Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1189$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $5$ | |
| Generators: | (1,2)(3,4)(5,6)(7,8)(9,13,10,14)(11,16,12,15), (1,5)(2,6)(3,8)(4,7)(9,10)(15,16), (1,9)(2,10)(3,12)(4,11)(5,14)(6,13)(7,16)(8,15), (9,10)(11,12)(13,14)(15,16), (1,4)(2,3)(5,6)(11,12)(13,15)(14,16) | |
| $|\Aut(F/K)|$: | $2$ |
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: $(((C_4 \times C_2): C_2):C_2):C_2$ x 4, 16T87, 16T105 x 2, 16T109 x 4 128: $C_2 \wr C_2\wr C_2$ x 2, 16T245 x 2, 32T1237 256: 16T477, 16T509, 16T531 512: 32T12264 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 8: $(((C_4 \times C_2): C_2):C_2):C_2$
Low degree siblings
16T1189 x 7, 32T36138 x 4, 32T36139 x 4, 32T36140 x 4, 32T36141 x 4, 32T36142 x 4, 32T36143 x 4, 32T36144 x 4, 32T52448 x 4, 32T52450 x 4, 32T64551 x 2, 32T85213 x 2, 32T85222 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 61 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. |