Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1605$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $5$ | |
| Generators: | (1,7,2,8)(3,6,4,5)(9,10)(11,12), (1,2)(3,4), (1,10,3,11,2,9,4,12)(5,13,7,15,6,14,8,16), (1,5)(2,6)(3,4)(9,13,10,14), (9,10)(13,14) | |
| $|\Aut(F/K)|$: | $2$ |
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 36, $C_2^3$ x 15 16: $D_4\times C_2$ x 54, $C_2^4$ 32: $C_2^2 \wr C_2$ x 24, $C_2^3 : D_4 $ x 6, $C_2^2 \times D_4$ x 9 64: $(((C_4 \times C_2): C_2):C_2):C_2$ x 24, 16T87 x 9, 16T98 x 2, 16T105 x 6, 16T109 x 18 128: 16T245 x 12, 32T1237 x 9, 32T1241 x 6 256: 16T531 x 18, 64T? 512: 32T13330 x 3 1024: 16T1152 2048: 32T183808 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
16T1605 x 15, 32T207740 x 8, 32T207741 x 16, 32T207742 x 8, 32T207743 x 8, 32T207744 x 16, 32T207745 x 8, 32T207746 x 8, 32T207747 x 16, 32T207748 x 8, 32T207749 x 8, 32T207750 x 16, 32T212804 x 8, 32T212806 x 8, 32T212812 x 16, 32T245696 x 4, 32T245719 x 8, 32T300179 x 8, 32T327287 x 4, 32T327307 x 4, 32T374964 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 124 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. |