Show commands:
Magma
magma: G := TransitiveGroup(10, 7);
Group action invariants
Degree $n$: | $10$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $7$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $A_{5}$ | ||
CHM label: | $A_{5}(10)$ | ||
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: | (1,9)(3,4)(5,10)(6,7), (1,3,5,7,9)(2,4,6,8,10) | magma: Generators(G);
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Low degree resolvents
noneResolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 5: None
Low degree siblings
5T4, 6T12, 12T33, 15T5, 20T15, 30T9Siblings are shown 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 |
1A | $1^{10}$ | $1$ | $1$ | $0$ | $()$ |
2A | $2^{4},1^{2}$ | $15$ | $2$ | $4$ | $( 1, 3)( 4,10)( 5, 9)( 6, 8)$ |
3A | $3^{3},1$ | $20$ | $3$ | $6$ | $( 1,10, 7)( 2, 3, 4)( 5, 9, 6)$ |
5A1 | $5^{2}$ | $12$ | $5$ | $8$ | $( 1, 6,10, 5, 3)( 2, 4, 7, 8, 9)$ |
5A2 | $5^{2}$ | $12$ | $5$ | $8$ | $( 1, 9, 4,10, 6)( 2, 3, 7, 8, 5)$ |
Malle's constant $a(G)$: $1/4$
magma: ConjugacyClasses(G);
Group invariants
Order: | $60=2^{2} \cdot 3 \cdot 5$ | 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: | 60.5 | magma: IdentifyGroup(G);
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Character table: |
1A | 2A | 3A | 5A1 | 5A2 | ||
Size | 1 | 15 | 20 | 12 | 12 | |
2 P | 1A | 1A | 3A | 5A2 | 5A1 | |
3 P | 1A | 2A | 1A | 5A2 | 5A1 | |
5 P | 1A | 2A | 3A | 1A | 1A | |
Type | ||||||
60.5.1a | R | |||||
60.5.3a1 | R | |||||
60.5.3a2 | R | |||||
60.5.4a | R | |||||
60.5.5a | R |
magma: CharacterTable(G);