Properties

Label 28T47
Order \(392\)
n \(28\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_7\times D_{14}:C_2$

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Group action invariants

Degree $n$ :  $28$
Transitive number $t$ :  $47$
Group :  $C_7\times D_{14}:C_2$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,25,5,16,9,20,13,23,3,28,8,18,12,21,2,26,6,15,10,19,14,24,4,27,7,17,11,22), (1,21)(2,22)(3,24)(4,23)(5,26)(6,25)(7,28)(8,27)(9,15)(10,16)(11,18)(12,17)(13,19)(14,20)
$|\Aut(F/K)|$:  $14$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
7:  $C_7$
8:  $D_{4}$
14:  $D_{7}$, $C_{14}$ x 3
28:  $D_{14}$, 28T2
56:  28T5, 28T6
98:  $C_7 \wr C_2$
196:  28T34

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: $D_{4}$

Degree 7: None

Degree 14: $C_7 \wr C_2$

Low degree siblings

28T47 x 5

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 119 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $392=2^{3} \cdot 7^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [392, 27]
Character table: Data not available.