Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1590$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $5$ | |
| Generators: | (1,10,2,9)(3,11)(4,12)(5,13)(6,14)(7,15,8,16), (1,15,2,16)(3,5,4,6)(7,9)(8,10)(11,13)(12,14), (3,4)(7,9)(8,10)(11,13)(12,14)(15,16), (1,5)(2,6)(3,16,4,15)(7,11)(8,12)(9,13)(10,14), (15,16) | |
| $|\Aut(F/K)|$: | $2$ |
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 8, 16T87, 16T105 x 2, 16T109 x 4 128: $C_2 \wr C_2\wr C_2$ x 4, 16T245 x 4, 32T1237 256: 16T477 x 2, 16T509 x 2, 16T531 x 2, 16T536 512: 32T12264 x 2, 32T13404 1024: 16T1116, 16T1124 x 2 2048: 32T101073 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$, $D_{4}$ x 2
Degree 8: $D_4\times C_2$
Low degree siblings
16T1553 x 32, 16T1555 x 16, 16T1590 x 15, 32T206952 x 32, 32T206953 x 16, 32T206954 x 16, 32T206955 x 16, 32T206956 x 16, 32T206957 x 16, 32T206958 x 16, 32T206959 x 16, 32T206960 x 16, 32T206961 x 16, 32T206962 x 16, 32T206963 x 16, 32T206964 x 16, 32T206965 x 16, 32T206966 x 16, 32T206974 x 8, 32T206975 x 8, 32T206976 x 8, 32T206977 x 16, 32T206978 x 16, 32T206979 x 16, 32T206980 x 8, 32T206981 x 8, 32T206982 x 8, 32T206983 x 16, 32T206984 x 16, 32T206985 x 8, 32T206986 x 8, 32T206987 x 8, 32T206988 x 8, 32T206989 x 16, 32T206990 x 16, 32T206991 x 16, 32T206992 x 8, 32T206993 x 8, 32T206994 x 8, 32T206995 x 16, 32T206996 x 8, 32T207519 x 32, 32T207520 x 8, 32T207521 x 16, 32T207522 x 16, 32T207523 x 16, 32T207524 x 8, 32T207525 x 32, 32T207526 x 8, 32T207527 x 16, 32T207528 x 16, 32T207529 x 8, 32T207530 x 16, 32T207531 x 16, 32T207532 x 8, 32T207533 x 32, 32T207534 x 16, 32T207535 x 16, 32T207536 x 16, 32T207537 x 8, 32T207538 x 32, 32T207539 x 8, 32T207540 x 16, 32T207541 x 8, 32T207542 x 16, 32T207543 x 16, 32T207544 x 8, 32T207545 x 8, 32T207546 x 8, 32T207547 x 8, 32T207548 x 16, 32T207549 x 16, 32T207550 x 8, 32T207551 x 8, 32T220154 x 16, 32T220173 x 16, 32T220752 x 8, 32T224506 x 16, 32T244452 x 4, 32T244584 x 4, 32T248519 x 8, 32T249478 x 8, 32T262070 x 4, 32T313906 x 8, 32T314025 x 8, 32T320275 x 4, 32T375655 x 4, 32T396450 x 4Siblings 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. |