Show commands:
Magma
magma: G := TransitiveGroup(40, 247579);
Group action invariants
| Degree $n$: | $40$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $247579$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_5^8.C_2^3.C_2^6.C_2^3$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,23,40,18,5,24,39,19,4,25,38,20,3,21,37,16,2,22,36,17)(6,26,12,34,10,27,14,31,9,28,11,33,8,29,13,35,7,30,15,32), (1,6,4,10)(2,9,3,7)(5,8)(11,36,13,40)(12,38)(14,37,15,39)(17,20)(18,19)(21,23,24,22)(26,27,30,29)(31,35,34,33,32), (1,26,9,23,5,30,7,22,4,29,10,21,3,28,8,25,2,27,6,24)(11,17,39,31,15,16,40,34,14,20,36,32,13,19,37,35,12,18,38,33) | magma: Generators(G);
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Low degree resolvents
$\card{(G/N)}$ Galois groups for stem field(s) $2$: $C_2$ x 7 $4$: $C_4$ x 4, $C_2^2$ x 7 $8$: $D_{4}$ x 14, $C_4\times C_2$ x 6, $C_2^3$, $Q_8$ x 2 $16$: $D_4\times C_2$ x 7, $C_2^2:C_4$ x 4, $Q_8:C_2$ x 6 $32$: $C_2^2 \wr C_2$ x 3, $C_2^3 : C_4 $ x 4 $64$: $(((C_4 \times C_2): C_2):C_2):C_2$ x 4 Resolvents shown for degrees $\leq 10$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$ x 3
Degree 5: None
Degree 8: $C_2^2 \wr C_2$
Degree 10: None
Degree 20: None
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
Conjugacy classes not computed
magma: ConjugacyClasses(G);
Group invariants
| Order: | $1600000000=2^{12} \cdot 5^{8}$ | 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: | 1600000000.iyu | magma: IdentifyGroup(G);
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| Character table: | not computed |
magma: CharacterTable(G);