Show commands:
Magma
magma: G := TransitiveGroup(17, 6);
Group action invariants
| Degree $n$: | $17$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $6$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $\PSL(2,16)$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | yes | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| 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);
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Low degree resolvents
noneResolvents 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 |
| $1^{17}$ | $1$ | $1$ | $()$ | |
| $3^{5},1^{2}$ | $272$ | $3$ | $( 2, 7, 6)( 3,12, 4)( 5, 9,17)( 8,16,15)(10,11,14)$ | |
| $5^{3},1^{2}$ | $272$ | $5$ | $( 2,10,16, 9, 4)( 3, 7,11,15,17)( 5,12, 6,14, 8)$ | |
| $5^{3},1^{2}$ | $272$ | $5$ | $( 2, 9,10, 4,16)( 3,15, 7,17,11)( 5,14,12, 8, 6)$ | |
| $15,1^{2}$ | $272$ | $15$ | $( 2, 8, 3,10, 5, 7,16,12,11, 9, 6,15, 4,14,17)$ | |
| $15,1^{2}$ | $272$ | $15$ | $( 2,15,12,10,17, 6,16, 3,14, 9, 7, 8, 4,11, 5)$ | |
| $15,1^{2}$ | $272$ | $15$ | $( 2,12,17,16,14, 7, 4, 5,15,10, 6, 3, 9, 8,11)$ | |
| $15,1^{2}$ | $272$ | $15$ | $( 2, 3, 5,16,11, 6, 4,17, 8,10, 7,12, 9,15,14)$ | |
| $17$ | $240$ | $17$ | $( 1, 6,17, 9,14,13,11,15, 3, 8,10, 5, 7,12,16, 4, 2)$ | |
| $17$ | $240$ | $17$ | $( 1,14, 3, 7, 2, 9,15, 5, 4,17,11,10,16, 6,13, 8,12)$ | |
| $17$ | $240$ | $17$ | $( 1,17,14,11, 3,10, 7,16, 2, 6, 9,13,15, 8, 5,12, 4)$ | |
| $17$ | $240$ | $17$ | $( 1, 3, 2,15, 4,11,16,13,12,14, 7, 9, 5,17,10, 6, 8)$ | |
| $17$ | $240$ | $17$ | $( 1,11, 7, 6,15,12,17, 3,16, 9, 8, 4,14,10, 2,13, 5)$ | |
| $17$ | $240$ | $17$ | $( 1,15,16,14, 5, 6, 3, 4,13, 7,17, 8, 2,11,12, 9,10)$ | |
| $17$ | $240$ | $17$ | $( 1, 7,15,17,16, 8,14, 2, 5,11, 6,12, 3, 9, 4,10,13)$ | |
| $17$ | $240$ | $17$ | $( 1,16, 5, 3,13,17, 2,12,10,15,14, 6, 4, 7, 8,11, 9)$ | |
| $2^{8},1$ | $255$ | $2$ | $( 1, 6)( 2, 5)( 3, 4)( 7,16)( 8,15)( 9,14)(10,13)(11,12)$ |
magma: ConjugacyClasses(G);
Group invariants
| Order: | $4080=2^{4} \cdot 3 \cdot 5 \cdot 17$ | magma: Order(G);
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| Cyclic: | no | magma: IsCyclic(G);
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| Abelian: | no | magma: IsAbelian(G);
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| Solvable: | no | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 4080.a | magma: IdentifyGroup(G);
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| Character table: |
| Size | |
| 2 P | |
| 3 P | |
| 5 P | |
| 17 P | |
| Type |
magma: CharacterTable(G);