Show commands:
Magma
magma: G := TransitiveGroup(38, 46);
Group action invariants
| Degree $n$: | $38$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{19}^2:(C_9\times D_{18})$ | ||
| 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: | (1,7,15,13,4,11,14,18,17,3,16,8,10,19,12,9,5,6)(21,28,27,38,31,32)(22,36,34,37,23,25)(24,33,29,35,26,30), (1,27,9,34,19,38,3,24,2,35,15,25,17,22,10,23,6,29)(4,32,8,26,13,28,5,21,14,36,11,31,12,20,18,30,16,33)(7,37) | 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 $9$: $C_9$ $12$: $D_{6}$, $C_6\times C_2$ $18$: $S_3\times C_3$, $D_{9}$, $C_{18}$ x 3 $36$: $C_6\times S_3$, $D_{18}$, 36T2 $54$: $C_9\times S_3$, 18T19 $108$: 36T63, 36T69 $162$: 18T74 $324$: 36T461 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
The 121 conjugacy class representatives for $C_{19}^2:(C_9\times D_{18})$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $116964=2^{2} \cdot 3^{4} \cdot 19^{2}$ | 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: | 116964.i | magma: IdentifyGroup(G);
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| Character table: | 121 x 121 character table |
magma: CharacterTable(G);