Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D16×C53 ⋊ C2 |
| Sylow | C53 ⋊ #2221 |
148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|b^2=df,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,e^c=eg,h^c=h^52598 conjugacy classes — view the full character table.
| maximal subgroup of | #27304773, #27304775, #27304780, … |
| maximal normal subgroup of | #27304773, #27304775, #27304780, … |
| maximal quotient of | #27298295, #27298312, #27298346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6627);