↑

Properties

Label 16T808
16T808 1 4 1->4 5 1->5 9 1->9 2 3 2->3 6 2->6 10 2->10 3->1 3->4 8 3->8 12 3->12 4->2 7 4->7 11 4->11 5->6 5->7 14 5->14 6->8 13 6->13 7->6 7->8 7->8 16 7->16 8->5 15 8->15 9->10 9->10 11->12 11->12 11->12 13->14 13->14 13->14 13->14 15->16 15->16 15->16
Degree $16$
Order $512$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group yes
Group: $C_2^6:C_2^3$

Related objects

Downloads

Learn more

Show commands: Magma

Copy content magma:G := TransitiveGroup(16, 808);
 

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 $t$:  $808$
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:  $(1,9)(2,10)(3,12)(4,11)(5,14)(6,13)(7,16)(8,15)$, $(5,6)(7,8)(13,14)(15,16)$, $(9,10)(11,12)(13,14)(15,16)$, $(3,4)(7,8)(11,12)(15,16)$, $(1,5)(2,6)(3,8)(4,7)(9,10)(13,14)$, $(1,4,2,3)(5,7,6,8)(11,12)(13,14)$
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: $C_2$

Degree 4: $D_{4}$ x 3

Degree 8: $C_2^2 \wr C_2$

Low degree siblings

16T794 x 4, 16T804 x 12, 16T808 x 7, 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