Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #1467 |
236 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 68 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=f,c^2=fg,e^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^30,e^b=ef,h^e=h^52448 conjugacy classes — view the full character table.
| maximal subgroup of | #28298618, #28298619, #28298839, … |
| maximal normal subgroup of | #28298618, #28298619, #28298839, … |
| maximal quotient of | #28299620, #28299622, #28299631, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19772);