Properties

Label 28T47
Degree $28$
Order $392$
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)
$|\Aut(F/K)|$:  $14$
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)

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: not available.