Properties

 Label 23T4 Degree $23$ Order $506$ Cyclic no Abelian no Solvable yes Primitive yes $p$-group no Group: $F_{23}$

Related objects

Group action invariants

 Degree $n$: $23$ Transitive number $t$: $4$ Group: $F_{23}$ Parity: $-1$ Primitive: yes Nilpotency class: $-1$ (not nilpotent) $|\Aut(F/K)|$: $1$ Generators: (2,6,3,11,5,21,9,18,17,12,10,23,19,22,14,20,4,16,7,8,13,15), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$11$:  $C_{11}$
$22$:  22T1

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - none

Low degree siblings

46T5

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

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

Group invariants

 Order: $506=2 \cdot 11 \cdot 23$ Cyclic: no Abelian: no Solvable: yes GAP id: [506, 1]
 Character table: not available.