Show commands:
Magma
magma: G := TransitiveGroup(11, 7);
Group action invariants
| Degree $n$: | $11$ | 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: | $A_{11}$ | ||
| CHM label: | $A11$ | ||
| 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), (3,4,5,6,7,8,9,10,11) | 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
| Cycle Type | Size | Order | Representative |
| $ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $1$ | $1$ | $()$ |
| $ 3, 3, 3, 1, 1 $ | $123200$ | $3$ | $( 2, 9, 3)( 4,10, 7)( 6, 8,11)$ |
| $ 9, 1, 1 $ | $2217600$ | $9$ | $( 2, 4, 6, 9,10, 8, 3, 7,11)$ |
| $ 3, 1, 1, 1, 1, 1, 1, 1, 1 $ | $330$ | $3$ | $(2,3,6)$ |
| $ 7, 1, 1, 1, 1 $ | $237600$ | $7$ | $( 1, 5, 8, 9,11, 4, 7)$ |
| $ 7, 3, 1 $ | $950400$ | $21$ | $( 1, 4, 9, 5, 7,11, 8)( 2, 3, 6)$ |
| $ 7, 3, 1 $ | $950400$ | $21$ | $( 1, 4, 9, 5, 7,11, 8)( 2, 6, 3)$ |
| $ 2, 2, 1, 1, 1, 1, 1, 1, 1 $ | $990$ | $2$ | $( 2,10)( 3, 6)$ |
| $ 7, 2, 2 $ | $712800$ | $14$ | $( 1, 9, 7, 8, 4, 5,11)( 2,10)( 3, 6)$ |
| $ 5, 1, 1, 1, 1, 1, 1 $ | $11088$ | $5$ | $( 1, 9, 4,11, 5)$ |
| $ 4, 2, 1, 1, 1, 1, 1 $ | $41580$ | $4$ | $( 2, 3)( 6, 8, 7,10)$ |
| $ 5, 2, 2, 1, 1 $ | $498960$ | $10$ | $( 1, 5,11, 4, 9)( 6, 7)( 8,10)$ |
| $ 5, 4, 2 $ | $997920$ | $20$ | $( 1, 4, 5, 9,11)( 2, 3)( 6, 8, 7,10)$ |
| $ 3, 3, 1, 1, 1, 1, 1 $ | $18480$ | $3$ | $( 1, 9,11)( 4, 5, 8)$ |
| $ 4, 2, 2, 2, 1 $ | $207900$ | $4$ | $( 1, 4)( 2, 6,10, 3)( 5, 9)( 8,11)$ |
| $ 3, 3, 2, 2, 1 $ | $277200$ | $6$ | $( 1,11, 9)( 2,10)( 3, 6)( 4, 8, 5)$ |
| $ 6, 4, 1 $ | $1663200$ | $12$ | $( 1, 5,11, 4, 9, 8)( 2, 3,10, 6)$ |
| $ 5, 3, 3 $ | $443520$ | $15$ | $( 1, 7, 3)( 2, 5, 8, 9,10)( 4,11, 6)$ |
| $ 5, 3, 1, 1, 1 $ | $443520$ | $15$ | $( 1, 3, 7)( 2, 9, 5,10, 8)$ |
| $ 3, 2, 2, 1, 1, 1, 1 $ | $69300$ | $6$ | $( 1, 9,11)( 2, 3)( 6,10)$ |
| $ 2, 2, 2, 2, 1, 1, 1 $ | $17325$ | $2$ | $( 1, 5)( 3, 6)( 4,11)( 8, 9)$ |
| $ 4, 4, 1, 1, 1 $ | $207900$ | $4$ | $( 1, 6,11, 8)( 3, 4, 9, 5)$ |
| $ 3, 2, 2, 2, 2 $ | $34650$ | $6$ | $( 1,11)( 2,10, 7)( 3, 9)( 4, 5)( 6, 8)$ |
| $ 4, 4, 3 $ | $415800$ | $12$ | $( 1, 8,11, 6)( 2, 7,10)( 3, 5, 9, 4)$ |
| $ 11 $ | $1814400$ | $11$ | $( 1, 3, 7, 4,11, 5,10, 9, 6, 8, 2)$ |
| $ 11 $ | $1814400$ | $11$ | $( 1, 2, 8, 6, 9,10, 5,11, 4, 7, 3)$ |
| $ 5, 5, 1 $ | $798336$ | $5$ | $( 1, 3, 8, 9, 4)( 5,10, 6,11, 7)$ |
| $ 8, 2, 1 $ | $2494800$ | $8$ | $( 1, 3, 2, 8, 6,11, 5, 4)( 7,10)$ |
| $ 4, 3, 2, 1, 1 $ | $831600$ | $12$ | $( 2,10, 3,11)( 4, 9, 6)( 7, 8)$ |
| $ 6, 3, 2 $ | $1108800$ | $6$ | $( 1, 6,11, 5, 3, 4)( 2, 7,10)( 8, 9)$ |
| $ 6, 2, 1, 1, 1 $ | $554400$ | $6$ | $( 1, 4, 3, 5,11, 6)( 8, 9)$ |
magma: ConjugacyClasses(G);
Group invariants
| Order: | $19958400=2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$ | 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: | 19958400.a | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);