Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1291$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,12,2,11)(3,9,7,16,5,14,4,10,8,15,6,13), (3,5,8)(4,6,7)(9,15,10,16)(11,13,12,14) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $S_3$, $C_6$ 18: $S_3\times C_3$ 288: $A_4\wr C_2$ 576: 24T1482 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 8: $A_4\wr C_2$
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 $ | $1$ | $1$ | $()$ |
| $ 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ | $2$ | $2$ | $( 9,10)(11,12)(13,14)(15,16)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2 $ | $1$ | $2$ | $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)$ |
| $ 4, 4, 1, 1, 1, 1, 1, 1, 1, 1 $ | $12$ | $4$ | $( 9,14,10,13)(11,15,12,16)$ |
| $ 4, 4, 2, 2, 2, 2 $ | $12$ | $4$ | $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,14,10,13)(11,15,12,16)$ |
| $ 4, 4, 4, 4 $ | $36$ | $4$ | $( 1, 6, 2, 5)( 3, 7, 4, 8)( 9,14,10,13)(11,15,12,16)$ |
| $ 3, 3, 3, 3, 1, 1, 1, 1 $ | $16$ | $3$ | $( 3, 5, 8)( 4, 6, 7)(11,16,14)(12,15,13)$ |
| $ 6, 3, 3, 2, 1, 1 $ | $32$ | $6$ | $( 3, 5, 8)( 4, 6, 7)( 9,10)(11,15,14,12,16,13)$ |
| $ 6, 6, 2, 2 $ | $16$ | $6$ | $( 1, 2)( 3, 6, 8, 4, 5, 7)( 9,10)(11,15,14,12,16,13)$ |
| $ 3, 3, 3, 3, 1, 1, 1, 1 $ | $16$ | $3$ | $( 3, 8, 5)( 4, 7, 6)(11,14,16)(12,13,15)$ |
| $ 6, 3, 3, 2, 1, 1 $ | $32$ | $6$ | $( 3, 8, 5)( 4, 7, 6)( 9,10)(11,13,16,12,14,15)$ |
| $ 6, 6, 2, 2 $ | $16$ | $6$ | $( 1, 2)( 3, 7, 5, 4, 8, 6)( 9,10)(11,13,16,12,14,15)$ |
| $ 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $8$ | $3$ | $(11,14,16)(12,13,15)$ |
| $ 6, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ | $8$ | $6$ | $( 9,10)(11,13,16,12,14,15)$ |
| $ 3, 3, 2, 2, 2, 2, 1, 1 $ | $8$ | $6$ | $( 1, 2)( 3, 4)( 5, 6)( 7, 8)(11,14,16)(12,13,15)$ |
| $ 6, 2, 2, 2, 2, 2 $ | $8$ | $6$ | $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,13,16,12,14,15)$ |
| $ 4, 4, 3, 3, 1, 1 $ | $48$ | $12$ | $( 1, 6, 2, 5)( 3, 7, 4, 8)(11,14,16)(12,13,15)$ |
| $ 6, 4, 4, 2 $ | $48$ | $12$ | $( 1, 6, 2, 5)( 3, 7, 4, 8)( 9,10)(11,13,16,12,14,15)$ |
| $ 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $8$ | $3$ | $( 3, 5, 8)( 4, 6, 7)$ |
| $ 3, 3, 2, 2, 2, 2, 1, 1 $ | $8$ | $6$ | $( 3, 5, 8)( 4, 6, 7)( 9,10)(11,12)(13,14)(15,16)$ |
| $ 6, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ | $8$ | $6$ | $( 1, 2)( 3, 6, 8, 4, 5, 7)$ |
| $ 6, 2, 2, 2, 2, 2 $ | $8$ | $6$ | $( 1, 2)( 3, 6, 8, 4, 5, 7)( 9,10)(11,12)(13,14)(15,16)$ |
| $ 4, 4, 3, 3, 1, 1 $ | $48$ | $12$ | $( 3, 5, 8)( 4, 6, 7)( 9,14,10,13)(11,15,12,16)$ |
| $ 6, 4, 4, 2 $ | $48$ | $12$ | $( 1, 2)( 3, 6, 8, 4, 5, 7)( 9,14,10,13)(11,15,12,16)$ |
| $ 3, 3, 3, 3, 1, 1, 1, 1 $ | $32$ | $3$ | $( 3, 8, 5)( 4, 7, 6)(11,16,14)(12,15,13)$ |
| $ 6, 3, 3, 2, 1, 1 $ | $32$ | $6$ | $( 3, 8, 5)( 4, 7, 6)( 9,10)(11,15,14,12,16,13)$ |
| $ 6, 3, 3, 2, 1, 1 $ | $32$ | $6$ | $( 1, 2)( 3, 7, 5, 4, 8, 6)(11,16,14)(12,15,13)$ |
| $ 6, 6, 2, 2 $ | $32$ | $6$ | $( 1, 2)( 3, 7, 5, 4, 8, 6)( 9,10)(11,15,14,12,16,13)$ |
| $ 12, 4 $ | $96$ | $12$ | $( 1,12, 2,11)( 3, 9, 7,16, 5,14, 4,10, 8,15, 6,13)$ |
| $ 6, 6, 2, 2 $ | $96$ | $6$ | $( 1,11)( 2,12)( 3,10, 8,16, 5,13)( 4, 9, 7,15, 6,14)$ |
| $ 12, 4 $ | $96$ | $12$ | $( 1,15, 7,14, 6,12, 2,16, 8,13, 5,11)( 3, 9, 4,10)$ |
| $ 6, 6, 2, 2 $ | $96$ | $6$ | $( 1,16, 8,14, 6,11)( 2,15, 7,13, 5,12)( 3,10)( 4, 9)$ |
| $ 8, 8 $ | $144$ | $8$ | $( 1,13, 8,12, 2,14, 7,11)( 3, 9, 6,15, 4,10, 5,16)$ |
| $ 4, 4, 4, 4 $ | $24$ | $4$ | $( 1, 9, 2,10)( 3,14, 4,13)( 5,11, 6,12)( 7,15, 8,16)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2 $ | $24$ | $2$ | $( 1,10)( 2, 9)( 3,13)( 4,14)( 5,12)( 6,11)( 7,16)( 8,15)$ |
Group invariants
| Order: | $1152=2^{7} \cdot 3^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |