Properties

Label 17T10
Order \(355687428096000\)
n \(17\)
Cyclic No
Abelian No
Solvable No
Primitive Yes
$p$-group No
Group: $S_{17}$

Related objects

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Group action invariants

Degree $n$ :  $17$
Transitive number $t$ :  $10$
Group :  $S_{17}$
Parity:  $-1$
Primitive:  Yes
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17), (1,2)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - none

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 297 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $355687428096000=2^{15} \cdot 3^{6} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13 \cdot 17$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.