Label 42T46
Degree $42$
Order $252$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_7\times S_3^2$

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Group action invariants

Degree $n$:  $42$
Transitive number $t$:  $46$
Group:  $C_7\times S_3^2$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $7$
Generators:  (1,23,2,24,3,22)(4,27,6,26,5,25)(7,30,9,28,8,29)(10,32,11,31,12,33)(13,36,15,35,14,34)(16,39,17,38,18,37)(19,41,21,40,20,42), (1,34,26,16,7,42,32,23,15,6,37,28,19,11,3,36,27,17,8,41,33,24,13,5,38,29,20,12,2,35,25,18,9,40,31,22,14,4,39,30,21,10)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$6$:  $S_3$ x 2
$7$:  $C_7$
$12$:  $D_{6}$ x 2
$36$:  $S_3^2$

Resolvents shown for degrees $\leq 10$


Degree 2: $C_2$

Degree 3: None

Degree 6: $S_3^2$

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:  $252=2^{2} \cdot 3^{2} \cdot 7$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  [252, 35]
Character table: not available.