Show commands:
Magma
magma: G := TransitiveGroup(46, 49);
Group action invariants
| Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $49$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{22}.A_{23}.C_2$ | ||
| 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: | (1,37,18)(2,38,17)(3,35,10,8)(4,36,9,7)(5,43,20,30,27,40,25,42,22,23,46,31,15,11,6,44,19,29,28,39,26,41,21,24,45,32,16,12)(13,33,14,34), (1,23,20,46,40,31,10,15,27,22,18,12,25,7,38,2,24,19,45,39,32,9,16,28,21,17,11,26,8,37)(3,44,6,33,30,35,42,13,4,43,5,34,29,36,41,14) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $25852016738884976640000$: $S_{23}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $S_{23}$
Low degree siblings
46T48Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 34,075 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $108431217215972213061058560000=2^{41} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$ | 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: | 108431217215972213061058560000.b | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);