Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#353 ⋊ C2 |
| Sylow | C53 ⋊ #2196 |
354 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 41 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^a=bd,c^a=ce,f^a=fg,h^a=h^52,e^b=efg,h^b=h^52,d^c=df,h^c=h^52,e^d=eg358 conjugacy classes — view the full character table.
| maximal subgroup of | #27304804, #27304805, #27304809, … |
| maximal normal subgroup of | #27304804, #27304805, #27304809, … |
| maximal quotient of | #27296122, #27296157, #27296295, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6496);