Properties

Label 17T6
Degree $17$
Order $4080$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $\PSL(2,16)$

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Show commands: Magma

magma: G := TransitiveGroup(17, 6);
 

Group action invariants

Degree $n$:  $17$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $6$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $\PSL(2,16)$
Parity:  $1$
magma: IsEven(G);
 
Primitive:  yes
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $1$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (2,3)(4,9)(5,7)(6,8)(10,14)(11,13)(12,15)(16,17), (1,16)(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15), (1,6,13,5,4,2,15,10,14,12,3,9,7,11,8)
magma: Generators(G);
 

Low degree resolvents

none

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - none

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

LabelCycle TypeSizeOrderRepresentative
$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1$ $1$ $()$
$ 17 $ $240$ $17$ $( 1, 6,17, 9,14,13,11,15, 3, 8,10, 5, 7,12,16, 4, 2)$
$ 17 $ $240$ $17$ $( 1,14, 3, 7, 2, 9,15, 5, 4,17,11,10,16, 6,13, 8,12)$
$ 17 $ $240$ $17$ $( 1,17,14,11, 3,10, 7,16, 2, 6, 9,13,15, 8, 5,12, 4)$
$ 17 $ $240$ $17$ $( 1, 3, 2,15, 4,11,16,13,12,14, 7, 9, 5,17,10, 6, 8)$
$ 17 $ $240$ $17$ $( 1,11, 7, 6,15,12,17, 3,16, 9, 8, 4,14,10, 2,13, 5)$
$ 17 $ $240$ $17$ $( 1,15,16,14, 5, 6, 3, 4,13, 7,17, 8, 2,11,12, 9,10)$
$ 17 $ $240$ $17$ $( 1, 7,15,17,16, 8,14, 2, 5,11, 6,12, 3, 9, 4,10,13)$
$ 17 $ $240$ $17$ $( 1,16, 5, 3,13,17, 2,12,10,15,14, 6, 4, 7, 8,11, 9)$
$ 3, 3, 3, 3, 3, 1, 1 $ $272$ $3$ $( 1,12, 8)( 3,15,13)( 4, 9,16)( 5, 7,11)( 6,14,17)$
$ 5, 5, 5, 1, 1 $ $272$ $5$ $( 1, 5,17,13, 9)( 3,16,12, 7, 6)( 4, 8,11,14,15)$
$ 5, 5, 5, 1, 1 $ $272$ $5$ $( 1,13, 5, 9,17)( 3, 7,16, 6,12)( 4,14, 8,15,11)$
$ 15, 1, 1 $ $272$ $15$ $( 1, 7,14,13,16, 8, 5, 6,15, 9,12,11,17, 3, 4)$
$ 15, 1, 1 $ $272$ $15$ $( 1,11, 6,13, 4,12, 5,14, 3, 9, 8, 7,17,15,16)$
$ 15, 1, 1 $ $272$ $15$ $( 1, 6, 4, 5, 3, 8,17,16,11,13,12,14, 9, 7,15)$
$ 15, 1, 1 $ $272$ $15$ $( 1,14,16, 5,15,12,17, 4, 7,13, 8, 6, 9,11, 3)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 1 $ $255$ $2$ $( 1, 6)( 2, 3)( 4,12)( 5,16)( 7,14)( 8,11)( 9,17)(13,15)$

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $4080=2^{4} \cdot 3 \cdot 5 \cdot 17$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  no
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  4080.a
magma: IdentifyGroup(G);
 
Character table:

Size
2 P
3 P
5 P
17 P
Type

magma: CharacterTable(G);