Show commands:
Magma
magma: G := TransitiveGroup(12, 272);
Group action invariants
| Degree $n$: | $12$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $272$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $M_{11}$ | ||
| CHM label: | $M_{11}(12)$ | ||
| 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: | (1,7,3,10,5,9,6,12)(2,11,8,4), (1,6,3,9)(2,7,12,10,4,5,11,8) | magma: Generators(G);
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Low degree resolvents
noneResolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: None
Degree 4: None
Degree 6: None
Low degree siblings
11T6, 22T22Siblings 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 | Representative |
| $1^{12}$ | $1$ | $1$ | $()$ | |
| $11,1$ | $720$ | $11$ | $( 1, 2, 6, 4, 3,11, 9, 8,10,12, 7)$ | |
| $11,1$ | $720$ | $11$ | $( 1, 7,12,10, 8, 9,11, 3, 4, 6, 2)$ | |
| $2^{4},1^{4}$ | $165$ | $2$ | $( 1,10)( 2, 8)( 4, 6)( 5, 9)$ | |
| $4^{2},2^{2}$ | $990$ | $4$ | $( 1, 8,10, 2)( 3,12)( 4, 9, 6, 5)( 7,11)$ | |
| $8,4$ | $990$ | $8$ | $( 1, 4, 8, 9,10, 6, 2, 5)( 3, 7,12,11)$ | |
| $8,4$ | $990$ | $8$ | $( 1, 5, 2, 6,10, 9, 8, 4)( 3,11,12, 7)$ | |
| $5^{2},1^{2}$ | $1584$ | $5$ | $( 1, 7,11, 8,10)( 3,12, 4, 6, 5)$ | |
| $3^{3},1^{3}$ | $440$ | $3$ | $( 1,10, 9)( 3, 5,11)( 4, 7, 8)$ | |
| $6,3,2,1$ | $1320$ | $6$ | $( 1, 8,10, 4, 9, 7)( 2,12)( 3,11, 5)$ |
magma: ConjugacyClasses(G);
Group invariants
| Order: | $7920=2^{4} \cdot 3^{2} \cdot 5 \cdot 11$ | 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: | 7920.a | magma: IdentifyGroup(G);
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| Character table: |
| Size | |
| 2 P | |
| 3 P | |
| 5 P | |
| 11 P | |
| Type |
magma: CharacterTable(G);