Show commands:
Magma
magma: G := TransitiveGroup(20, 887);
Group action invariants
| Degree $n$: | $20$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $887$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^8.(D_4\times S_5)$ | ||
| 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: | (1,18,5,14,10,2,17,6,13,9)(3,19,12,8,16)(4,20,11,7,15), (1,16,13,7,2,15,14,8)(3,18,11,6)(4,17,12,5)(9,20)(10,19), (1,9,17,13,2,10,18,14)(3,12,20,8)(4,11,19,7)(5,6) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 7 $4$: $C_2^2$ x 7 $8$: $D_{4}$ x 2, $C_2^3$ $16$: $D_4\times C_2$ $120$: $S_5$ $240$: $S_5\times C_2$ x 3 $480$: 20T117 $960$: 20T174 $1920$: $(C_2^4:A_5) : C_2$ $3840$: $C_2 \wr S_5$ x 3 $7680$: 20T368 $15360$: 20T466 $61440$: 20T667 $122880$: 20T794 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: $S_5$
Degree 10: $S_5\times C_2$
Low degree siblings
20T886 x 4, 20T887 x 3, 40T106464 x 4, 40T106465 x 4, 40T106491 x 2, 40T106516 x 2, 40T106517 x 2, 40T106549 x 4, 40T106550 x 4, 40T106551 x 4, 40T106552 x 4, 40T106571 x 2, 40T106600 x 2, 40T106608 x 2, 40T106662 x 2, 40T106669 x 2, 40T106672 x 4, 40T106674 x 4, 40T106757 x 2, 40T106759 x 2, 40T106762 x 2, 40T106766 x 2, 40T106771 x 4, 40T106826 x 4, 40T106827 x 4, 40T106828 x 4, 40T106829 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 201 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $245760=2^{14} \cdot 3 \cdot 5$ | 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: | 245760.b | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);