Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1392$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $5$ | |
| Generators: | (1,15,13,12)(2,16,14,11)(3,9,7,5)(4,10,8,6), (1,10,2,9)(5,14,6,13)(11,12)(15,16), (1,10,2,9)(3,11)(4,12)(5,13)(6,14)(7,16,8,15) | |
| $|\Aut(F/K)|$: | $2$ |
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 20, $C_4\times C_2$ x 6, $C_2^3$ 16: $D_4\times C_2$ x 10, $C_2^2:C_4$ x 12, $Q_8:C_2$ x 4, $C_4\times C_2^2$ 32: $C_2^2 \wr C_2$ x 8, $C_2^3 : C_4 $ x 8, $C_4 \times D_4$ x 4, $C_2 \times (C_2^2:C_4)$ x 3, 16T30 x 2, 16T34 x 12, 16T37 x 4, $C_4^2:C_2$ x 2 64: $(((C_4 \times C_2): C_2):C_2):C_2$ x 8, 16T76 x 4, 16T79, 32T239 x 4, 32T241 x 2, 32T308 x 4, 32T320 x 4 128: 16T208 x 4, 16T230 x 4, 16T240 x 2, 16T350 x 8, 64T? 256: 32T3707 x 2, 32T4130 512: 16T903 1024: 32T58047 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 8: $C_2^2:C_4$
Low degree siblings
16T1342 x 8, 16T1392 x 7, 16T1421 x 16, 32T97883 x 4, 32T97884 x 8, 32T97885 x 8, 32T97886 x 8, 32T97887 x 8, 32T97888 x 8, 32T97889 x 4, 32T97890 x 4, 32T97891 x 4, 32T97892 x 4, 32T97893 x 4, 32T98484 x 4, 32T98485 x 16, 32T98486 x 16, 32T98487 x 8, 32T98488 x 8, 32T98489 x 16, 32T98490 x 8, 32T98491 x 8, 32T98492 x 8, 32T98493 x 4, 32T98494 x 8, 32T98495 x 8, 32T98496 x 4, 32T98497 x 4, 32T98498 x 4, 32T98499 x 4, 32T98816 x 32, 32T98817 x 8, 32T98818 x 8, 32T98819 x 32, 32T98820 x 8, 32T98821 x 8, 32T98822 x 8, 32T98823 x 8, 32T107460 x 4, 32T107464 x 4, 32T138744 x 2, 32T138782 x 2, 32T142262 x 4, 32T142286 x 4, 32T172906 x 2, 32T181389 x 4, 32T181470 x 4, 32T191320 x 2, 32T201428 x 2, 32T204371 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 80 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $2048=2^{11}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |