# Properties

 Label 24T41 Degree $24$ Order $48$ Cyclic no Abelian no Solvable yes Primitive no $p$-group no Group: $C_3\times SD_{16}$

## Group action invariants

 Degree $n$: $24$ Transitive number $t$: $41$ Group: $C_3\times SD_{16}$ Parity: $-1$ Primitive: no Nilpotency class: $3$ $|\Aut(F/K)|$: $6$ Generators: (1,16,18,7,9,23,2,15,17,8,10,24)(3,6,20,22,11,13,4,5,19,21,12,14), (1,17,9)(2,18,10)(3,8,11,16,19,23)(4,7,12,15,20,24)(5,21,14,6,22,13)

## Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$3$:  $C_3$
$4$:  $C_2^2$
$6$:  $C_6$ x 3
$8$:  $D_{4}$
$12$:  $C_6\times C_2$
$16$:  $QD_{16}$
$24$:  $D_4 \times C_3$

Resolvents shown for degrees $\leq 47$

## Subfields

Degree 2: $C_2$

Degree 3: $C_3$

Degree 4: $D_{4}$

Degree 6: $C_6$

Degree 8: $QD_{16}$

Degree 12: $D_4 \times C_3$

## 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 Type Size Order Representative $1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $1$ $1$ $()$ $2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1$ $4$ $2$ $( 3,16)( 4,15)( 5, 6)( 7,20)( 8,19)(11,23)(12,24)(13,14)(21,22)$ $2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2$ $1$ $2$ $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22) (23,24)$ $24$ $2$ $24$ $( 1, 3, 5, 8,10,12,13,15,17,19,22,23, 2, 4, 6, 7, 9,11,14,16,18,20,21,24)$ $12, 12$ $4$ $12$ $( 1, 3,18,20, 9,11, 2, 4,17,19,10,12)( 5, 7,21,23,14,15, 6, 8,22,24,13,16)$ $24$ $2$ $24$ $( 1, 4, 5, 7,10,11,13,16,17,20,22,24, 2, 3, 6, 8, 9,12,14,15,18,19,21,23)$ $12, 12$ $2$ $12$ $( 1, 5,10,13,17,22, 2, 6, 9,14,18,21)( 3, 8,12,15,19,23, 4, 7,11,16,20,24)$ $6, 6, 6, 3, 3$ $4$ $6$ $( 1, 5, 9,14,17,22)( 2, 6,10,13,18,21)( 3,20,11, 4,19,12)( 7,24,15)( 8,23,16)$ $8, 8, 8$ $2$ $8$ $( 1, 7,13,20, 2, 8,14,19)( 3, 9,15,21, 4,10,16,22)( 5,11,17,24, 6,12,18,23)$ $4, 4, 4, 4, 4, 4$ $4$ $4$ $( 1, 7, 2, 8)( 3,22, 4,21)( 5,12, 6,11)( 9,15,10,16)(13,19,14,20)(17,24,18,23)$ $8, 8, 8$ $2$ $8$ $( 1, 8,13,19, 2, 7,14,20)( 3,10,15,22, 4, 9,16,21)( 5,12,17,23, 6,11,18,24)$ $3, 3, 3, 3, 3, 3, 3, 3$ $1$ $3$ $( 1, 9,17)( 2,10,18)( 3,11,19)( 4,12,20)( 5,14,22)( 6,13,21)( 7,15,24) ( 8,16,23)$ $6, 6, 6, 3, 3$ $4$ $6$ $( 1, 9,17)( 2,10,18)( 3,23,19,16,11, 8)( 4,24,20,15,12, 7)( 5,13,22, 6,14,21)$ $6, 6, 6, 6$ $1$ $6$ $( 1,10,17, 2, 9,18)( 3,12,19, 4,11,20)( 5,13,22, 6,14,21)( 7,16,24, 8,15,23)$ $12, 12$ $4$ $12$ $( 1,11,10,20,17, 3, 2,12, 9,19,18, 4)( 5,15,13,23,22, 7, 6,16,14,24,21, 8)$ $24$ $2$ $24$ $( 1,11,22, 8,18, 4,13,24, 9,19, 5,16, 2,12,21, 7,17, 3,14,23,10,20, 6,15)$ $24$ $2$ $24$ $( 1,12,22, 7,18, 3,13,23, 9,20, 5,15, 2,11,21, 8,17, 4,14,24,10,19, 6,16)$ $4, 4, 4, 4, 4, 4$ $2$ $4$ $( 1,13, 2,14)( 3,15, 4,16)( 5,17, 6,18)( 7,20, 8,19)( 9,21,10,22)(11,24,12,23)$ $3, 3, 3, 3, 3, 3, 3, 3$ $1$ $3$ $( 1,17, 9)( 2,18,10)( 3,19,11)( 4,20,12)( 5,22,14)( 6,21,13)( 7,24,15) ( 8,23,16)$ $6, 6, 6, 6$ $1$ $6$ $( 1,18, 9, 2,17,10)( 3,20,11, 4,19,12)( 5,21,14, 6,22,13)( 7,23,15, 8,24,16)$ $12, 12$ $2$ $12$ $( 1,21,18,14, 9, 6, 2,22,17,13,10, 5)( 3,24,20,16,11, 7, 4,23,19,15,12, 8)$

## Group invariants

 Order: $48=2^{4} \cdot 3$ Cyclic: no Abelian: no Solvable: yes GAP id: [48, 26]
 Character table: not available.