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Properties

Label 36T91408
Degree $36$
Order $816293376$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_3^6.(C_3^6.C_2^6:S_4)$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(36, 91408);
 

Group invariants

Abstract group:  $C_3^6.(C_3^6.C_2^6:S_4)$
Copy content magma:IdentifyGroup(G);
 
Order:  $816293376=2^{9} \cdot 3^{13}$
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  yes
Copy content magma:IsSolvable(G);
 
Nilpotency class:   not nilpotent
Copy content magma:NilpotencyClass(G);
 

Group action invariants

Degree $n$:  $36$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $91408$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $-1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $1$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,19,36,18,3,21,34,17,2,20,35,16)(4,14,23,29)(5,15,24,30)(6,13,22,28)(7,10,26,33)(8,11,27,32)(9,12,25,31)$, $(1,14,3,15)(2,13)(7,8,9)(10,36)(11,34,12,35)(16,32,18,31)(17,33)(19,30,21,29)(20,28)(22,27)(23,25)(24,26)$, $(1,35,2,34,3,36)(4,14,8,11,6,15,7,12,5,13,9,10)(22,29,27,31,23,28,25,32,24,30,26,33)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 7
$4$:  $C_2^2$ x 7
$6$:  $S_3$
$8$:  $C_2^3$
$12$:  $D_{6}$ x 3
$24$:  $S_4$ x 3, $S_3 \times C_2^2$
$48$:  $S_4\times C_2$ x 9
$96$:  $V_4^2:S_3$, 12T48 x 3
$192$:  $V_4^2:(S_3\times C_2)$ x 2, $C_2^3:S_4$ x 3
$384$:  12T136 x 2, 12T139
$768$:  16T1068
$1536$:  24T3032
$279936$:  18T863 x 2
$1119744$:  36T37258 x 2

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: $C_2^2:S_4$

Degree 18: None

Low degree siblings

36T91902

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

Conjugacy classes not computed

Copy content magma:ConjugacyClasses(G);
 

Character table

Character table not computed

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed