Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #2884 |
716 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,c^2=g,d^2=g,b^a=be,e^a=eg,h^a=h^52,f^b=fg,d^c=dg925 conjugacy classes — view the full character table.
| maximal subgroup of | #27301684, #27301688, #27301698, … |
| maximal normal subgroup of | #27301684, #27301688, #27301698, … |
| maximal quotient of | #27349921, #27349925, #27350025, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 12974);