Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C53×H(3,𝔽4) ⋊ C2 |
| Sylow | C53 ⋊ #2199 |
270 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|b^a=bd,c^a=ce,f^a=fg,h^a=h^52,c^b=cg,e^b=efg,d^c=df,e^d=eg511 conjugacy classes — view the full character table.
| maximal subgroup of | #27304821, #27304823, #27304828, … |
| maximal normal subgroup of | #27304821, #27304823, #27304828, … |
| maximal quotient of | #27296139, #27296179, #27296308, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6511);