Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×D8×C53 ⋊ C4 |
| Sylow | C53 ⋊ #2957 |
452 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 158 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=f,c^2=f,e^2=g,f^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^30,e^b=eg,d^c=dg,h^c=h^30,h^f=h^52226 conjugacy classes — view the full character table.
| maximal subgroup of | #28311506, #28311520, #28311652, … |
| maximal normal subgroup of | #28311506, #28311520, #28311652, … |
| maximal quotient of | #28316406, #28316413, #28316421, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21286);