Show commands:
Magma
magma: G := TransitiveGroup(16, 1202);
Group action invariants
| Degree $n$: | $16$ | magma: t, n := TransitiveGroupIdentification(G); n;
| |
| Transitive number $t$: | $1202$ | magma: t, n := TransitiveGroupIdentification(G); t;
| |
| Group: | $C_4\wr C_2^2$ | ||
| Parity: | $-1$ | magma: IsEven(G);
| |
| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
|
| $\card{\Aut(F/K)}$: | $4$ | magma: Order(Centralizer(SymmetricGroup(n), G));
| |
| Generators: | (1,14)(2,13)(3,15)(4,16)(5,9,6,10)(7,11,8,12), (1,10,3,12,2,9,4,11)(5,13)(6,14)(7,16)(8,15), (1,7,3,6,2,8,4,5)(9,14,12,16,10,13,11,15) | magma: Generators(G);
|
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 7 $4$: $C_4$ x 4, $C_2^2$ x 7 $8$: $D_{4}$ x 12, $C_4\times C_2$ x 6, $C_2^3$ $16$: $D_4\times C_2$ x 6, $C_2^2:C_4$ x 12, $C_4\times C_2^2$ $32$: $C_4\wr C_2$ x 6, $C_2^2 \wr C_2$ x 4, $C_2 \times (C_2^2:C_4)$ x 3 $64$: $(C_4^2 : C_2):C_2$ x 3, $(((C_4 \times C_2): C_2):C_2):C_2$, 16T79, 16T106 x 3, 16T111 x 3, 16T138 x 3, 16T146 $128$: 32T1151, 32T1153 x 3, 32T1154 x 3 $256$: 16T500 x 3, 64T? x 4 $512$: 128T? Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 8: $(((C_4 \times C_2): C_2):C_2):C_2$
Low degree siblings
16T1202 x 15, 32T36265 x 24, 32T36266 x 24, 32T36267 x 8, 32T56437 x 24Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 106 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $1024=2^{10}$ | magma: Order(G);
| |
| Cyclic: | no | magma: IsCyclic(G);
| |
| Abelian: | no | magma: IsAbelian(G);
| |
| Solvable: | yes | magma: IsSolvable(G);
| |
| Nilpotency class: | $4$ | ||
| Label: | 1024.dgl | magma: IdentifyGroup(G);
|
| Character table: not available. |
magma: CharacterTable(G);