Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#332 ⋊ C2 |
| Sylow | C53 ⋊ #1561 |
210 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 210 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=e,b^2=f,c^2=g,d^2=g,e^2=fg,b^a=bd,c^a=cg,d^a=df,d^b=dg,e^b=efg,h^c=h^52520 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1561, C2×#20273451, #27352653, … |
| maximal normal subgroup of | D53×#1561, C2×#20273451, #27352653, … |
| maximal quotient of | #27272191, #27272208, #27272337, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 3246);