Show commands:
Magma
magma: G := TransitiveGroup(46, 50);
Group action invariants
Degree $n$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $50$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $C_2^{23}.A_{23}.C_2$ | ||
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: | (1,29,39,14,46,36,7,11)(2,30,40,13,45,35,8,12)(3,32,16,18,27,44,21,25,5,37,24,20,41,4,31,15,17,28,43,22,26,6,38,23,19,42)(9,34)(10,33), (3,35,22,30,45,8,44,27,17,40,19,14,42,23,5,33,10,25,15,11,37,32)(4,36,21,29,46,7,43,28,18,39,20,13,41,24,6,34,9,26,16,12,38,31) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $25852016738884976640000$: $S_{23}$ $51704033477769953280000$: 46T45 $108431217215972213061058560000$: 46T48 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $S_{23}$
Low degree siblings
46T50Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 68,150 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
Order: | $216862434431944426122117120000=2^{42} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$ | 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: | 216862434431944426122117120000.a | magma: IdentifyGroup(G);
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Character table: not available. |
magma: CharacterTable(G);