Show commands:
Magma
magma: G := TransitiveGroup(37, 10);
Group action invariants
Degree $n$: | $37$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
Transitive number $t$: | $10$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
Group: | $A_{37}$ | ||
Parity: | $1$ | magma: IsEven(G);
| |
Primitive: | yes | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
|
$\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
| |
Generators: | (3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37), (1,2,3) | magma: Generators(G);
|
Low degree resolvents
noneResolvents shown for degrees $\leq 47$
Subfields
Prime degree - 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 10,871 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
Order: | $6881876545613172523157989790790451200000000=2^{33} \cdot 3^{17} \cdot 5^{8} \cdot 7^{5} \cdot 11^{3} \cdot 13^{2} \cdot 17^{2} \cdot 19 \cdot 23 \cdot 29 \cdot 31 \cdot 37$ | magma: Order(G);
| |
Cyclic: | no | magma: IsCyclic(G);
| |
Abelian: | no | magma: IsAbelian(G);
| |
Solvable: | no | magma: IsSolvable(G);
| |
Nilpotency class: | not nilpotent | ||
Label: | 6881876545613172523157989790790451200000000.a | magma: IdentifyGroup(G);
|
Character table: not available. |
magma: CharacterTable(G);