Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#341 ⋊ C2 |
| Sylow | C53 ⋊ #1738 |
372 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 137 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,d^2=g,e^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=cg,h^c=h^52772 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1738, C2×#20274440, #27381514, … |
| maximal normal subgroup of | D53×#1738, C2×#20274440, #27381514, … |
| maximal quotient of | #27273552, #27273562, #27273566, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4235);