Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×Q32×C53 ⋊ C2 |
| Sylow | C53 ⋊ #2189 |
220 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 51 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=g,c^2=g,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,d^b=df,f^b=fg,h^b=h^52,h^c=h^52601 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2189, C2×#20276654, #27537866, … |
| maximal normal subgroup of | D53×#2189, C2×#20276654, #27537866, … |
| maximal quotient of | #27296216, #27296560, #27297320, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6449);