Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #2090 |
176 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 67 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=d,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,h^a=h^52,c^b=cf,f^b=fg,h^b=h^52,e^c=eg,f^c=fg598 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2090, C2×#20276229, #27413211, … |
| maximal normal subgroup of | D53×#2090, C2×#20276229, #27413211, … |
| maximal quotient of | #27289023, #27289024, #27289030, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6024);