Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×AGL(1,ℤ/8)×C53 ⋊ C2 |
| Sylow | C53 ⋊ #3267 |
500 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|c^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=de,e^b=eg,h^c=h^52,e^d=eg601 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#3267, C2×#20286234, #28259161, … |
| maximal normal subgroup of | D53×#3267, C2×#20286234, #28259161, … |
| maximal quotient of | #27373478, #27373598, #27373733, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 16029);