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Properties

Label 20T427
Order \(10240\)
n \(20\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $20$
Transitive number $t$ :  $427$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,3,2,4)(5,7,6,8)(9,10)(15,16)(17,19,18,20), (1,14,20,11,5,4,15,17,9,7)(2,13,19,12,6,3,16,18,10,8)
$|\Aut(F/K)|$:  $2$

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: None

Degree 4: None

Degree 5: $C_5$

Degree 10: $C_2 \times (C_2^4 : C_5)$

Low degree siblings

20T409 x 48, 20T427 x 47, 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.