Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ C4×Q32 |
150 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 59 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=g,c^2=eg,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,d^b=df,f^b=fg,h^c=h^52616 conjugacy classes — view the full character table.
| maximal subgroup of | C4×Q32×D53, C2×#20276571, #27537370, … |
| maximal normal subgroup of | C4×Q32×D53, C2×#20276571, #27537370, … |
| maximal quotient of | #27295823, #27296005, #27296011, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6366);