Properties

Label 24T16
Order \(48\)
n \(24\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_3\times OD_{16}$

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
3:  $C_3$
4:  $C_4$ x 2, $C_2^2$
6:  $C_6$ x 3
8:  $C_4\times C_2$
12:  $C_{12}$ x 2, $C_6\times C_2$
16:  $C_8:C_2$
24:  24T2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 3: $C_3$

Degree 4: $C_4$

Degree 6: $C_6$

Degree 8: $C_8:C_2$

Degree 12: $C_{12}$

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

Group invariants

Order:  $48=2^{4} \cdot 3$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [48, 24]
Character table: Data not available.