Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×Q8×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1763 |
324 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 100 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,b^2=f,c^2=eg,d^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=cg,h^b=h^30,h^f=h^52304 conjugacy classes — view the full character table.
| maximal subgroup of | #28302534, #28302535, #28302536, … |
| maximal normal subgroup of | #28302534, #28302535, #28302536, … |
| maximal quotient of | #28301631, #28301632, #28301637, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20282);