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Properties

Label 36T42303
Degree $36$
Order $1769472$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2\times C_2^{10}.C_6^2:D_{12}$

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Copy content magma:G := TransitiveGroup(36, 42303);
 

Group invariants

Abstract group:  $C_2\times C_2^{10}.C_6^2:D_{12}$
Copy content magma:IdentifyGroup(G);
 
Order:  $1769472=2^{16} \cdot 3^{3}$
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 $t$:  $42303$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $-1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $2$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,34,17,10,4,35,14,12,5,31,15,8)(2,33,18,9,3,36,13,11,6,32,16,7)(19,26,23,30,22,28,20,25,24,29,21,27)$, $(1,7)(2,8)(3,11,4,12)(5,9,6,10)(13,35)(14,36)(15,34)(16,33)(17,32)(18,31)(19,29)(20,30)(21,28,22,27)(23,26,24,25)$, $(1,4,6,2,3,5)(7,23,34)(8,24,33)(9,19,36)(10,20,35)(11,21,32,12,22,31)(13,15,18,14,16,17)(25,27,29,26,28,30)$
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
$6$:  $S_3$
$8$:  $D_{4}$ x 2, $C_2^3$
$12$:  $D_{6}$ x 3
$16$:  $D_4\times C_2$
$24$:  $S_4$, $S_3 \times C_2^2$, $D_{12}$ x 2
$48$:  $S_4\times C_2$ x 3, 24T29
$72$:  $C_3^2:D_4$
$96$:  12T48, 12T54 x 2
$144$:  12T77
$192$:  $V_4^2:(S_3\times C_2)$, 24T394
$216$:  12T118
$384$:  12T136, 12T152 x 2
$432$:  24T1304
$768$:  24T2479
$864$:  24T2660
$1728$:  36T2513
$3456$:  24T7225
$6912$:  36T6965
$55296$:  16T1858
$110592$:  24T17883
$221184$:  24T19224
$442368$:  36T29588
$884736$:  24T21392

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 3: $S_3$

Degree 4: None

Degree 6: $D_{6}$, $C_3^2:D_4$

Degree 9: None

Degree 12: None

Degree 18: 18T104

Low degree siblings

36T42302 x 4, 36T42303 x 3

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