Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#323 ⋊ C2 |
| Sylow | C53 ⋊ #1316 |
294 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 37 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=d,d^2=f,b^a=bc,c^a=ce,e^a=eg,d^b=de,h^b=h^52,d^c=dg598 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1316, C2×#20272642, #27293176, … |
| maximal normal subgroup of | D53×#1316, C2×#20272642, #27293176, … |
| maximal quotient of | #27270710, #27270718, #27270837, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2437);