Properties

Label 21T1
Order \(21\)
n \(21\)
Cyclic Yes
Abelian Yes
Solvable Yes
Primitive No
$p$-group No
Group: $C_{21}$

Related objects

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Group action invariants

Degree $n$ :  $21$
Transitive number $t$ :  $1$
Group :  $C_{21}$
Parity:  $1$
Primitive:  No
Nilpotency class:  $1$
Generators:  (1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18)(19,20,21), (1,4,9,10,14,17,20)(2,5,7,11,15,18,21)(3,6,8,12,13,16,19)
$|\Aut(F/K)|$:  $21$

Low degree resolvents

|G/N|Galois groups for stem field(s)
3:  $C_3$
7:  $C_7$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 7: $C_7$

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

Cycle TypeSizeOrderRepresentative
$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1$ $1$ $()$
$ 3, 3, 3, 3, 3, 3, 3 $ $1$ $3$ $( 1, 2, 3)( 4, 5, 6)( 7, 8, 9)(10,11,12)(13,14,15)(16,17,18)(19,20,21)$
$ 3, 3, 3, 3, 3, 3, 3 $ $1$ $3$ $( 1, 3, 2)( 4, 6, 5)( 7, 9, 8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)$
$ 7, 7, 7 $ $1$ $7$ $( 1, 4, 9,10,14,17,20)( 2, 5, 7,11,15,18,21)( 3, 6, 8,12,13,16,19)$
$ 21 $ $1$ $21$ $( 1, 5, 8,10,15,16,20, 2, 6, 9,11,13,17,21, 3, 4, 7,12,14,18,19)$
$ 21 $ $1$ $21$ $( 1, 6, 7,10,13,18,20, 3, 5, 9,12,15,17,19, 2, 4, 8,11,14,16,21)$
$ 21 $ $1$ $21$ $( 1, 7,13,20, 5,12,17, 2, 8,14,21, 6,10,18, 3, 9,15,19, 4,11,16)$
$ 21 $ $1$ $21$ $( 1, 8,15,20, 6,11,17, 3, 7,14,19, 5,10,16, 2, 9,13,21, 4,12,18)$
$ 7, 7, 7 $ $1$ $7$ $( 1, 9,14,20, 4,10,17)( 2, 7,15,21, 5,11,18)( 3, 8,13,19, 6,12,16)$
$ 7, 7, 7 $ $1$ $7$ $( 1,10,20, 9,17, 4,14)( 2,11,21, 7,18, 5,15)( 3,12,19, 8,16, 6,13)$
$ 21 $ $1$ $21$ $( 1,11,19, 9,18, 6,14, 2,12,20, 7,16, 4,15, 3,10,21, 8,17, 5,13)$
$ 21 $ $1$ $21$ $( 1,12,21, 9,16, 5,14, 3,11,20, 8,18, 4,13, 2,10,19, 7,17, 6,15)$
$ 21 $ $1$ $21$ $( 1,13, 5,17, 8,21,10, 3,15, 4,16, 7,20,12, 2,14, 6,18, 9,19,11)$
$ 7, 7, 7 $ $1$ $7$ $( 1,14, 4,17, 9,20,10)( 2,15, 5,18, 7,21,11)( 3,13, 6,16, 8,19,12)$
$ 21 $ $1$ $21$ $( 1,15, 6,17, 7,19,10, 2,13, 4,18, 8,20,11, 3,14, 5,16, 9,21,12)$
$ 21 $ $1$ $21$ $( 1,16,11, 4,19,15, 9, 3,18,10, 6,21,14, 8, 2,17,12, 5,20,13, 7)$
$ 7, 7, 7 $ $1$ $7$ $( 1,17,10, 4,20,14, 9)( 2,18,11, 5,21,15, 7)( 3,16,12, 6,19,13, 8)$
$ 21 $ $1$ $21$ $( 1,18,12, 4,21,13, 9, 2,16,10, 5,19,14, 7, 3,17,11, 6,20,15, 8)$
$ 21 $ $1$ $21$ $( 1,19,18,14,12, 7, 4, 3,21,17,13,11, 9, 6, 2,20,16,15,10, 8, 5)$
$ 7, 7, 7 $ $1$ $7$ $( 1,20,17,14,10, 9, 4)( 2,21,18,15,11, 7, 5)( 3,19,16,13,12, 8, 6)$
$ 21 $ $1$ $21$ $( 1,21,16,14,11, 8, 4, 2,19,17,15,12, 9, 5, 3,20,18,13,10, 7, 6)$

Group invariants

Order:  $21=3 \cdot 7$
Cyclic:  Yes
Abelian:  Yes
Solvable:  Yes
GAP id:  [21, 2]
Character table: Data not available.