Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#108×C53 ⋊ C2 |
| Sylow | C53 ⋊ #2916 |
440 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,b^2=e,e^2=g,f^2=g,b^a=be,e^a=eg,d^c=dg,h^d=h^52772 conjugacy classes — view the full character table.
| maximal subgroup of | #27300428, #27300429, #27300433, … |
| maximal normal subgroup of | #27300428, #27300429, #27300433, … |
| maximal quotient of | #27353077, #27353078, #27353082, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13118);