Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#447 ⋊ C2 |
| Sylow | C53 ⋊ D4×D8 |
620 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,e^d=eg,h^d=h^52529 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D8×D53, C2×#20286385, #28259380, … |
| maximal normal subgroup of | D4×D8×D53, C2×#20286385, #28259380, … |
| maximal quotient of | #27373432, #27373437, #27373442, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 16180);