Label 42T20
Degree $42$
Order $126$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{21}\times S_3$

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Group action invariants

Degree $n$:  $42$
Transitive number $t$:  $20$
Group:  $C_{21}\times S_3$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $21$
Generators:  (4,5,6)(10,12,11)(16,18,17)(22,24,23)(28,30,29)(34,35,36)(40,41,42), (1,5,7,12,13,18,21,22,26,29,33,34,37,40,3,6,8,11,14,17,19,24,27,28,31,35,38,41,2,4,9,10,15,16,20,23,25,30,32,36,39,42)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$6$:  $S_3$, $C_6$
$7$:  $C_7$
$18$:  $S_3\times C_3$

Resolvents shown for degrees $\leq 10$


Degree 2: $C_2$

Degree 3: None

Degree 6: $S_3\times C_3$

Degree 7: $C_7$

Degree 14: $C_{14}$

Degree 21: 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 63 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $126=2 \cdot 3^{2} \cdot 7$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  [126, 12]
Character table: not available.