Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#423 ⋊ C2 |
| Sylow | C53 ⋊ #1800 |
336 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 97 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=f,b^2=d,f^2=g,b^a=bd,c^a=ce,e^a=eg,f^c=fg,h^c=h^52760 conjugacy classes — view the full character table.
| maximal subgroup of | #27275638, #27275641, #27275648, … |
| maximal normal subgroup of | #27275638, #27275641, #27275648, … |
| maximal quotient of | #27276746, #27276754, #27276762, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4499);