Properties

Label 38T47
Order \(233928\)
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 $t$ :  $47$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,24,9,23,19,36,3,38,2,31,15,27,17,22,10,30,6,21)(4,26,8,35,13,32,5,33,14,20,11,37,12,25,18,29,16,34)(7,28), (1,37,14,28)(2,29,13,36)(3,21,12,25)(4,32,11,33)(5,24,10,22)(6,35,9,30)(7,27,8,38)(15,20,19,26)(16,31,18,34)(17,23)
$|\Aut(F/K)|$:  $1$

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:  $S_3\times C_3$, $D_{9}$, $C_{18}$ x 3
24:  $(C_6\times C_2):C_2$, $D_4 \times C_3$
36:  $C_6\times S_3$, $D_{18}$, 36T2
54:  $C_9\times S_3$, 18T19
72:  12T42, 36T15, 36T24
108:  36T63, 36T69
162:  18T74
216:  36T181, 36T189
324:  36T461
648:  36T966

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 209 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $233928=2^{3} \cdot 3^{4} \cdot 19^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.