Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #1549 |
240 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 101 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=fg,d^2=g,e^2=fg,b^a=bd,c^a=cf,d^a=df,h^a=h^52,d^b=dg,e^b=efg760 conjugacy classes — view the full character table.
| maximal subgroup of | #27275852, #27275855, #27275857, … |
| maximal normal subgroup of | #27275852, #27275855, #27275857, … |
| maximal quotient of | #27272094, #27272165, #27272227, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 3195);