Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C53 ⋊ #2254 |
128 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=d,c^2=efg,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^c=h^52610 conjugacy classes — view the full character table.
| maximal subgroup of | #27298052, #27298053, #27298054, … |
| maximal normal subgroup of | #27298052, #27298053, #27298054, … |
| maximal quotient of | #27300528, #27302124, #27302692, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6790);