Show commands:
Magma
magma: G := TransitiveGroup(20, 1015);
Group action invariants
Degree $n$: | $20$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $1015$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $C_2^{10}.C_2\wr S_5$ | ||
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: | (1,4,15)(2,3,16)(5,12,13)(6,11,14)(7,20,17,10)(8,19,18,9), (1,12)(2,11)(3,14)(4,13)(5,16)(6,15)(7,19,8,20)(9,18)(10,17), (1,8,4,12,18,13,2,7,3,11,17,14)(5,15)(6,16)(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 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 $122880$: 20T799 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $S_5$
Degree 10: $C_2 \wr S_5$
Low degree siblings
20T1015 x 15, 40T162300 x 8, 40T162378 x 8, 40T162506 x 8, 40T162681 x 8, 40T162682 x 8, 40T162685 x 8, 40T162686 x 8, 40T162820 x 8, 40T162822 x 8, 40T162888 x 8, 40T162890 x 8, 40T163186 x 8, 40T163188 x 8, 40T163195 x 8, 40T163198 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 506 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
Order: | $3932160=2^{18} \cdot 3 \cdot 5$ | 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: | 3932160.a | magma: IdentifyGroup(G);
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Character table: not available. |
magma: CharacterTable(G);