Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×M16×C53 ⋊ C2 |
| Sylow | C53 ⋊ #2896 |
772 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,d^2=g,e^2=g,b^a=be,c^a=cg,e^a=eg,h^a=h^52,e^b=eg,h^b=h^521084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27289553, #27289559, #27289585, … |
| maximal normal subgroup of | #27289553, #27289559, #27289585, … |
| maximal quotient of | #27350468, #27350528, #27350547, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13030);