Galois Group: 20T409

• Label: 20T409
• Order: \(10240\)
• n: \(20\)
• Cyclic: No
• Abelian: No
• Solvable: Yes
• Primitive: No
• $p$-group: No

Group action invariants

Degree $n$ :		$20$
Transitive number $t$ :		$409$
Parity:		$-1$
Primitive:		No
Nilpotency class:		$-1$ (not nilpotent)
Generators:		(1,2)(11,12)(13,14)(15,16)(19,20), (1,7,13,20,6,12,17,3,9,16,2,8,14,19,5,11,18,4,10,15)
$|\Aut(F/K)|$:		$2$

Low degree resolvents

|G/N|	Galois groups for stem field(s)
2:	$C_2$ x 3
4:	$C_2^2$
5:	$C_5$
8:	$D_{4}$
10:	$C_{10}$ x 3
20:	20T3
40:	20T12
80:	$C_2^4 : C_5$
160:	$C_2 \times (C_2^4 : C_5)$ x 3
320:	20T72
640:	20T130
2560:	20T256
5120:	20T329

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: None

Degree 5: $C_5$

Degree 10: $C_{10}$

Low degree siblings

20T409 x 47, 20T427 x 48, 40T5881 x 24, 40T5942 x 48, 40T5943 x 48, 40T6403 x 96, 40T6647 x 96, 40T7167 x 96, 40T7428 x 24, 40T7430 x 48, 40T7431 x 96, 40T7432 x 96, 40T7433 x 96, 40T7499 x 24, 40T7739 x 48, 40T8085 x 48, 40T9225 x 96, 40T9227 x 96, 40T9239 x 96, 40T9912 x 24, 40T9919 x 48, 40T9932 x 96, 40T9933 x 96, 40T9935 x 96, 40T9942 x 48, 40T10013 x 48, 40T10014 x 48, 40T10015 x 96, 40T10016 x 96, 40T10017 x 192, 40T10018 x 192, 40T10019 x 192, 40T10020 x 192, 40T10021 x 192, 40T10022 x 192, 40T10166 x 48, 40T10167 x 48, 40T10168 x 96, 40T10169 x 96, 40T10170 x 96, 40T10171 x 96, 40T10172 x 96, 40T10173 x 192, 40T10174 x 192, 40T10175 x 192, 40T10176 x 192, 40T10177 x 192, 40T10178 x 192, 40T10179 x 192, 40T10180 x 192, 40T10181 x 192, 40T10182 x 192, 40T10183 x 192, 40T10184 x 192, 40T10185 x 192, 40T10186 x 192, 40T10187 x 192, 40T10188 x 192, 40T10189 x 192, 40T10190 x 192, 40T10191 x 192, 40T10192 x 192, 40T10193 x 192, 40T10194 x 192, 40T10195 x 192, 40T10196 x 192, 40T10197 x 192, 40T10255 x 48, 40T10256 x 48, 40T10266 x 96, 40T10271 x 96, 40T10280 x 96, 40T10281 x 96, 40T10293 x 96, 40T10303 x 192, 40T10304 x 192, 40T10305 x 192, 40T10306 x 192, 40T10307 x 192, 40T10308 x 192, 40T10309 x 192, 40T10310 x 192, 40T10311 x 192, 40T10312 x 192, 40T10313 x 192, 40T10314 x 192, 40T10315 x 192, 40T10316 x 192, 40T10317 x 192, 40T10318 x 192, 40T10319 x 192, 40T10320 x 192, 40T10321 x 192, 40T10322 x 192, 40T10323 x 192, 40T10324 x 192, 40T10325 x 192, 40T10326 x 192, 40T10327 x 192

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 136 conjugacy classes of elements. Data not shown.

Group invariants

Order:		$10240=2^{11} \cdot 5$
Cyclic:		No
Abelian:		No
Solvable:		Yes
GAP id:		Data not available

Character table: Data not available.