Properties

Label 21T93
Order \(61236\)
n \(21\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $21$
Transitive number $t$ :  $93$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,14,3,13,2,15)(4,10)(5,11)(6,12)(16,19)(17,21)(18,20), (1,6,7,12,15,17,21,2,5,8,11,13,18,19)(3,4,9,10,14,16,20)
$|\Aut(F/K)|$:  $1$

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
20412:  21T68

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 7: $D_{7}$

Low degree siblings

21T93 x 25, 42T1043 x 26, 42T1044 x 26, 42T1045 x 26, 42T1047 x 13, 42T1048 x 26

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 171 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $61236=2^{2} \cdot 3^{7} \cdot 7$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.