Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1697$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $5$ | |
| Generators: | (3,11)(4,12)(9,10)(15,16), (1,2)(3,4), (1,15)(2,16)(3,5,4,6)(7,9,8,10)(11,13)(12,14), (1,6)(2,5)(3,16)(4,15)(7,12)(8,11)(9,14)(10,13), (1,2)(3,4)(5,14,6,13)(15,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 31 4: $C_2^2$ x 155 8: $D_{4}$ x 24, $C_2^3$ x 155 16: $D_4\times C_2$ x 84, $C_2^4$ x 31 32: $C_2^2 \wr C_2$ x 16, $C_2^3 : D_4 $ x 8, $C_2^2 \times D_4$ x 42, 32T39 64: $(((C_4 \times C_2): C_2):C_2):C_2$ x 8, 16T69 x 4, 16T105 x 12, 32T273 x 3 128: 16T198 x 6, 16T245 x 12, 32T1369 256: 32T3426, 32T4287 x 2 512: 16T794 x 2, 16T807 1024: 32T39192 2048: 16T1334 x 3 4096: 64T? Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 8: $(((C_4 \times C_2): C_2):C_2):C_2$
Low degree siblings
16T1696 x 32, 16T1697 x 31, 32T399523 x 48, 32T399524 x 96, 32T399525 x 96, 32T399526 x 48, 32T399527 x 48, 32T399528 x 96, 32T399529 x 48, 32T399530 x 96, 32T399531 x 48, 32T399532 x 48, 32T399533 x 48, 32T399534 x 48, 32T399535 x 48, 32T399536 x 48, 32T399537 x 48, 32T399538 x 16, 32T399539 x 48, 32T399540 x 32, 32T399541 x 16, 32T399542 x 48, 32T399543 x 96, 32T399544 x 96, 32T399545 x 48, 32T399546 x 48, 32T399547 x 96, 32T399548 x 96, 32T399549 x 16, 32T399550 x 48, 32T399551 x 48, 32T399552 x 48, 32T399553 x 48, 32T399554 x 48, 32T399555 x 48, 32T399556 x 48, 32T399557 x 48, 32T399558 x 48, 32T399559 x 16, 32T404838 x 48, 32T407549 x 48Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 152 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $8192=2^{13}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |