Properties

Label 42T20
Order \(126\)
n \(42\)
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)
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)
$|\Aut(F/K)|$:  $21$

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 $\leq 10$

Subfields

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: Data not available.