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Properties

Label 16T794
16T794 1 2 1->2 6 1->6 8 1->8 14 1->14 5 2->5 7 2->7 13 2->13 3 4 3->4 3->6 3->7 12 3->12 4->5 4->8 11 4->11 5->3 9 5->9 6->4 10 6->10 7->1 15 7->15 8->2 16 8->16 9->6 9->10 9->12 9->14 10->5 10->11 10->13 11->3 11->9 11->16 12->4 12->10 12->15 13->14 13->15 14->16 15->14 16->13
Degree $16$
Order $512$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group yes
Group: $C_2^6:C_2^3$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(16, 794);
 

Group invariants

Abstract group:  $C_2^6:C_2^3$
Copy content magma:IdentifyGroup(G);
 
Order:  $512=2^{9}$
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:  $3$
Copy content magma:NilpotencyClass(G);
 

Group action invariants

Degree $n$:  $16$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $794$
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:  $(1,6)(2,5)(3,7)(4,8)(9,14)(10,13)(11,16)(12,15)$, $(1,2)(3,4)$, $(1,8,2,7)(3,6,4,5)(9,12,10,11)(13,15,14,16)$, $(9,10)(13,14)$, $(1,14)(2,13)(3,12,4,11)(5,9,6,10)(7,15)(8,16)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 31
$4$:  $C_2^2$ x 155
$8$:  $D_{4}$ x 24, $C_2^3$ x 155
$16$:  $D_4\times C_2$ x 84, $C_2^4$ x 31
$32$:  $C_2^2 \wr C_2$ x 16, $Q_8:C_2^2$ x 8, $C_2^2 \times D_4$ x 42, 32T39
$64$:  16T69 x 4, 16T105 x 12, 32T273 x 3
$128$:  16T198 x 6, 32T1369
$256$:  32T3426

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$ x 7

Degree 4: $C_2^2$ x 7

Degree 8: $C_2^3$

Low degree siblings

16T794 x 3, 16T804 x 12, 16T808 x 8, 16T809 x 16, 32T9708 x 6, 32T9709 x 12, 32T9710 x 24, 32T9711 x 6, 32T9712 x 16, 32T9713 x 12, 32T9786 x 24, 32T9787 x 24, 32T9788 x 6, 32T9789 x 12, 32T9790 x 12, 32T9791 x 6, 32T9792 x 12, 32T9811 x 12, 32T9812 x 24, 32T9813 x 12, 32T9814 x 24, 32T9815 x 24, 32T20119 x 12

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

68 x 68 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed