Show commands:
Magma
magma: G := TransitiveGroup(46, 21);
Group invariants
| Abstract group: | $C_{23}^2:(C_{11}\times D_{11})$ | magma: IdentifyGroup(G);
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| Order: | $128018=2 \cdot 11^{2} \cdot 23^{2}$ | 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 | magma: NilpotencyClass(G);
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Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $21$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
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| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | $(1,40,4,24,20,46,21,33,11,25,19,36,8,41,3,37,7,31,13,45,22,43)(2,27,17,39,5,34,10,38,6,44,23,30,14,32,12,35,9,28,16,29,15,42)(18,26)$, $(1,29,19,25,5,46,21,45,6,33,10,27,12,24,13,34,2,39,8,30,11,37)(3,26,20,35,17,28,4,36,9,40,23,42,7,43,22,32,18,38,16,41,15,31)(14,44)$ | magma: Generators(G);
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Low degree resolvents
$\card{(G/N)}$ Galois groups for stem field(s) $2$: $C_2$ $11$: $C_{11}$ $22$: $D_{11}$, 22T1 $242$: 22T7 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 23: None
Low degree siblings
There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
Conjugacy classes not computedmagma: ConjugacyClasses(G);
Character table
104 x 104 character tablemagma: CharacterTable(G);
Regular extensions
Data not computed