Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1445$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $5$ | |
| Generators: | (1,9,4,11)(2,10,3,12)(7,8)(13,15,14,16), (1,16,3,13)(2,15,4,14)(5,10,7,12)(6,9,8,11), (1,2)(3,4)(5,7)(6,8)(9,11)(10,12)(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: $C_2^2$ x 7 8: $D_{4}$ x 12, $C_2^3$ 16: $D_4\times C_2$ x 6, $Q_8:C_2$ 32: $C_2^2 \wr C_2$ x 3, 16T34 x 3, $C_4^2:C_2$ 64: $(((C_4 \times C_2): C_2):C_2):C_2$ x 6, 32T320 128: $C_2 \wr C_2\wr C_2$ x 4, 16T342 x 4, 16T350 x 3 256: 32T5807 x 4, 32T6030 512: 16T956, 16T969 x 2 1024: 32T41928 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
16T1439 x 16, 16T1445 x 63, 16T1461 x 16, 32T99003 x 16, 32T99004 x 16, 32T99005 x 8, 32T99006 x 16, 32T99007 x 8, 32T99008 x 8, 32T99009 x 16, 32T99010 x 8, 32T99011 x 16, 32T99012 x 8, 32T99013 x 8, 32T99053 x 64, 32T99054 x 32, 32T99055 x 128, 32T99056 x 32, 32T99057 x 32, 32T99058 x 128, 32T99059 x 32, 32T99060 x 32, 32T99061 x 32, 32T99197 x 64, 32T99198 x 32, 32T99199 x 128, 32T99200 x 128, 32T99201 x 32, 32T99202 x 16, 32T99203 x 32, 32T99204 x 16, 32T99205 x 128, 32T99206 x 64, 32T99207 x 32, 32T99208 x 32, 32T99209 x 16, 32T99210 x 8, 32T99211 x 16, 32T99212 x 8, 32T99213 x 16, 32T99214 x 8, 32T99215 x 16, 32T99216 x 8, 32T99217 x 32, 32T99218 x 32, 32T99219 x 32, 32T99220 x 8, 32T99221 x 8, 32T99222 x 32, 32T99223 x 16, 32T99224 x 16, 32T110223 x 8, 32T116047 x 16Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 74 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. |