Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×H(3,𝔽4) ⋊ C2 |
| Sylow | C53 ⋊ #2202 |
248 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 248 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|d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^52,d^b=dg,e^b=efg,d^c=df,e^c=eg,e^d=eg511 conjugacy classes — view the full character table.
| maximal subgroup of | #27304822, #27304823, #27304829, … |
| maximal normal subgroup of | #27304822, #27304823, #27304829, … |
| maximal quotient of | #27296155, #27296330, #27296423, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6527);