Show commands:
Magma
magma: G := TransitiveGroup(40, 315063);
Group action invariants
| Degree $n$: | $40$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
| Transitive number $t$: | $315063$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
| Group: | $A_5^8.C_2^5.C_2.C_4^2$ | ||
| Parity: | $-1$ | magma: IsEven(G);
| |
| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
|
| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
| |
| Generators: | (1,40,23,19,5,36,25,18,4,37,22,17,3,38,24,20)(2,39,21,16)(6,34,7,32,8,35,10,31)(9,33)(11,30,15,29)(12,26)(13,27,14,28), (1,12,24,32,5,14,25,33,3,13,22,34,2,15,21,31)(4,11,23,35)(6,39,27,17,10,36,28,16,7,40,30,20)(8,37,26,18,9,38,29,19) | magma: Generators(G);
|
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_4$ x 6, $C_2^2$ $8$: $D_{4}$ x 3, $C_4\times C_2$ x 3, $Q_8$ $16$: $C_2^2:C_4$ x 3 $32$: $C_2^3 : C_4 $ x 6 Resolvents shown for degrees $\leq 10$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 5: None
Degree 8: $C_2^3: C_4$
Degree 10: None
Degree 20: None
Low degree siblings
There are no siblings with degree $\leq 10$
Data on whether or not a number field with this Galois group has arithmetically equivalent fields has not been computed.
Conjugacy classes
The 47980 conjugacy class representatives for $A_5^8.C_2^5.C_2.C_4^2$ are not computed
magma: ConjugacyClasses(G);
Group invariants
| Order: | $171992678400000000=2^{26} \cdot 3^{8} \cdot 5^{8}$ | magma: Order(G);
| |
| Cyclic: | no | magma: IsCyclic(G);
| |
| Abelian: | no | magma: IsAbelian(G);
| |
| Solvable: | no | magma: IsSolvable(G);
| |
| Nilpotency class: | not nilpotent | ||
| Label: | 171992678400000000.dv | magma: IdentifyGroup(G);
| |
| Character table: | not computed |
magma: CharacterTable(G);