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Magma
magma: G := TransitiveGroup(22, 40);
Group action invariants
Degree $n$: | $22$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $40$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $\PSL(2,11)\wr C_2$ | ||
Parity: | $-1$ | magma: IsEven(G);
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Primitive: | no | 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: | (2,4,9,6,3)(5,11,8,7,10)(12,13,20)(14,17,18,22,21,19)(15,16), (1,13,3,12,6,18,9,17,7,21,8,14,10,15,4,20,5,19,11,22,2,16) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 11: None
Low degree siblings
22T40, 24T21362Siblings are shown with degree $\leq 47$
A number field with this Galois group has exactly one arithmetically equivalent field.
Conjugacy classes
Cycle Type | Size | Order | Representative |
$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $1$ | $1$ | $()$ |
$ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ | $3025$ | $2$ | $( 3, 4)( 5, 7)( 6, 9)( 8,11)(12,18)(13,15)(17,20)(19,21)$ |
$ 3, 3, 3, 3, 3, 3, 1, 1, 1, 1 $ | $12100$ | $3$ | $( 3, 5, 8)( 4,11, 7)( 6, 9,10)(12,18,14)(13,20,21)(15,19,17)$ |
$ 5, 5, 5, 5, 1, 1 $ | $17424$ | $5$ | $( 2, 3, 6, 9, 4)( 5,10, 7, 8,11)(12,18,15,22,13)(14,17,21,19,20)$ |
$ 5, 5, 5, 5, 1, 1 $ | $17424$ | $5$ | $( 2, 3,10, 9, 7)( 4, 5,11, 8, 6)(12,15,20,19,21)(13,14,18,17,22)$ |
$ 6, 6, 3, 3, 2, 2 $ | $12100$ | $6$ | $( 1, 2)( 3, 4, 8, 7, 5,11)( 6, 9,10)(12,18,14)(13,15,21,17,20,19)(16,22)$ |
$ 11, 11 $ | $3600$ | $11$ | $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,17,21,18,14,19,16,22,13,15,20)$ |
$ 11, 11 $ | $3600$ | $11$ | $( 1, 2, 3, 6,10, 7, 5, 9,11, 8, 4)(12,14,17,20,18,19,21,15,16,22,13)$ |
$ 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $110$ | $2$ | $(12,18)(13,15)(17,20)(19,21)$ |
$ 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $220$ | $3$ | $(12,18,14)(13,20,21)(15,19,17)$ |
$ 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $264$ | $5$ | $(12,18,15,22,13)(14,17,21,19,20)$ |
$ 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $264$ | $5$ | $(12,15,20,19,21)(13,14,18,17,22)$ |
$ 6, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $220$ | $6$ | $(12,18,14)(13,15,21,17,20,19)(16,22)$ |
$ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $120$ | $11$ | $(12,17,21,18,14,19,16,22,13,15,20)$ |
$ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $120$ | $11$ | $(12,14,17,20,18,19,21,15,16,22,13)$ |
$ 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1 $ | $12100$ | $6$ | $( 3, 4)( 5, 7)( 6, 9)( 8,11)(12,18,14)(13,20,21)(15,19,17)$ |
$ 5, 5, 2, 2, 2, 2, 1, 1, 1, 1 $ | $14520$ | $10$ | $( 3, 4)( 5, 7)( 6, 9)( 8,11)(12,18,15,22,13)(14,17,21,19,20)$ |
$ 5, 5, 2, 2, 2, 2, 1, 1, 1, 1 $ | $14520$ | $10$ | $( 3, 4)( 5, 7)( 6, 9)( 8,11)(12,15,20,19,21)(13,14,18,17,22)$ |
$ 6, 3, 2, 2, 2, 2, 2, 1, 1, 1 $ | $12100$ | $6$ | $( 3, 4)( 5, 7)( 6, 9)( 8,11)(12,18,14)(13,15,21,17,20,19)(16,22)$ |
$ 11, 2, 2, 2, 2, 1, 1, 1 $ | $6600$ | $22$ | $( 3, 4)( 5, 7)( 6, 9)( 8,11)(12,17,21,18,14,19,16,22,13,15,20)$ |
$ 11, 2, 2, 2, 2, 1, 1, 1 $ | $6600$ | $22$ | $( 3, 4)( 5, 7)( 6, 9)( 8,11)(12,14,17,20,18,19,21,15,16,22,13)$ |
$ 5, 5, 3, 3, 3, 1, 1, 1 $ | $29040$ | $15$ | $( 3, 5, 8)( 4,11, 7)( 6, 9,10)(12,18,15,22,13)(14,17,21,19,20)$ |
$ 5, 5, 3, 3, 3, 1, 1, 1 $ | $29040$ | $15$ | $( 3, 5, 8)( 4,11, 7)( 6, 9,10)(12,15,20,19,21)(13,14,18,17,22)$ |
$ 6, 3, 3, 3, 3, 2, 1, 1 $ | $24200$ | $6$ | $( 3, 5, 8)( 4,11, 7)( 6, 9,10)(12,18,14)(13,15,21,17,20,19)(16,22)$ |
$ 11, 3, 3, 3, 1, 1 $ | $13200$ | $33$ | $( 3, 5, 8)( 4,11, 7)( 6, 9,10)(12,17,21,18,14,19,16,22,13,15,20)$ |
$ 11, 3, 3, 3, 1, 1 $ | $13200$ | $33$ | $( 3, 5, 8)( 4,11, 7)( 6, 9,10)(12,14,17,20,18,19,21,15,16,22,13)$ |
$ 5, 5, 5, 5, 1, 1 $ | $34848$ | $5$ | $( 2, 3, 6, 9, 4)( 5,10, 7, 8,11)(12,15,20,19,21)(13,14,18,17,22)$ |
$ 6, 5, 5, 3, 2, 1 $ | $29040$ | $30$ | $( 2, 3, 6, 9, 4)( 5,10, 7, 8,11)(12,18,14)(13,15,21,17,20,19)(16,22)$ |
$ 11, 5, 5, 1 $ | $15840$ | $55$ | $( 2, 3, 6, 9, 4)( 5,10, 7, 8,11)(12,17,21,18,14,19,16,22,13,15,20)$ |
$ 11, 5, 5, 1 $ | $15840$ | $55$ | $( 2, 3, 6, 9, 4)( 5,10, 7, 8,11)(12,14,17,20,18,19,21,15,16,22,13)$ |
$ 6, 5, 5, 3, 2, 1 $ | $29040$ | $30$ | $( 2, 3,10, 9, 7)( 4, 5,11, 8, 6)(12,18,14)(13,15,21,17,20,19)(16,22)$ |
$ 11, 5, 5, 1 $ | $15840$ | $55$ | $( 2, 3,10, 9, 7)( 4, 5,11, 8, 6)(12,17,21,18,14,19,16,22,13,15,20)$ |
$ 11, 5, 5, 1 $ | $15840$ | $55$ | $( 2, 3,10, 9, 7)( 4, 5,11, 8, 6)(12,14,17,20,18,19,21,15,16,22,13)$ |
$ 11, 6, 3, 2 $ | $13200$ | $66$ | $( 1, 2)( 3, 4, 8, 7, 5,11)( 6, 9,10)(12,17,21,18,14,19,16,22,13,15,20)$ |
$ 11, 6, 3, 2 $ | $13200$ | $66$ | $( 1, 2)( 3, 4, 8, 7, 5,11)( 6, 9,10)(12,14,17,20,18,19,21,15,16,22,13)$ |
$ 11, 11 $ | $7200$ | $11$ | $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,14,17,20,18,19,21,15,16,22,13)$ |
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ | $660$ | $2$ | $( 1,16)( 2,22)( 3,13)( 4,15)( 5,20)( 6,12)( 7,17)( 8,21)( 9,18)(10,14)(11,19)$ |
$ 4, 4, 4, 4, 2, 2, 2 $ | $36300$ | $4$ | $( 1,16)( 2,22)( 3,15, 4,13)( 5,17, 7,20)( 6,18, 9,12)( 8,19,11,21)(10,14)$ |
$ 22 $ | $39600$ | $22$ | $( 1,22, 2,13, 3,15, 4,20, 5,12, 6,17, 7,21, 8,18, 9,14,10,19,11,16)$ |
$ 22 $ | $39600$ | $22$ | $( 1,22, 2,13, 3,12, 6,14,10,17, 7,20, 5,18, 9,19,11,21, 8,15, 4,16)$ |
$ 6, 6, 6, 2, 2 $ | $72600$ | $6$ | $( 1,16)( 2,22)( 3,20, 5,21, 8,13)( 4,19,11,17, 7,15)( 6,18, 9,14,10,12)$ |
$ 12, 6, 4 $ | $72600$ | $12$ | $( 1,22, 2,16)( 3,15, 4,21, 8,17, 7,20, 5,19,11,13)( 6,18, 9,14,10,12)$ |
$ 10, 10, 2 $ | $87120$ | $10$ | $( 1,16)( 2,13, 3,12, 6,18, 9,15, 4,22)( 5,14,10,17, 7,21, 8,19,11,20)$ |
$ 10, 10, 2 $ | $87120$ | $10$ | $( 1,16)( 2,13, 3,14,10,18, 9,17, 7,22)( 4,20, 5,19,11,21, 8,12, 6,15)$ |
magma: ConjugacyClasses(G);
Group invariants
Order: | $871200=2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2}$ | 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: | 871200.e | magma: IdentifyGroup(G);
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Character table: not available. |
magma: CharacterTable(G);