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Magma
magma: G := TransitiveGroup(17, 6);
Group invariants
| Abstract group: | $\PSL(2,16)$ | magma: IdentifyGroup(G);
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| 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 | magma: NilpotencyClass(G);
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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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| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | yes | magma: IsPrimitive(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 | Index | Representative |
| $1^{17}$ | $1$ | $1$ | $0$ | $()$ | |
| $2^{8},1$ | $255$ | $2$ | $8$ | $( 1, 3)( 2, 6)( 4, 8)( 5,13)( 7, 9)(11,12)(14,17)(15,16)$ | |
| $17$ | $240$ | $17$ | $16$ | $( 1, 6, 2, 5, 8,10,16,11, 7, 9,17,13, 3,15, 4,14,12)$ | |
| $17$ | $240$ | $17$ | $16$ | $( 1, 8, 7, 3,12, 5,11,13,14, 2,16,17, 4, 6,10, 9,15)$ | |
| $17$ | $240$ | $17$ | $16$ | $( 1, 2, 8,16, 7,17, 3, 4,12, 6, 5,10,11, 9,13,15,14)$ | |
| $17$ | $240$ | $17$ | $16$ | $( 1, 7,12,11,14,16, 4,10,15, 8, 3, 5,13, 2,17, 6, 9)$ | |
| $17$ | $240$ | $17$ | $16$ | $( 1,16, 3, 6,11,15, 2, 7, 4, 5, 9,14, 8,17,12,10,13)$ | |
| $17$ | $240$ | $17$ | $16$ | $( 1,11, 4, 8,13, 6, 7,14,10, 3, 2, 9,12,16,15, 5,17)$ | |
| $17$ | $240$ | $17$ | $16$ | $( 1, 3,11, 2, 4, 9, 8,12,13,16, 6,15, 7, 5,14,17,10)$ | |
| $17$ | $240$ | $17$ | $16$ | $( 1, 4,13, 7,10, 2,12,15,17,11, 8, 6,14, 3, 9,16, 5)$ | |
| $5^{3},1^{2}$ | $272$ | $5$ | $12$ | $( 1,11,12,17, 6)( 2,15,10, 3,13)( 5, 8, 7, 9,16)$ | |
| $5^{3},1^{2}$ | $272$ | $5$ | $12$ | $( 1,17,11, 6,12)( 2, 3,15,13,10)( 5, 9, 8,16, 7)$ | |
| $3^{5},1^{2}$ | $272$ | $3$ | $10$ | $( 1, 2, 5)( 3, 9,17)( 6,13,16)( 7,12,10)( 8,11,15)$ | |
| $15,1^{2}$ | $272$ | $15$ | $14$ | $( 1, 9,15, 6, 7, 2,17, 8,13,12, 5, 3,11,16,10)$ | |
| $15,1^{2}$ | $272$ | $15$ | $14$ | $( 1, 3, 8, 6,10, 5,17,15,16,12, 2, 9,11,13, 7)$ | |
| $15,1^{2}$ | $272$ | $15$ | $14$ | $( 1, 8,10,17,16, 2,11, 7, 3, 6, 5,15,12, 9,13)$ | |
| $15,1^{2}$ | $272$ | $15$ | $14$ | $( 1,15, 7,17,13, 5,11,10, 9, 6, 2, 8,12, 3,16)$ |
Malle's constant $a(G)$: $1/8$
magma: ConjugacyClasses(G);
Character table
| 1A | 2A | 3A | 5A1 | 5A2 | 15A1 | 15A2 | 15A4 | 15A7 | 17A1 | 17A2 | 17A3 | 17A4 | 17A5 | 17A6 | 17A7 | 17A8 | ||
| Size | 1 | 255 | 272 | 272 | 272 | 272 | 272 | 272 | 272 | 240 | 240 | 240 | 240 | 240 | 240 | 240 | 240 | |
| 2 P | 1A | 1A | 3A | 5A2 | 5A1 | 15A7 | 15A1 | 15A2 | 15A4 | 17A4 | 17A8 | 17A5 | 17A1 | 17A3 | 17A7 | 17A6 | 17A2 | |
| 3 P | 1A | 2A | 1A | 5A2 | 5A1 | 5A1 | 5A2 | 5A1 | 5A2 | 17A6 | 17A5 | 17A1 | 17A7 | 17A4 | 17A2 | 17A8 | 17A3 | |
| 5 P | 1A | 2A | 3A | 1A | 1A | 3A | 3A | 3A | 3A | 17A7 | 17A3 | 17A4 | 17A6 | 17A1 | 17A8 | 17A2 | 17A5 | |
| 17 P | 1A | 2A | 3A | 5A2 | 5A1 | 15A7 | 15A1 | 15A2 | 15A4 | 1A | 1A | 1A | 1A | 1A | 1A | 1A | 1A | |
| Type |
magma: CharacterTable(G);
Regular extensions
Data not computed