Properties

Label 23T1
Order \(23\)
n \(23\)
Cyclic Yes
Abelian Yes
Solvable Yes
Primitive Yes
$p$-group Yes
Group: $C_{23}$

Related objects

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Group action invariants

Degree $n$ :  $23$
Transitive number $t$ :  $1$
Group :  $C_{23}$
Parity:  $1$
Primitive:  Yes
Nilpotency class:  $1$
Generators:  (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)
$|\Aut(F/K)|$:  $23$

Low degree resolvents

None

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - none

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 $ $1$ $1$ $()$
$ 23 $ $1$ $23$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)$
$ 23 $ $1$ $23$ $( 1, 3, 5, 7, 9,11,13,15,17,19,21,23, 2, 4, 6, 8,10,12,14,16,18,20,22)$
$ 23 $ $1$ $23$ $( 1, 4, 7,10,13,16,19,22, 2, 5, 8,11,14,17,20,23, 3, 6, 9,12,15,18,21)$
$ 23 $ $1$ $23$ $( 1, 5, 9,13,17,21, 2, 6,10,14,18,22, 3, 7,11,15,19,23, 4, 8,12,16,20)$
$ 23 $ $1$ $23$ $( 1, 6,11,16,21, 3, 8,13,18,23, 5,10,15,20, 2, 7,12,17,22, 4, 9,14,19)$
$ 23 $ $1$ $23$ $( 1, 7,13,19, 2, 8,14,20, 3, 9,15,21, 4,10,16,22, 5,11,17,23, 6,12,18)$
$ 23 $ $1$ $23$ $( 1, 8,15,22, 6,13,20, 4,11,18, 2, 9,16,23, 7,14,21, 5,12,19, 3,10,17)$
$ 23 $ $1$ $23$ $( 1, 9,17, 2,10,18, 3,11,19, 4,12,20, 5,13,21, 6,14,22, 7,15,23, 8,16)$
$ 23 $ $1$ $23$ $( 1,10,19, 5,14,23, 9,18, 4,13,22, 8,17, 3,12,21, 7,16, 2,11,20, 6,15)$
$ 23 $ $1$ $23$ $( 1,11,21, 8,18, 5,15, 2,12,22, 9,19, 6,16, 3,13,23,10,20, 7,17, 4,14)$
$ 23 $ $1$ $23$ $( 1,12,23,11,22,10,21, 9,20, 8,19, 7,18, 6,17, 5,16, 4,15, 3,14, 2,13)$
$ 23 $ $1$ $23$ $( 1,13, 2,14, 3,15, 4,16, 5,17, 6,18, 7,19, 8,20, 9,21,10,22,11,23,12)$
$ 23 $ $1$ $23$ $( 1,14, 4,17, 7,20,10,23,13, 3,16, 6,19, 9,22,12, 2,15, 5,18, 8,21,11)$
$ 23 $ $1$ $23$ $( 1,15, 6,20,11, 2,16, 7,21,12, 3,17, 8,22,13, 4,18, 9,23,14, 5,19,10)$
$ 23 $ $1$ $23$ $( 1,16, 8,23,15, 7,22,14, 6,21,13, 5,20,12, 4,19,11, 3,18,10, 2,17, 9)$
$ 23 $ $1$ $23$ $( 1,17,10, 3,19,12, 5,21,14, 7,23,16, 9, 2,18,11, 4,20,13, 6,22,15, 8)$
$ 23 $ $1$ $23$ $( 1,18,12, 6,23,17,11, 5,22,16,10, 4,21,15, 9, 3,20,14, 8, 2,19,13, 7)$
$ 23 $ $1$ $23$ $( 1,19,14, 9, 4,22,17,12, 7, 2,20,15,10, 5,23,18,13, 8, 3,21,16,11, 6)$
$ 23 $ $1$ $23$ $( 1,20,16,12, 8, 4,23,19,15,11, 7, 3,22,18,14,10, 6, 2,21,17,13, 9, 5)$
$ 23 $ $1$ $23$ $( 1,21,18,15,12, 9, 6, 3,23,20,17,14,11, 8, 5, 2,22,19,16,13,10, 7, 4)$
$ 23 $ $1$ $23$ $( 1,22,20,18,16,14,12,10, 8, 6, 4, 2,23,21,19,17,15,13,11, 9, 7, 5, 3)$
$ 23 $ $1$ $23$ $( 1,23,22,21,20,19,18,17,16,15,14,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)$

Group invariants

Order:  $23$ (is prime)
Cyclic:  Yes
Abelian:  Yes
Solvable:  Yes
GAP id:  [23, 1]
Character table: Data not available.