Properties

Label 45T11
Order \(135\)
n \(45\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_5\times He_3$

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Group action invariants

Degree $n$ :  $45$
Transitive number $t$ :  $11$
Group :  $C_5\times He_3$
Parity:  $1$
Primitive:  No
Nilpotency class:  $2$
Generators:  (1,34,23,10,45,33,21,9,41,30,17,5,39,25,14)(2,36,22,12,44,32,20,7,40,29,18,4,37,27,13)(3,35,24,11,43,31,19,8,42,28,16,6,38,26,15), (1,45,40,39,34,32,30,25,22,21,17,13,10,9,4)(2,44,42,37,36,31,29,27,24,20,18,15,12,7,6)(3,43,41,38,35,33,28,26,23,19,16,14,11,8,5)
$|\Aut(F/K)|$:  $15$

Low degree resolvents

|G/N|Galois groups for stem field(s)
3:  $C_3$ x 4
5:  $C_5$
9:  $C_3^2$
27:  $C_3^2:C_3$

Resolvents shown for degrees $\leq 10$

Subfields

Degree 3: $C_3$

Degree 5: $C_5$

Degree 9: $C_3^2:C_3$

Degree 15: $C_{15}$

Low degree siblings

There are no siblings with degree $\leq 10$
Data on whether or not a number field with this Galois group has arithmetically equivalent fields has not been computed.

Conjugacy Classes

There are 55 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $135=3^{3} \cdot 5$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [135, 3]
Character table: Data not available.