Show commands:
Magma
magma: G := TransitiveGroup(40, 89829);
Group action invariants
| Degree $n$: | $40$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $89829$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^6.C_2^8:C_{10}$ | ||
| 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: | (1,33,21,30,11,2,34,22,29,12)(3,35,24,31,10,4,36,23,32,9)(5,39,18,27,16,6,40,17,28,15)(7,38,20,25,13,8,37,19,26,14), (1,30,35,9,22,3,32,33,11,24,2,29,36,10,21,4,31,34,12,23)(5,28,37,13,17,8,26,39,16,19,6,27,38,14,18,7,25,40,15,20), (1,40,24,32,14,7,35,17,27,12)(2,39,23,31,13,8,36,18,28,11)(3,38,21,29,15,6,33,20,26,10)(4,37,22,30,16,5,34,19,25,9) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $5$: $C_5$ $10$: $C_{10}$ x 3 $80$: $C_2^4 : C_5$ x 17 $160$: $C_2 \times (C_2^4 : C_5)$ x 51 Resolvents shown for degrees $\leq 10$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $C_5$
Degree 8: None
Degree 10: $C_2 \times (C_2^4 : C_5)$ x 3
Degree 20: 20T341
Low degree siblings
There are no siblings with degree $\leq 10$
Data on whether or not a number field with this Galois group has arithmetically equivalent fields has not been computed.
Conjugacy classes
There are 313 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $163840=2^{15} \cdot 5$ | 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: | yes | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 163840.klc | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);