Properties

Label 21T98
Order \(91854\)
n \(21\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Related objects

Learn more about

Group action invariants

Degree $n$ :  $21$
Transitive number $t$ :  $98$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,10,5)(2,11,4)(3,12,6)(7,14,17)(8,13,18)(9,15,16)(19,20,21), (1,20,11,6,7,16,2,19,12,5,8,17,3,21,10,4,9,18)
$|\Aut(F/K)|$:  $3$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
3:  $C_3$ x 4
6:  $C_6$ x 4
9:  $C_3^2$
18:  $C_6 \times C_3$
42:  $F_7$
126:  21T9
30618:  21T77

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 7: $F_7$

Low degree siblings

21T98 x 5, 42T1211 x 6, 42T1223 x 3, 42T1225 x 6

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 168 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $91854=2 \cdot 3^{8} \cdot 7$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.