Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #1820 |
300 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 93 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,b^2=g,c^2=d,b^a=bd,c^a=ce,e^a=eg,h^a=h^52,f^c=fg1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271120, #27271121, #27276270, … |
| maximal normal subgroup of | #27271120, #27271121, #27276270, … |
| maximal quotient of | #27277418, #27277424, #27277430, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4587);