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. |