Show commands:
Magma
magma: G := TransitiveGroup(20, 1110);
Group action invariants
| Degree $n$: | $20$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $1110$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{10}.S_{10}$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $2$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,9,8,16)(2,10,7,15)(3,19,17,14,5)(4,20,18,13,6), (1,17,3,2,18,4)(5,6)(7,12,19,9,13,16,8,11,20,10,14,15) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $3628800$: $S_{10}$ $7257600$: 20T1021 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: None
Degree 10: $S_{10}$
Low degree siblings
20T1110 x 3, 40T268331 x 2, 40T268347 x 2, 40T268348 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 481 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $3715891200=2^{18} \cdot 3^{4} \cdot 5^{2} \cdot 7$ | 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: | 3715891200.a | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);