Show commands:
Magma
magma: G := TransitiveGroup(20, 53);
Group action invariants
| Degree $n$: | $20$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $53$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{10}\wr C_2$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $10$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,11,9,20,7,17,5,15,4,14,2,12,10,19,8,18,6,16,3,13), (1,12)(2,11)(3,14)(4,13)(5,16)(6,15)(7,18)(8,17)(9,19)(10,20) | 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 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 5: None
Degree 10: $D_5\times C_5$
Low degree siblings
20T53 x 3, 40T152 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 65 conjugacy class representatives for $C_{10}\wr C_2$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $200=2^{3} \cdot 5^{2}$ | 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: | 200.31 | magma: IdentifyGroup(G);
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| Character table: | 65 x 65 character table |
magma: CharacterTable(G);