Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #1585 |
168 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 71 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,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cfg,d^a=df,h^a=h^52,d^b=df,h^c=h^52766 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1585, C2×#20273573, #27353659, … |
| maximal normal subgroup of | D53×#1585, C2×#20273573, #27353659, … |
| maximal quotient of | #27274899, #27274962, #27275366, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 3368);