Properties

Label 30T39
Degree $30$
Order $150$
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)
$|\Aut(F/K)|$:  $15$
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)

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: not available.