Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1561$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $6$ | |
| Generators: | (1,6,4,8)(2,5,3,7)(9,16,11,13)(10,15,12,14), (1,5,15,9,4,7,14,12,2,6,16,10,3,8,13,11), (1,3)(2,4)(7,8)(9,12)(10,11)(13,15)(14,16) | |
| $|\Aut(F/K)|$: | $2$ |
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 12, $C_4\times C_2$ x 6, $C_2^3$ 16: $D_4\times C_2$ x 6, $C_2^2:C_4$ x 12, $C_4\times C_2^2$ 32: $C_2^2 \wr C_2$ x 4, $C_2^3 : C_4 $ x 4, $C_2 \times (C_2^2:C_4)$ x 3 64: $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, $(((C_4 \times C_2): C_2):C_2):C_2$ x 4, 16T76 x 2, 16T79, 16T146 x 2 128: $C_2 \wr C_2\wr C_2$ x 4, 16T235 x 2, 16T240, 32T1151 x 2 256: 16T478, 16T482 x 2, 16T532, 16T537, 16T542 x 2 512: 32T12279, 32T12349 x 2 1024: 16T1178 2048: 32T159745 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
16T1561 x 31, 32T207072 x 16, 32T207073 x 16, 32T207074 x 16, 32T207075 x 16, 32T207076 x 16, 32T207077 x 16, 32T207078 x 16, 32T207079 x 16, 32T207080 x 16, 32T207081 x 16, 32T207082 x 16, 32T207083 x 16, 32T207084 x 16, 32T207085 x 16, 32T207086 x 16, 32T220866 x 16, 32T250096 x 8, 32T313985 x 8, 32T314046 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 94 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. |