Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#102×C53 ⋊ C2 |
| Sylow | C53 ⋊ #2034 |
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|c^2=dg,e^2=g,b^a=bd,c^a=ce,e^a=eg,c^b=cf,h^b=h^52,e^c=eg,h^c=h^52760 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2034, C2×#20275903, #27411570, … |
| maximal normal subgroup of | D53×#2034, C2×#20275903, #27411570, … |
| maximal quotient of | #27287366, #27287373, #27287456, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5698);