Properties

Label 21T156
Order \(96018048000\)
n \(21\)
Cyclic No
Abelian No
Solvable No
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $21$
Transitive number $t$ :  $156$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,13,16,7,14,17,4,12,20,2,10,18,3,9,15)(5,11,19)(6,8,21), (1,11,4,8)(2,9,6,10)(3,13)(5,14)(7,12)(16,17,20,21,19)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
6:  $S_3$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 7: None

Low degree siblings

42T7460, 45T7533 x 2

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 255 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $96018048000=2^{10} \cdot 3^{7} \cdot 5^{3} \cdot 7^{3}$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.