Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×AGL(1,ℤ/8)×C53 ⋊ C2 |
| Sylow | C53 ⋊ #3006 |
806 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,h^c=h^52604 conjugacy classes — view the full character table.
| maximal subgroup of | #27421352, #27421356, #27421385, … |
| maximal normal subgroup of | #27421352, #27421356, #27421385, … |
| maximal quotient of | #27356483, #27356522, #27356561, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13758);