Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #1299 |
150 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 65 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,b^2=e,c^2=f,d^2=f,e^2=g,b^a=bc,c^a=cf,e^a=efg,c^b=cg,h^b=h^52766 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1299, C2×#20272604, #27274254, … |
| maximal normal subgroup of | D53×#1299, C2×#20272604, #27274254, … |
| maximal quotient of | #27270645, #27270656, #27270659, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2399);