Show commands:
Magma
magma: G := TransitiveGroup(38, 47);
Group action invariants
| Degree $n$: | $38$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $47$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $F_{19}\wr C_2$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,24,9,23,19,36,3,38,2,31,15,27,17,22,10,30,6,21)(4,26,8,35,13,32,5,33,14,20,11,37,12,25,18,29,16,34)(7,28), (1,37,14,28)(2,29,13,36)(3,21,12,25)(4,32,11,33)(5,24,10,22)(6,35,9,30)(7,27,8,38)(15,20,19,26)(16,31,18,34)(17,23) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $3$: $C_3$ $4$: $C_2^2$ $6$: $S_3$, $C_6$ x 3 $8$: $D_{4}$ $9$: $C_9$ $12$: $D_{6}$, $C_6\times C_2$ $18$: $S_3\times C_3$, $D_{9}$, $C_{18}$ x 3 $24$: $(C_6\times C_2):C_2$, $D_4 \times C_3$ $36$: $C_6\times S_3$, $D_{18}$, 36T2 $54$: $C_9\times S_3$, 18T19 $72$: 12T42, 36T15, 36T24 $108$: 36T63, 36T69 $162$: 18T74 $216$: 36T181, 36T189 $324$: 36T461 $648$: 36T966 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 19: 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
There are 209 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $233928=2^{3} \cdot 3^{4} \cdot 19^{2}$ | 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 | ||
| Label: | 233928.h | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);