Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #1574 |
158 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 64 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=d,c^2=f,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^30,c^b=cfg,h^b=h^52,h^c=h^52,h^e=h^52298 conjugacy classes — view the full character table.
| maximal subgroup of | #28303780, #28303783, #28303784, … |
| maximal normal subgroup of | #28303780, #28303783, #28303784, … |
| maximal quotient of | #28300199, #28302107, #28303041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20088);