Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1123$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $4$ | |
| Generators: | (1,2)(3,4), (1,9,5,13,2,10,6,14)(3,12,7,15,4,11,8,16), (1,5,2,6)(3,4)(9,13)(10,14), (1,7,2,8)(3,5,4,6)(9,15,10,16)(11,14,12,13), (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 12, $C_2^3$ x 15 16: $D_4\times C_2$ x 18, $Q_8:C_2$ x 4, $C_2^4$ 32: $C_2^2 \wr C_2$ x 4, $C_2^3 : D_4 $ x 2, $C_2 \times (C_4\times C_2):C_2$ x 2, $C_2^2 \times D_4$ x 3 64: $(((C_4 \times C_2): C_2):C_2):C_2$ x 4, 16T73, 16T105, 16T115 x 4, 16T117 128: 16T245 x 2, 32T1074 256: 16T473, 16T494 x 2 512: 32T15122 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 8: $Q_8:C_2$
Low degree siblings
16T1123 x 3, 16T1169 x 8, 16T1241 x 4, 32T35594 x 2, 32T35595 x 4, 32T35596 x 4, 32T35597 x 4, 32T35598 x 4, 32T35599 x 4, 32T35600 x 2, 32T35601 x 2, 32T35602 x 2, 32T35603 x 2, 32T35604 x 2, 32T35955 x 8, 32T35956 x 4, 32T35957 x 4, 32T35958 x 4, 32T35959 x 4, 32T35960 x 4, 32T35961 x 4, 32T36557 x 2, 32T36558 x 2, 32T36559 x 4, 32T36560 x 2, 32T36561 x 4, 32T36562 x 2, 32T36563 x 2, 32T36564 x 4, 32T36565 x 2, 32T52412 x 2, 32T52413 x 2, 32T54837 x 2, 32T54840 x 2, 32T55512 x 2, 32T55517 x 2, 32T55576 x 2, 32T55580 x 2, 32T64496 x 2, 32T64569 x 2, 32T71212, 32T71259, 32T85210 x 2, 32T85228 x 2, 32T86552, 32T87360, 32T96662, 32T96664Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 55 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1024=2^{10}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |