Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1559$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $6$ | |
| Generators: | (1,12,16,7,4,10,14,5)(2,11,15,8,3,9,13,6), (1,7,4,6,2,8,3,5)(9,15,10,16)(11,13)(12,14), (1,13,3,15)(2,14,4,16)(5,8)(6,7)(9,12)(10,11) | |
| $|\Aut(F/K)|$: | $2$ |
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: $((C_8 : C_2):C_2):C_2$ x 4, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, 16T76 x 2, 16T79, 16T146 x 2 128: $C_2 \wr C_2\wr C_2$ x 4, 16T227 x 2, 16T240, 32T1151 x 2 256: 16T482 x 2, 16T502, 16T532, 16T542 x 2, 16T543 512: 32T12349 x 2, 32T13346 1024: 16T1174 2048: 32T126555 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
16T1559 x 31, 16T1609 x 16, 16T1616 x 16, 32T207038 x 32, 32T207039 x 16, 32T207040 x 16, 32T207041 x 16, 32T207042 x 16, 32T207043 x 16, 32T207044 x 16, 32T207045 x 16, 32T207046 x 16, 32T207047 x 16, 32T207048 x 16, 32T207049 x 16, 32T207050 x 16, 32T207051 x 16, 32T207052 x 16, 32T207786 x 8, 32T207787 x 8, 32T207788 x 8, 32T207789 x 16, 32T207790 x 16, 32T207791 x 16, 32T207792 x 8, 32T207793 x 8, 32T207794 x 8, 32T207795 x 16, 32T207796 x 16, 32T207797 x 8, 32T207798 x 8, 32T207799 x 8, 32T207800 x 8, 32T207801 x 16, 32T207802 x 16, 32T207803 x 16, 32T207804 x 8, 32T207805 x 8, 32T207806 x 8, 32T207807 x 16, 32T207808 x 8, 32T207866 x 8, 32T207867 x 8, 32T207868 x 16, 32T207869 x 32, 32T207870 x 16, 32T207871 x 8, 32T207872 x 16, 32T207873 x 16, 32T207874 x 8, 32T207875 x 16, 32T207876 x 32, 32T207877 x 32, 32T207878 x 16, 32T207879 x 8, 32T207880 x 32, 32T207881 x 16, 32T207882 x 8, 32T207883 x 16, 32T207884 x 16, 32T207885 x 16, 32T207886 x 16, 32T207887 x 16, 32T207888 x 8, 32T207889 x 16, 32T207890 x 16, 32T207891 x 16, 32T207892 x 8, 32T207893 x 8, 32T207894 x 8, 32T207895 x 8, 32T207896 x 8, 32T207897 x 8, 32T207898 x 8, 32T220802 x 8, 32T242221 x 4, 32T242309 x 4, 32T249279 x 8, 32T250241 x 8, 32T309813 x 4, 32T313973 x 8, 32T314020 x 8, 32T321217 x 4, 32T365371 x 4, 32T396522 x 4Siblings 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. |