Show commands:
Magma
magma: G := TransitiveGroup(20, 799);
Group action invariants
| Degree $n$: | $20$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $799$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{10}.S_5$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $4$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,2)(3,4)(5,16,6,15)(7,14,8,13)(9,18,12,20)(10,17,11,19), (1,3)(2,4)(5,10)(6,9)(7,11)(8,12)(13,17,14,18)(15,19,16,20), (1,12,8,2,11,7)(3,9,6,4,10,5)(13,18,15,20)(14,17,16,19) | 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 $8$: $C_2^3$ $120$: $S_5$ $240$: $S_5\times C_2$ x 3 $480$: 20T117 $1920$: $(C_2^4:A_5) : C_2$ x 3 $3840$: $C_2 \wr S_5$ x 9 $7680$: 20T368 x 3 $30720$: 20T555 $61440$: 20T664 x 3 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $S_5$
Degree 10: $C_2 \wr S_5$ x 3
Low degree siblings
20T799 x 23, 40T45858 x 6, 40T45918 x 36, 40T45949 x 72, 40T46012 x 36, 40T46027 x 24Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 252 conjugacy class representatives for $C_2^{10}.S_5$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $122880=2^{13} \cdot 3 \cdot 5$ | 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: | 122880.i | magma: IdentifyGroup(G);
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| Character table: | 252 x 252 character table |
magma: CharacterTable(G);