Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #1362 |
98 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=g,c^2=fg,d^2=efg,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,h^a=h^52,c^b=cf,d^b=defg,e^b=eg,f^b=fg601 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1362, C2×#20272764, #27295336, … |
| maximal normal subgroup of | D53×#1362, C2×#20272764, #27295336, … |
| maximal quotient of | #27270820, #27270825, #27270828, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2559);