Show commands:
Magma
magma: G := TransitiveGroup(16, 1905);
Group action invariants
Degree $n$: | $16$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
Transitive number $t$: | $1905$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
Group: | $C_2^6.S_4^2:D_4$ | ||
Parity: | $-1$ | magma: IsEven(G);
| |
Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
|
$\card{\Aut(F/K)}$: | $2$ | magma: Order(Centralizer(SymmetricGroup(n), G));
| |
Generators: | (1,11,3,13,16,9,2,12,4,14,15,10)(5,8)(6,7), (1,16,3)(2,15,4)(7,12,13,9,8,11,14,10), (1,3)(2,4)(5,16,6,15)(7,12,13,9,8,11,14,10) | magma: Generators(G);
|
Low degree resolvents
$\card{(G/N)}$ Galois groups for stem field(s) $2$: $C_2$ x 7 $4$: $C_2^2$ x 7 $8$: $D_{4}$ x 6, $C_2^3$ $16$: $D_4\times C_2$ x 3 $32$: $C_2^2 \wr C_2$ $72$: $C_3^2:D_4$ $144$: 12T77 $288$: 12T125 $1152$: $S_4\wr C_2$ $2304$: 12T235 $4608$: 12T260 $73728$: 16T1864 $147456$: 32T2077237 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 8: $S_4\wr C_2$
Low degree siblings
16T1905 x 15, 32T2265666 x 8, 32T2265667 x 8, 32T2265668 x 8, 32T2265669 x 8, 32T2265670 x 8, 32T2265671 x 8, 32T2265672 x 8, 32T2265673 x 8, 32T2265674 x 8, 32T2265675 x 8, 32T2265676 x 8, 32T2265677 x 8, 32T2265678 x 8, 32T2265679 x 8, 32T2265680 x 8, 32T2265730 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
Conjugacy classes not computed
magma: ConjugacyClasses(G);
Group invariants
Order: | $294912=2^{15} \cdot 3^{2}$ | magma: Order(G);
| |
Cyclic: | no | magma: IsCyclic(G);
| |
Abelian: | no | magma: IsAbelian(G);
| |
Solvable: | yes | magma: IsSolvable(G);
| |
Nilpotency class: | not nilpotent | ||
Label: | 294912.a | magma: IdentifyGroup(G);
| |
Character table: | not computed |
magma: CharacterTable(G);