Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $876$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $4$ | |
| Generators: | (1,8,5,4)(2,7,6,3)(9,13)(10,14), (1,15,4,9,2,16,3,10)(5,12,8,14,6,11,7,13), (1,11,7,13,5,16,3,10)(2,12,8,14,6,15,4,9) | |
| $|\Aut(F/K)|$: | $4$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_4$ x 4, $C_2^2$ x 7 8: $D_{4}$ x 8, $C_4\times C_2$ x 6, $C_2^3$ 16: $D_4\times C_2$ x 4, $C_2^2:C_4$ x 4, $Q_8:C_2$ x 2, $C_4\times C_2^2$ 32: $C_4\wr C_2$ x 4, $C_2^2 \wr C_2$, $C_4 \times D_4$ x 2, $C_2 \times (C_2^2:C_4)$, 16T34 x 2, 16T37 64: $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, 16T111 x 2, 32T239 128: $C_2 \wr C_2\wr C_2$ x 2, 16T208, 16T211, 16T222, 16T345 x 2 256: 32T3766, 32T4357 x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 8: $C_4\wr C_2$, $C_2 \wr C_2\wr C_2$ x 2
Low degree siblings
16T876 x 31, 32T10321 x 16, 32T10322 x 16, 32T10323 x 8, 32T10324 x 16, 32T10325 x 8, 32T18737 x 4, 32T18742 x 4, 32T18745 x 8, 32T21150 x 4, 32T21158 x 8, 32T21160 x 8, 32T21178 x 16, 32T21446 x 8, 32T21448 x 16Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 65 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $512=2^{9}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [512, 46818] |
| Character table: Data not available. |