Properties

Label 38T43
Degree $38$
Order $77976$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $38$
Transitive number $t$:  $43$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,20,15,29)(2,22,14,27)(3,24,13,25)(4,26,12,23)(5,28,11,21)(6,30,10,38)(7,32,9,36)(8,34)(16,31,19,37)(17,33,18,35), (1,11,16,9,15,18,10,6,4,3,12,7,14,8,5,13,17,19)(20,38,22,32,21,35,31,24,26)(23,29,30,27,36,28,33,37,25)

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
$8$:  $D_{4}$
$12$:  $D_{6}$, $C_6\times C_2$
$18$:  $S_3\times C_3$, $D_{9}$
$24$:  $(C_6\times C_2):C_2$, $D_4 \times C_3$
$36$:  $C_6\times S_3$, $D_{18}$
$54$:  18T19
$72$:  12T42, 36T24
$108$:  36T69
$216$:  36T189

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 75 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $77976=2^{3} \cdot 3^{3} \cdot 19^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.