Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #1366 |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=f,c^2=fg,d^2=ef,e^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,h^a=h^23,c^b=cf,d^b=def,e^b=eg,h^d=h^52205 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20289736, D53⋊#1366, #28309714, … |
| maximal normal subgroup of | C2×#20289736, D53⋊#1366, #28309714, … |
| maximal quotient of | #28298253, #28298254, #28298694, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19531);