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 ⋊ #2957 |
452 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,h^b=h^52,d^c=dg,h^c=h^52772 conjugacy classes — view the full character table.
| maximal subgroup of | #27300228, #27300232, #27300235, … |
| maximal normal subgroup of | #27300228, #27300232, #27300235, … |
| maximal quotient of | #27353549, #27353556, #27353565, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13426);