Properties

Label 38T43
Order \(77976\)
n \(38\)
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)
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)
$|\Aut(F/K)|$:  $1$

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:  $S_3\times C_3$, $D_{9}$
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:  Data not available
Character table: Data not available.