Properties

Label 38T35
Degree $38$
Order $25992$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $38$
Transitive number $t$:  $35$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
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)

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:  not available
Character table: not available.