Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #2115 |
220 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 105 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,e^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^52,c^b=cg,e^b=eg1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271099, #27271100, #27271102, … |
| maximal normal subgroup of | #27271099, #27271100, #27271102, … |
| maximal quotient of | #27293157, #27293229, #27293298, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6131);