Properties

Label 42T46
Order \(252\)
n \(42\)
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)
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)
$|\Aut(F/K)|$:  $7$

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 $\leq 10$

Subfields

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: Data not available.