# Properties

 Label 23T2 Degree $23$ Order $46$ Cyclic no Abelian no Solvable yes Primitive yes $p$-group no Group: $D_{23}$

# Related objects

## Group action invariants

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

## Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$

Resolvents shown for degrees $\leq 47$

## Subfields

Prime degree - none

## Low degree siblings

46T2

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

## Group invariants

 Order: $46=2 \cdot 23$ Cyclic: no Abelian: no Solvable: yes GAP id: [46, 1]
 Character table:  2 1 1 . . . . . . . . . . . 23 1 . 1 1 1 1 1 1 1 1 1 1 1 1a 2a 23a 23b 23c 23d 23e 23f 23g 23h 23i 23j 23k 2P 1a 1a 23b 23d 23f 23h 23j 23k 23i 23g 23e 23c 23a 3P 1a 2a 23c 23f 23i 23k 23h 23e 23b 23a 23d 23g 23j 5P 1a 2a 23e 23j 23h 23c 23b 23g 23k 23f 23a 23d 23i 7P 1a 2a 23g 23i 23b 23e 23k 23d 23c 23j 23f 23a 23h 11P 1a 2a 23k 23a 23j 23b 23i 23c 23h 23d 23g 23e 23f 13P 1a 2a 23j 23c 23g 23f 23d 23i 23a 23k 23b 23h 23e 17P 1a 2a 23f 23k 23e 23a 23g 23j 23d 23b 23h 23i 23c 19P 1a 2a 23d 23h 23k 23g 23c 23a 23e 23i 23j 23f 23b 23P 1a 2a 1a 1a 1a 1a 1a 1a 1a 1a 1a 1a 1a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