Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #1281 |
152 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=e,d^2=g,e^2=f,b^a=bc,c^a=cf,h^a=h^52,d^b=df1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27270850, #27270851, #27270895, … |
| maximal normal subgroup of | #27270850, #27270851, #27270895, … |
| maximal quotient of | #27270622, #27270626, #27270628, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2355);