Properties

Label 42T24
Order \(168\)
n \(42\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_{14}\times A_4$

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Group action invariants

Degree $n$ :  $42$
Transitive number $t$ :  $24$
Group :  $C_{14}\times A_4$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,18,27,39,8,19,34)(2,17,28,40,7,20,33)(3,14,29,41,10,21,36)(4,13,30,42,9,22,35)(5,16,26,38,11,23,31,6,15,25,37,12,24,32), (1,5,3)(2,6,4)(7,12,9)(8,11,10)(13,17,16)(14,18,15)(19,24,21)(20,23,22)(25,30,28)(26,29,27)(31,36,34)(32,35,33)(37,41,39)(38,42,40)
$|\Aut(F/K)|$:  $14$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
3:  $C_3$
6:  $C_6$
7:  $C_7$
12:  $A_4$
24:  $A_4\times C_2$

Resolvents shown for degrees $\leq 10$

Subfields

Degree 2: None

Degree 3: $C_3$

Degree 6: $A_4\times C_2$

Degree 7: $C_7$

Degree 14: None

Degree 21: $C_{21}$

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 56 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $168=2^{3} \cdot 3 \cdot 7$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [168, 52]
Character table: Data not available.