Properties

Label 21T37
Order \(4116\)
n \(21\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

Degree $n$ :  $21$
Transitive number $t$ :  $37$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,3,5,7,2,4,6)(8,21,9,18,10,15,11,19,12,16,13,20,14,17), (1,10,15,6,8,16)(2,11,18,5,14,20)(3,12,21,4,13,17)(7,9,19)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
6:  $S_3$
12:  $D_{6}$
14:  $D_{7}$
28:  $D_{14}$
84:  21T8
588:  14T25

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 7: None

Low degree siblings

21T37 x 5, 42T392 x 6, 42T393 x 6, 42T394 x 6, 42T400 x 3, 42T401 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 79 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $4116=2^{2} \cdot 3 \cdot 7^{3}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.