Properties

Label 38T44
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 $t$:  $44$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,29,19,24,14,37,8,26,16,28,18,38,9,31,2,34,5,30)(3,20,10,36,7,21,11,22,12,27,17,33,4,25,15,23,13,32)(6,35), (1,27,15,34,12,23,14,24,19,36,3,28)(2,37,8,21,4,38,13,33,7,30,11,32)(5,29,6,20,18,26,10,22,9,31,16,25)(17,35)

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
$8$:  $D_{4}$
$9$:  $C_9$
$12$:  $D_{6}$, $C_6\times C_2$
$18$:  $S_3\times C_3$, $C_{18}$ x 3
$24$:  $(C_6\times C_2):C_2$, $D_4 \times C_3$
$36$:  $C_6\times S_3$, 36T2
$54$:  $C_9\times S_3$
$72$:  12T42, 36T15
$108$:  36T63
$216$:  36T181

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 90 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.