Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#131×C53 ⋊ C2 |
| Sylow | C53 ⋊ #3067 |
452 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|b^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^52,f^c=fg1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27301048, #27301050, #27301104, … |
| maximal normal subgroup of | #27301048, #27301050, #27301104, … |
| maximal quotient of | #27366334, #27366362, #27366402, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14230);