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 ⋊ #3274 |
556 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,c^b=cg,d^b=de,e^b=eg,h^c=h^52,e^d=eg601 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#3274, C2×#20286329, #28259266, … |
| maximal normal subgroup of | D53×#3274, C2×#20286329, #28259266, … |
| maximal quotient of | #27375373, #27375460, #27375466, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 16124);