Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×H(5,𝔽2)×C53 ⋊ C2 |
| Sylow | C53 ⋊ #3585 |
1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|f^2=g,b^a=bf,e^a=eg,f^a=fg,h^a=h^52,f^b=fg,d^c=dg925 conjugacy classes — view the full character table.
| maximal subgroup of | #27415386, #27415387, #27415408, … |
| maximal normal subgroup of | #27415386, #27415387, #27415408, … |
| maximal quotient of | #28247663, #28247675, #28247776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19290);