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Properties

Label 36T92348
Degree $36$
Order $816293376$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_3^8.(C_6^4.(D_4\times D_6))$

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Copy content magma:G := TransitiveGroup(36, 92348);
 

Group invariants

Abstract group:  $C_3^8.(C_6^4.(D_4\times D_6))$
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 $t$:  $92348$
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:  $(1,17,3,16,2,18)(4,13,8,11)(5,15,7,12)(6,14,9,10)(19,34,20,36,21,35)(22,33,26,29)(23,31,27,30)(24,32,25,28)$, $(1,32,36,30)(2,33,35,29)(3,31,34,28)(4,23,8,25,5,24,9,27,6,22,7,26)(10,21,11,19)(12,20)(13,17)(14,18,15,16)$, $(1,16)(2,18)(3,17)(4,10,6,11,5,12)(7,15,9,13,8,14)(19,36)(20,34)(21,35)(22,30,23,29,24,28)(25,31,27,32,26,33)$, $(1,14,36,10,2,13,34,11,3,15,35,12)(4,7,6,8,5,9)(16,29,20,31)(17,30,19,32)(18,28,21,33)(22,27,24,25,23,26)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 15
$4$:  $C_2^2$ x 35
$6$:  $S_3$
$8$:  $D_{4}$ x 4, $C_2^3$ x 15
$12$:  $D_{6}$ x 7
$16$:  $D_4\times C_2$ x 6, $C_2^4$
$24$:  $S_4$, $S_3 \times C_2^2$ x 7
$32$:  $C_2^2 \times D_4$
$48$:  $S_4\times C_2$ x 7, 12T28 x 2, 24T30
$72$:  $C_3^2:D_4$
$96$:  12T48 x 7, 24T143
$144$:  12T77 x 3
$192$:  $V_4^2:(S_3\times C_2)$, 12T86 x 2, 24T400
$288$:  24T654
$384$:  12T136 x 3, 24T1076
$432$:  12T156
$768$:  12T186 x 2, 24T2481
$864$:  24T2646
$1536$:  24T4787
$1728$:  24T4943
$3456$:  36T4476
$3888$:  18T440
$6912$:  24T9626
$7776$:  36T7260
$13824$:  36T9778
$15552$:  36T10082
$31104$:  36T13539
$34992$:  18T675
$62208$:  36T17293
$69984$:  36T17550
$124416$:  36T20815
$139968$:  36T21098
$279936$:  36T25385
$559872$:  18T901, 36T30523
$1119744$:  36T36567, 36T37470
$10077696$:  36T59853
$90699264$:  36T77769

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 3: $S_3$

Degree 4: None

Degree 6: $D_{6}$

Degree 9: None

Degree 12: 12T136

Degree 18: None

Low degree siblings

36T92348 x 5

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