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Properties

Label 16T1905
16T1905 1 3 1->3 11 1->11 16 1->16 2 4 2->4 12 2->12 15 2->15 3->1 13 3->13 4->2 14 4->14 5 8 5->8 5->16 6 7 6->7 6->15 7->12 7->12 8->11 8->11 9 9->2 9->8 9->8 10 10->1 10->7 10->7 11->3 11->14 11->14 12->4 12->13 12->13 13->9 13->9 13->16 14->10 14->10 14->15 15->4 15->5 15->10 16->3 16->6 16->9
Degree $16$
Order $294912$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^8.S_4\wr C_2$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(16, 1905);
 

Group invariants

Abstract group:  $C_2^8.S_4\wr C_2$
Copy content magma:IdentifyGroup(G);
 
Order:  $294912=2^{15} \cdot 3^{2}$
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 $n$:  $16$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $1905$
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:  $(1,11,3,13,16,9,2,12,4,14,15,10)(5,8)(6,7)$, $(1,16,3)(2,15,4)(7,12,13,9,8,11,14,10)$, $(1,3)(2,4)(5,16,6,15)(7,12,13,9,8,11,14,10)$
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
$8$:  $D_{4}$ x 6, $C_2^3$
$16$:  $D_4\times C_2$ x 3
$32$:  $C_2^2 \wr C_2$
$72$:  $C_3^2:D_4$
$144$:  12T77
$288$:  12T125
$1152$:  $S_4\wr C_2$
$2304$:  12T235
$4608$:  12T260
$73728$:  16T1864
$147456$:  32T2077237

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: None

Degree 8: $S_4\wr C_2$

Low degree siblings

16T1905 x 15, 32T2265666 x 8, 32T2265667 x 8, 32T2265668 x 8, 32T2265669 x 8, 32T2265670 x 8, 32T2265671 x 8, 32T2265672 x 8, 32T2265673 x 8, 32T2265674 x 8, 32T2265675 x 8, 32T2265676 x 8, 32T2265677 x 8, 32T2265678 x 8, 32T2265679 x 8, 32T2265680 x 8, 32T2265730 x 8

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