Galois Group: 20T513

• Label: 20T513
• Order: \(20480\)
• n: \(20\)
• Cyclic: No
• Abelian: No
• Solvable: Yes
• Primitive: No
• $p$-group: No

Group action invariants

Degree $n$ :		$20$
Transitive number $t$ :		$513$
Parity:		$-1$
Primitive:		No
Nilpotency class:		$-1$ (not nilpotent)
Generators:		(1,14,6,17,9,2,13,5,18,10)(3,16,8,20,12)(4,15,7,19,11), (1,7,5,20)(2,8,6,19)(3,13,4,14)(9,11,17,15)(10,12,18,16)
$|\Aut(F/K)|$:		$2$

Low degree resolvents

|G/N|	Galois groups for stem field(s)
2:	$C_2$ x 3
4:	$C_4$ x 2, $C_2^2$
8:	$D_{4}$ x 2, $C_4\times C_2$
16:	$C_2^2:C_4$
20:	$F_5$
40:	$F_{5}\times C_2$
80:	20T19
320:	$(C_2^4 : C_5):C_4$ x 3
640:	$((C_2^4 : C_5):C_4)\times C_2$ x 3
1280:	20T191 x 3
5120:	20T306
10240:	20T406

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: None

Degree 5: $F_5$

Degree 10: $F_5$

Low degree siblings

20T513 x 11, 20T526 x 12, 40T11284 x 6, 40T11286 x 6, 40T11287 x 6, 40T11290 x 6, 40T11343 x 6, 40T11370 x 6, 40T11402 x 12, 40T11403 x 12, 40T11404 x 12, 40T11405 x 12, 40T12865 x 24, 40T12872 x 12, 40T12873 x 12, 40T12875 x 24, 40T12884 x 6, 40T12886 x 6, 40T12887 x 6, 40T12888 x 12, 40T12889 x 24, 40T12982 x 12, 40T12985 x 24, 40T12986 x 12, 40T12987 x 24, 40T12995 x 6, 40T12998 x 6, 40T13000 x 12, 40T13001 x 12, 40T13360 x 6, 40T13361 x 6, 40T13363 x 24, 40T13371 x 6, 40T13431 x 6, 40T13435 x 6, 40T13447 x 6, 40T13463 x 24, 40T13473 x 12, 40T13475 x 12, 40T13478 x 24, 40T13496 x 12, 40T13497 x 12, 40T13503 x 24, 40T13505 x 24, 40T13515 x 6, 40T13517 x 6, 40T13518 x 24, 40T13607 x 6, 40T13609 x 6, 40T13673 x 6, 40T13676 x 12, 40T13678 x 24, 40T14021 x 24, 40T14022 x 24, 40T14023 x 24, 40T14024 x 24, 40T14025 x 12, 40T14026 x 12, 40T14027 x 12, 40T14028 x 12, 40T14029 x 12, 40T14030 x 12, 40T14031 x 12, 40T14032 x 12, 40T14033 x 24, 40T14034 x 24, 40T14035 x 24, 40T14036 x 24, 40T14043 x 24, 40T14046 x 24, 40T14059 x 12, 40T14060 x 12, 40T14061 x 12, 40T14062 x 12, 40T14063 x 12, 40T14064 x 12, 40T14187 x 12, 40T14189 x 12, 40T14219 x 12, 40T14220 x 12

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 128 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.