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Properties

Label 16T1385
Order \(2048\)
n \(16\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group Yes

Related objects

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Group action invariants

Degree $n$ :  $16$
Transitive number $t$ :  $1385$
Parity:  $1$
Primitive:  No
Nilpotency class:  $5$
Generators:  (1,9)(2,10)(3,11)(4,12)(5,14,8,15)(6,13,7,16), (1,4,2,3)(5,8,6,7)(9,11,10,12)(13,15,14,16), (1,6,9,13,4,8,11,16)(2,5,10,14,3,7,12,15)
$|\Aut(F/K)|$:  $2$

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 8, $C_4\times C_2$ x 6, $C_2^3$
16:  $D_4\times C_2$ x 4, $C_2^2:C_4$ x 4, $Q_8:C_2$ x 2, $C_4\times C_2^2$
32:  $C_2^2 \wr C_2$, $C_2^3 : C_4 $ x 4, $C_4 \times D_4$ x 2, $C_2 \times (C_2^2:C_4)$, 16T34 x 2, 16T37
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, 32T239
128:  16T208, 16T218, 16T219 x 2, 16T227 x 2, 16T230
256:  32T3729, 32T4019 x 2
512:  16T815 x 2, 16T912
1024:  32T39431

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: $C_4$

Degree 8: $((C_8 : C_2):C_2):C_2$

Low degree siblings

16T1356 x 16, 16T1379 x 16, 16T1385 x 31, 32T98057 x 16, 32T98058 x 16, 32T98059 x 16, 32T98060 x 16, 32T98061 x 8, 32T98062 x 8, 32T98063 x 16, 32T98064 x 8, 32T98065 x 8, 32T98066 x 8, 32T98067 x 8, 32T98317 x 32, 32T98318 x 32, 32T98319 x 32, 32T98320 x 32, 32T98321 x 128, 32T98322 x 32, 32T98323 x 32, 32T98324 x 32, 32T98325 x 32, 32T98326 x 32, 32T98327 x 16, 32T98328 x 16, 32T98329 x 32, 32T98330 x 16, 32T98331 x 16, 32T98332 x 32, 32T98333 x 128, 32T98334 x 32, 32T98335 x 32, 32T98336 x 8, 32T98337 x 8, 32T98338 x 32, 32T98339 x 16, 32T98340 x 16, 32T98341 x 16, 32T98342 x 32, 32T98343 x 32, 32T98344 x 8, 32T98345 x 32, 32T98346 x 32, 32T98347 x 32, 32T98348 x 8, 32T98349 x 8, 32T98350 x 8, 32T98405 x 32, 32T98406 x 32, 32T98407 x 16, 32T98408 x 16, 32T98409 x 32, 32T98410 x 32, 32T98411 x 16, 32T98412 x 16, 32T98413 x 16, 32T98414 x 16, 32T110359 x 8, 32T115681 x 16

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 71 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.