Show commands:
Magma
magma: G := TransitiveGroup(10, 44);
Group action invariants
| Degree $n$: | $10$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $44$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $A_{10}$ | ||
| CHM label: | $A10$ | ||
| 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: | (1,2)(3,4,5,6,7,8,9,10), (1,2,3) | 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
45T1982Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
| Cycle Type | Size | Order | Representative |
| $ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $1$ | $1$ | $()$ |
| $ 2, 2, 1, 1, 1, 1, 1, 1 $ | $630$ | $2$ | $(2,3)(4,7)$ |
| $ 3, 3, 1, 1, 1, 1 $ | $8400$ | $3$ | $( 1,10, 5)( 6, 9, 8)$ |
| $ 4, 2, 2, 2 $ | $18900$ | $4$ | $( 1, 6)( 2, 7, 3, 4)( 5, 8)( 9,10)$ |
| $ 3, 3, 2, 2 $ | $25200$ | $6$ | $( 1, 5,10)( 2, 3)( 4, 7)( 6, 8, 9)$ |
| $ 6, 4 $ | $151200$ | $12$ | $( 1, 9, 5, 6,10, 8)( 2, 4, 3, 7)$ |
| $ 2, 2, 2, 2, 1, 1 $ | $4725$ | $2$ | $( 2, 8)( 3, 6)( 5, 9)( 7,10)$ |
| $ 4, 4, 1, 1 $ | $56700$ | $4$ | $( 2,10, 8, 7)( 3, 9, 6, 5)$ |
| $ 6, 2, 1, 1 $ | $151200$ | $6$ | $( 1, 9, 8, 5, 6,10)( 2, 3)$ |
| $ 3, 3, 3, 1 $ | $22400$ | $3$ | $( 1, 8, 7)( 2, 3, 9)( 4,10, 6)$ |
| $ 9, 1 $ | $201600$ | $9$ | $( 1, 4, 9, 8,10, 2, 7, 6, 3)$ |
| $ 9, 1 $ | $201600$ | $9$ | $( 1,10, 5, 8, 9, 4, 2, 3, 7)$ |
| $ 3, 1, 1, 1, 1, 1, 1, 1 $ | $240$ | $3$ | $(1,7,5)$ |
| $ 5, 1, 1, 1, 1, 1 $ | $6048$ | $5$ | $( 2, 9,10, 8, 4)$ |
| $ 5, 3, 1, 1 $ | $120960$ | $15$ | $( 1, 5, 7)( 2,10, 4, 9, 8)$ |
| $ 7, 1, 1, 1 $ | $86400$ | $7$ | $(2,9,4,3,6,7,5)$ |
| $ 7, 3 $ | $86400$ | $21$ | $( 1, 8,10)( 2, 7, 3, 9, 5, 6, 4)$ |
| $ 7, 3 $ | $86400$ | $21$ | $( 1,10, 8)( 2, 7, 3, 9, 5, 6, 4)$ |
| $ 4, 2, 1, 1, 1, 1 $ | $18900$ | $4$ | $( 3, 6, 4, 9)( 5,10)$ |
| $ 3, 2, 2, 1, 1, 1 $ | $25200$ | $6$ | $( 1, 8, 4)( 2, 3)( 7,10)$ |
| $ 8, 2 $ | $226800$ | $8$ | $( 1, 4)( 2,10, 9, 3, 8, 7, 5, 6)$ |
| $ 4, 3, 2, 1 $ | $151200$ | $12$ | $( 1, 2, 8)( 3, 9, 4, 6)( 5,10)$ |
| $ 5, 5 $ | $72576$ | $5$ | $( 1, 2, 7, 5, 4)( 3, 9, 6,10, 8)$ |
| $ 5, 2, 2, 1 $ | $90720$ | $10$ | $( 1, 2)( 3, 5)( 4, 8, 9,10, 6)$ |
magma: ConjugacyClasses(G);
Group invariants
| Order: | $1814400=2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7$ | 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: | 1814400.a | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);