Show commands:
Magma
magma: G := TransitiveGroup(22, 31);
Group action invariants
| Degree $n$: | $22$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $31$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $F_{11}\wr C_2$ | ||
| 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: | (1,17,2,16,3,15,4,14,5,13,6,12,7,22,8,21,9,20,10,19,11,18), (1,6,4,7,8)(2,10,9,5,11)(12,21,17,20,15,16,18,22,19,13) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $5$: $C_5$ $8$: $D_{4}$ $10$: $D_{5}$, $C_{10}$ x 3 $20$: $D_{10}$, 20T3 $40$: 20T7, 20T12 $50$: $D_5\times C_5$ $100$: 20T24 $200$: 20T53 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 11: None
Low degree siblings
44T218, 44T219, 44T220Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 77 conjugacy class representatives for $F_{11}\wr C_2$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $24200=2^{3} \cdot 5^{2} \cdot 11^{2}$ | 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: | yes | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 24200.bg | magma: IdentifyGroup(G);
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| Character table: | 77 x 77 character table |
magma: CharacterTable(G);