Properties

Label 30T39
Order \(150\)
n \(30\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_{15}\times D_5$

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Group action invariants

Degree $n$ :  $30$
Transitive number $t$ :  $39$
Group :  $C_{15}\times D_5$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,23,13,5,25,16,8,30,20,12,3,22,15,4,27,18,7,29,19,11,2,24,14,6,26,17,9,28,21,10), (1,15,26,8,19)(2,13,27,9,20)(3,14,25,7,21)(4,23,11,30,17)(5,24,12,28,18)(6,22,10,29,16)
$|\Aut(F/K)|$:  $15$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
3:  $C_3$
5:  $C_5$
6:  $C_6$
10:  $D_{5}$, $C_{10}$
15:  $C_{15}$
30:  $D_5\times C_3$, $C_{30}$
50:  $D_5\times C_5$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 3: $C_3$

Degree 5: None

Degree 6: $C_6$

Degree 10: $D_5\times C_5$

Degree 15: None

Low degree siblings

30T39

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 60 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $150=2 \cdot 3 \cdot 5^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [150, 8]
Character table: Data not available.