Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C16×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1384 |
132 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=e,c^2=f,e^2=fg,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,h^a=h^30,d^b=dg,h^d=h^52448 conjugacy classes — view the full character table.
| maximal subgroup of | #28299071, #28299072, #28299073, … |
| maximal normal subgroup of | #28299071, #28299072, #28299073, … |
| maximal quotient of | #28298316, #28298375, #28298529, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19578);