Properties

Label 38T44
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 $t$ :  $44$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
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)
$|\Aut(F/K)|$:  $1$

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:  $D_{4}$
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:  Data not available
Character table: Data not available.