Properties

Label 45T12
Order \(135\)
n \(45\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_5\times C_9:C_3$

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Group action invariants

Degree $n$ :  $45$
Transitive number $t$ :  $12$
Group :  $C_5\times C_9:C_3$
Parity:  $1$
Primitive:  No
Nilpotency class:  $2$
Generators:  (1,8,13,20,26,31,38,45,6,10,18,23,30,35,40,2,9,15,19,25,33,39,44,5,12,16,22,29,34,42,3,7,14,21,27,32,37,43,4,11,17,24,28,36,41), (1,20,38,10,30,2,19,39,12,29,3,21,37,11,28)(4,23,42,13,33)(5,24,40,14,31)(6,22,41,15,32)(7,25,45,17,34,9,26,43,16,35,8,27,44,18,36)
$|\Aut(F/K)|$:  $15$

Low degree resolvents

|G/N|Galois groups for stem field(s)
3:  $C_3$ x 4
5:  $C_5$
9:  $C_3^2$
27:  $C_9:C_3$

Resolvents shown for degrees $\leq 10$

Subfields

Degree 3: $C_3$

Degree 5: $C_5$

Degree 9: $C_9:C_3$

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, 4]
Character table: Data not available.