Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #1369 |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=c,c^2=e,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^52,d^b=dg1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271563, #27271564, #27271566, … |
| maximal normal subgroup of | #27271563, #27271564, #27271566, … |
| maximal quotient of | #27270830, #27270978, C2×#20272783 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2578);