• Order: \(163840\)
• n: \(20\)
• Cyclic: No
• Abelian: No
• Solvable: Yes
• Primitive: No
• $p$-group: No

Group action invariants

Degree $n$ :		$20$
Transitive number $t$ :		$853$
Parity:		$1$
Primitive:		No
Nilpotency class:		$-1$ (not nilpotent)
Generators:		(1,7,13,20,16,12,18,4,10,5)(2,8,14,19,15,11,17,3,9,6), (1,13)(2,14)(3,12,4,11)(5,10,16,19,6,9,15,20)(7,18)(8,17)
$|\Aut(F/K)|$:		$2$

Low degree resolvents

|G/N|	Galois groups for stem field(s)
2:	$C_2$ x 3
4:	$C_2^2$
10:	$D_{5}$
20:	$D_{10}$
160:	$(C_2^4 : C_5) : C_2$ x 5
320:	$C_2\times (C_2^4 : D_5)$ x 5
2560:	20T240
5120:	20T307, 32T397068 x 2
81920:	40T21245

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

20T849 x 32, 20T853 x 31, 40T48314 x 64, 40T48339 x 8, 40T48341 x 16, 40T49727 x 8, 40T49728 x 8, 40T49732 x 16, 40T49733 x 16, 40T49738 x 8, 40T49742 x 16, 40T50062 x 16, 40T50363 x 8, 40T50405 x 16, 40T50726 x 8, 40T50746 x 16, 40T50770 x 16, 40T50772 x 16, 40T51964 x 32, 40T51989 x 8, 40T52110 x 8, 40T52116 x 8, 40T52117 x 16, 40T52168 x 8, 40T52177 x 16, 40T52186 x 16, 40T52358 x 16, 40T52360 x 16, 40T52367 x 16, 40T52389 x 32, 40T52727 x 64, 40T54431 x 8, 40T54433 x 8, 40T54480 x 16, 40T54484 x 16, 40T54524 x 16, 40T54525 x 16, 40T54527 x 32, 40T54528 x 32, 40T54730 x 64, 40T54731 x 64, 40T54732 x 64, 40T55333 x 16, 40T55334 x 16, 40T55336 x 32, 40T55337 x 32, 40T80556 x 64, 40T80558 x 64, 40T80560 x 64, 40T80892 x 8, 40T81082 x 16, 40T81083 x 16, 40T81164 x 16, 40T81219 x 16, 40T81318 x 16, 40T81400 x 16, 40T81404 x 16, 40T81412 x 16, 40T81416 x 16, 40T81423 x 32, 40T81429 x 32, 40T81430 x 32, 40T81432 x 32, 40T81434 x 32, 40T81436 x 32, 40T81439 x 32, 40T81440 x 32, 40T81445 x 32, 40T81450 x 32, 40T104584 x 8, 40T104704 x 16, 40T104945 x 16, 40T105030 x 16, 40T105039 x 16, 40T105052 x 32, 40T105054 x 32, 40T105062 x 32, 40T105068 x 32, 40T105079 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 280 conjugacy classes of elements. Data not shown.

Group invariants

Order:		$163840=2^{15} \cdot 5$
Cyclic:		No
Abelian:		No
Solvable:		Yes
GAP id:		Data not available

Character table: Data not available.