Galois Group: 20T525

• Label: 20T525
• Order: \(20480\)
• n: \(20\)
• Cyclic: No
• Abelian: No
• Solvable: Yes
• Primitive: No
• $p$-group: No

Group action invariants

Degree $n$ :		$20$
Transitive number $t$ :		$525$
Parity:		$-1$
Primitive:		No
Nilpotency class:		$-1$ (not nilpotent)
Generators:		(19,20), (1,3,6,8,10,12,14,16,18,20)(2,4,5,7,9,11,13,15,17,19), (1,16,2,15)(3,13)(4,14)(5,11)(6,12)(7,9)(8,10)(17,19,18,20)
$|\Aut(F/K)|$:		$2$

Low degree resolvents

|G/N|	Galois groups for stem field(s)
2:	$C_2$ x 7
4:	$C_2^2$ x 7
8:	$D_{4}$ x 2, $C_2^3$
10:	$D_{5}$
16:	$D_4\times C_2$
20:	$D_{10}$ x 3
40:	20T8
80:	20T21
160:	$(C_2^4 : C_5) : C_2$
320:	$C_2\times (C_2^4 : D_5)$ x 3
640:	20T141
1280:	20T187
5120:	20T328
10240:	20T430

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: None

Degree 5: $D_{5}$

Degree 10: $D_{10}$

Low degree siblings

20T522 x 24, 20T525 x 23, 40T11270 x 12, 40T11276 x 12, 40T11278 x 6, 40T11307 x 6, 40T11321 x 12, 40T11322 x 12, 40T11396 x 24, 40T11397 x 24, 40T11398 x 24, 40T11399 x 24, 40T11772 x 12, 40T11791 x 12, 40T11793 x 24, 40T11971 x 6, 40T11983 x 12, 40T11990 x 6, 40T11995 x 12, 40T12003 x 12, 40T12005 x 24, 40T12851 x 24, 40T12934 x 6, 40T12941 x 12, 40T12947 x 12, 40T13060 x 12, 40T13086 x 24, 40T13729 x 6, 40T13796 x 12, 40T13823 x 12, 40T13824 x 12, 40T13833 x 12, 40T13838 x 12, 40T13841 x 24, 40T13843 x 24, 40T13852 x 24, 40T13934 x 12, 40T13969 x 24, 40T13977 x 24, 40T13992 x 24, 40T13993 x 24, 40T13994 x 24, 40T13995 x 24, 40T13996 x 48, 40T13997 x 48, 40T13998 x 48, 40T13999 x 48, 40T14065 x 24, 40T14066 x 24, 40T14067 x 24, 40T14068 x 24, 40T14069 x 24, 40T14070 x 24, 40T14071 x 48, 40T14108 x 24, 40T14109 x 24, 40T14110 x 48, 40T14193 x 24, 40T14197 x 24, 40T14200 x 24, 40T14203 x 24, 40T14210 x 24, 40T14211 x 24, 40T14213 x 24, 40T14214 x 24, 40T14215 x 48, 40T14216 x 48

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 152 conjugacy classes of elements. Data not shown.

Group invariants

Order:		$20480=2^{12} \cdot 5$
Cyclic:		No
Abelian:		No
Solvable:		Yes
GAP id:		Data not available

Character table: Data not available.