Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4⋊Q8×C53 ⋊ C4 |
| Sylow | C53 ⋊ #2126 |
258 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|a^2=e,c^2=g,d^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^30,d^b=dg,e^b=efg,h^b=h^52,h^c=h^52,e^d=eg,h^e=h^52208 conjugacy classes — view the full character table.
| maximal subgroup of | #28299211, #28299243, #28299271, … |
| maximal normal subgroup of | #28299211, #28299243, #28299271, … |
| maximal quotient of | #28307918, #28307968, #28308074, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20784);