Galois Group: 20T848

• Label: 20T848
• Order: \(163840\)
• n: \(20\)
• Cyclic: No
• Abelian: No
• Solvable: Yes
• Primitive: No
• $p$-group: No

Group action invariants

Degree $n$ :		$20$
Transitive number $t$ :		$848$
Parity:		$-1$
Primitive:		No
Nilpotency class:		$-1$ (not nilpotent)
Generators:		(1,14,12,3,2,13,11,4)(5,20,16,10)(6,19,15,9)(7,8)(17,18), (1,4,16,8,19,12,14,6,18,10)(2,3,15,7,20,11,13,5,17,9)
$|\Aut(F/K)|$:		$2$

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
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

20T848 x 15, 20T852 x 16, 40T49707 x 8, 40T49708 x 8, 40T49709 x 8, 40T49710 x 8, 40T49711 x 8, 40T49712 x 8, 40T49713 x 8, 40T49714 x 4, 40T49715 x 4, 40T49716 x 8, 40T50043 x 8, 40T50046 x 16, 40T50381 x 8, 40T50383 x 8, 40T50386 x 4, 40T50404 x 8, 40T50736 x 4, 40T50749 x 8, 40T50751 x 4, 40T50758 x 4, 40T51951 x 8, 40T51965 x 16, 40T52005 x 16, 40T52119 x 8, 40T52120 x 8, 40T52121 x 8, 40T52128 x 8, 40T52166 x 4, 40T52169 x 8, 40T52170 x 4, 40T52178 x 8, 40T52180 x 8, 40T52185 x 8, 40T52347 x 8, 40T52387 x 8, 40T52392 x 16, 40T55079 x 4, 40T55082 x 4, 40T55094 x 8, 40T55108 x 8, 40T55117 x 8, 40T55126 x 8, 40T55180 x 8, 40T55206 x 8, 40T55207 x 8, 40T55208 x 16, 40T55209 x 16, 40T55210 x 16, 40T55211 x 16, 40T55212 x 16, 40T80903 x 8, 40T80930 x 4, 40T80987 x 8, 40T81025 x 8, 40T81058 x 8, 40T81194 x 8, 40T81195 x 8, 40T81201 x 8, 40T81205 x 8, 40T81210 x 8, 40T81255 x 8, 40T81290 x 8, 40T81396 x 8, 40T81408 x 8, 40T81417 x 16, 40T81419 x 16, 40T81442 x 16, 40T81444 x 16, 40T81447 x 16, 40T104593 x 4, 40T104692 x 8, 40T104774 x 8, 40T104856 x 8, 40T104868 x 8, 40T105016 x 8, 40T105035 x 8, 40T105042 x 8, 40T105050 x 16, 40T105051 x 16, 40T105053 x 16, 40T105055 x 16, 40T105057 x 16, 40T105069 x 16, 40T105072 x 16, 40T105073 x 16, 40T105075 x 16, 40T105076 x 16, 40T105081 x 16

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 277 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.