Properties

Label 40T16
Order \(80\)
n \(40\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_5\times C_2^2:C_4$

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Group action invariants

Degree $n$ :  $40$
Transitive number $t$ :  $16$
Group :  $C_5\times C_2^2:C_4$
Parity:  $1$
Primitive:  No
Nilpotency class:  $2$
Generators:  (1,29,19,6,35,24,12,38,28,13,4,32,18,7,33,21,9,40,26,16)(2,30,20,5,36,23,11,37,27,14,3,31,17,8,34,22,10,39,25,15), (1,20,35,11,28,3,18,34,9,25)(2,19,36,12,27,4,17,33,10,26)(5,23,37,14,31,8,22,39,15,30)(6,24,38,13,32,7,21,40,16,29)
$|\Aut(F/K)|$:  $20$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_4$ x 2, $C_2^2$
5:  $C_5$
8:  $D_{4}$ x 2, $C_4\times C_2$
10:  $C_{10}$ x 3
16:  $C_2^2:C_4$

Resolvents shown for degrees $\leq 10$

Subfields

Degree 2: $C_2$

Degree 4: $C_4$, $D_{4}$ x 2

Degree 5: $C_5$

Degree 8: $C_2^2:C_4$

Degree 10: $C_{10}$

Degree 20: 20T1, 20T12 x 2

Low degree siblings

There are no siblings with degree $\leq 10$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 50 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $80=2^{4} \cdot 5$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [80, 21]
Character table: Data not available.