Properties

Label 38T35
Order \(25992\)
n \(38\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Learn more about

Group action invariants

Degree $n$ :  $38$
Transitive number $t$ :  $35$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,21,2,38,13,35)(3,36,5,32,8,26)(4,34,16,29,15,31)(6,30,19,23,10,22)(7,28,11,20,17,27)(9,24,14,33,12,37)(18,25), (1,32,9,27,16,25,15,28,7,33,19,35)(2,29,17,22,4,23,14,31,18,38,12,37)(3,26,6,36,11,21,13,34,10,24,5,20)(8,30)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
3:  $C_3$
4:  $C_2^2$
6:  $S_3$, $C_6$ x 3
8:  $D_{4}$
12:  $D_{6}$, $C_6\times C_2$
18:  $S_3\times C_3$
24:  $(C_6\times C_2):C_2$, $D_4 \times C_3$
36:  $C_6\times S_3$
72:  12T42

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 19: None

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 54 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $25992=2^{3} \cdot 3^{2} \cdot 19^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.