Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D53⋊#349 |
| Sylow | C53 ⋊ C2×#349 |
236 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 74 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,e^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^30,e^b=eg,h^c=h^52,h^e=h^52304 conjugacy classes — view the full character table.
| maximal subgroup of | #28298429, #28298432, #28298435, … |
| maximal normal subgroup of | #28298429, #28298432, #28298435, … |
| maximal quotient of | D53⋊#1314, #28307875, D53⋊#1322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20744);