Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1386 |
140 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 50 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=d,b^2=e,c^2=fg,e^2=f,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,h^a=h^30,c^b=cg,h^d=h^52292 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20289787, #28310310, #360×#6157, … |
| maximal normal subgroup of | C2×#20289787, #28310310, #360×#6157, … |
| maximal quotient of | #28298318, #28298378, #28298387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19582);