Properties

Label 28T33
Degree $28$
Order $196$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_7\times C_7:C_4$

Learn more about

Group action invariants

Degree $n$:  $28$
Transitive number $t$:  $33$
Group:  $C_7\times C_7:C_4$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $14$
Generators:  (1,2)(3,23,15,8,28,19,12,4,24,16,7,27,20,11)(5,6)(9,10)(13,14)(17,18)(21,22)(25,26), (1,27,5,3,9,8,14,12,17,16,21,20,25,23,2,28,6,4,10,7,13,11,18,15,22,19,26,24)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$4$:  $C_4$
$7$:  $C_7$
$14$:  $D_{7}$, $C_{14}$
$28$:  $C_{28}$, 28T3
$98$:  $C_7 \wr C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: $C_4$

Degree 7: None

Degree 14: $C_7 \wr C_2$

Low degree siblings

28T33 x 2

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 70 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $196=2^{2} \cdot 7^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  [196, 5]
Character table: not available.