Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1567$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $6$ | |
| Generators: | (1,12)(2,11)(3,10)(4,9)(5,13)(6,14)(7,15)(8,16), (1,4)(2,3)(5,8)(6,7)(9,11)(10,12)(13,15)(14,16), (9,10)(11,12)(13,14)(15,16), (1,3,2,4), (1,4,2,3)(5,12)(6,11)(7,9)(8,10) | |
| $|\Aut(F/K)|$: | $2$ |
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 1024: 16T1177, 16T1226 x 2 2048: 32T103724 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 8: $C_2 \wr C_2\wr C_2$
Low degree siblings
16T1567 x 31, 32T207173 x 16, 32T207174 x 16, 32T207175 x 16, 32T207176 x 16, 32T207177 x 16, 32T207178 x 16, 32T207179 x 16, 32T207180 x 16, 32T207181 x 16, 32T207182 x 16, 32T207183 x 16, 32T207184 x 16, 32T207185 x 16, 32T207186 x 16, 32T207187 x 16, 32T220719 x 16, 32T249529 x 8, 32T313918 x 8, 32T314043 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 106 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $4096=2^{12}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |