# Properties

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

# Related objects

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

 Label Cycle Type Size Order Representative $1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $1$ $1$ $()$ $17$ $240$ $17$ $( 1, 6,17, 9,14,13,11,15, 3, 8,10, 5, 7,12,16, 4, 2)$ $17$ $240$ $17$ $( 1,14, 3, 7, 2, 9,15, 5, 4,17,11,10,16, 6,13, 8,12)$ $17$ $240$ $17$ $( 1,17,14,11, 3,10, 7,16, 2, 6, 9,13,15, 8, 5,12, 4)$ $17$ $240$ $17$ $( 1, 3, 2,15, 4,11,16,13,12,14, 7, 9, 5,17,10, 6, 8)$ $17$ $240$ $17$ $( 1,11, 7, 6,15,12,17, 3,16, 9, 8, 4,14,10, 2,13, 5)$ $17$ $240$ $17$ $( 1,15,16,14, 5, 6, 3, 4,13, 7,17, 8, 2,11,12, 9,10)$ $17$ $240$ $17$ $( 1, 7,15,17,16, 8,14, 2, 5,11, 6,12, 3, 9, 4,10,13)$ $17$ $240$ $17$ $( 1,16, 5, 3,13,17, 2,12,10,15,14, 6, 4, 7, 8,11, 9)$ $3, 3, 3, 3, 3, 1, 1$ $272$ $3$ $( 1,12, 8)( 3,15,13)( 4, 9,16)( 5, 7,11)( 6,14,17)$ $5, 5, 5, 1, 1$ $272$ $5$ $( 1, 5,17,13, 9)( 3,16,12, 7, 6)( 4, 8,11,14,15)$ $5, 5, 5, 1, 1$ $272$ $5$ $( 1,13, 5, 9,17)( 3, 7,16, 6,12)( 4,14, 8,15,11)$ $15, 1, 1$ $272$ $15$ $( 1, 7,14,13,16, 8, 5, 6,15, 9,12,11,17, 3, 4)$ $15, 1, 1$ $272$ $15$ $( 1,11, 6,13, 4,12, 5,14, 3, 9, 8, 7,17,15,16)$ $15, 1, 1$ $272$ $15$ $( 1, 6, 4, 5, 3, 8,17,16,11,13,12,14, 9, 7,15)$ $15, 1, 1$ $272$ $15$ $( 1,14,16, 5,15,12,17, 4, 7,13, 8, 6, 9,11, 3)$ $2, 2, 2, 2, 2, 2, 2, 2, 1$ $255$ $2$ $( 1, 6)( 2, 3)( 4,12)( 5,16)( 7,14)( 8,11)( 9,17)(13,15)$

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);