Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #3383 |
324 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 131 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,b^2=eg,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^52,d^b=de,f^c=fg,h^d=h^52763 conjugacy classes — view the full character table.
| maximal subgroup of | #27541782, #27541788, #27541793, … |
| maximal normal subgroup of | #27541782, #27541788, #27541793, … |
| maximal quotient of | #27400707, Q16×#11719919, #27402527, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17401);