Properties

Label 36T117615
Degree $36$
Order $208971104256$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $36$
Transitive number $t$:  $117615$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$\card{\Aut(F/K)}$:  $1$
Generators:  (2,3)(4,30,9,32)(5,28,8,33)(6,29,7,31)(10,25,12,26)(11,27)(13,23,14,24,15,22)(20,21)(34,35), (1,4,17,22,3,6,18,24)(2,5,16,23)(7,21,27,36,9,20,25,34)(8,19,26,35)(10,33,13,30,11,31,15,29)(12,32,14,28)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$6$:  $S_3$
$12$:  $D_{6}$
$24$:  $S_4$ x 3
$48$:  $S_4\times C_2$ x 3
$96$:  $V_4^2:S_3$
$192$:  $C_2^3:S_4$ x 2, $V_4^2:(S_3\times C_2)$ x 2, 12T100
$384$:  16T747, 16T776
$768$:  12T184 x 2, 16T1063, 16T1068, 24T1724
$1536$:  12T226, 24T3293, 24T4779
$3072$:  16T1521, 32T205611
$6144$:  24T9591
$12288$:  32T720369
$49152$:  24T14783
$393216$:  24T19984

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: $S_3$

Degree 4: None

Degree 6: $S_4$

Degree 9: None

Degree 12: 12T190

Degree 18: None

Low degree siblings

36T117705

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 3,006 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $208971104256=2^{17} \cdot 3^{13}$
Cyclic:  no
Abelian:  no
Solvable:  yes
Label:  not available
Character table: not available.