Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #3299 |
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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=eg,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^52,d^b=de,f^c=fg,h^c=h^521075 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27373826, #27373834, #27373841, … |
| maximal normal subgroup of | #27373826, #27373834, #27373841, … |
| maximal quotient of | D4×#13133142, #27400333, #27401291, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 16387);