Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1177$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $4$ | |
| Generators: | (1,2)(3,4)(5,9)(6,10)(7,12)(8,11), (9,10)(11,12)(13,14)(15,16), (1,11,3,10)(2,12,4,9)(5,13,7,16)(6,14,8,15), (1,3)(2,4) | |
| $|\Aut(F/K)|$: | $4$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 15 4: $C_2^2$ x 35 8: $D_{4}$ x 20, $C_2^3$ x 15 16: $D_4\times C_2$ x 30, $C_2^4$ 32: $C_2^2 \wr C_2$ x 8, $C_2^3 : D_4 $ x 2, $C_2^2 \times D_4$ x 5 64: $(C_4^2 : C_2):C_2$ x 4, $(((C_4 \times C_2): C_2):C_2):C_2$ x 4, 16T87, 16T105 x 2, 16T109 x 4 128: $C_2 \wr C_2\wr C_2$ x 4, 16T245 x 2, 16T265 x 2, 32T1237 256: 16T477 x 2, 16T509 x 2, 16T511, 16T531, 16T538 512: 32T12264 x 2, 32T12969 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 8: $(C_4^2 : C_2):C_2$, $C_2 \wr C_2\wr C_2$ x 2
Low degree siblings
16T1177 x 127, 32T36029 x 32, 32T36030 x 64, 32T36031 x 64, 32T36032 x 64, 32T36033 x 64, 32T36034 x 32, 32T36035 x 64, 32T36036 x 32, 32T36037 x 64, 32T44596 x 16, 32T44616 x 16, 32T44624 x 32, 32T48169 x 16, 32T48264 x 32, 32T48267 x 32, 32T48291 x 16, 32T48303 x 32, 32T48385 x 32, 32T51962 x 32, 32T55736 x 32, 32T55864 x 16, 32T56654 x 16Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 76 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1024=2^{10}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |