Properties

Label 35T33
Degree $35$
Order $12005$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$5$:  $C_5$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 5: $C_5$

Degree 7: None

Low degree siblings

35T33 x 79

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 485 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $12005=5 \cdot 7^{4}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  [12005, 16]
Character table: not available.