Properties

Label 36T100886
Order \(3265173504\)
n \(36\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

Degree $n$ :  $36$
Transitive number $t$ :  $100886$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,32,24,20,11,6,3,31,23,19,10,4)(2,33,22,21,12,5)(7,34,29,26,18,15,9,36,28,25,17,13)(8,35,30,27,16,14), (1,17,36,19,3,18,34,21)(2,16,35,20)(4,26,7,23)(5,25,9,24,6,27,8,22)(10,33)(11,31,12,32)(13,30)(14,28,15,29)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
3:  $C_3$
4:  $C_4$ x 2, $C_2^2$
6:  $C_6$ x 3
8:  $C_4\times C_2$
12:  $A_4$
24:  $A_4\times C_2$ x 3
96:  $C_2^4:C_6$

Resolvents shown for degrees $\leq 10$

Subfields

Degree 2: $C_2$

Degree 3: $C_3$

Degree 4: None

Degree 6: $C_6$

Degree 9: None

Degree 12: 12T87

Degree 18: None

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 1,296 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $3265173504=2^{11} \cdot 3^{13}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.