Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C53 ⋊ C2 |
| Sylow | C53 ⋊ #1806 |
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 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,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^52,e^c=eg,h^c=h^521078 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27275999, #27276005, #27276006, … |
| maximal normal subgroup of | #27275999, #27276005, #27276006, … |
| maximal quotient of | #27276776, #27276781, #27276786, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4531);