Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #3079 |
416 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^52,f^c=fg1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27279941, #27279943, #27279948, … |
| maximal normal subgroup of | #27279941, #27279943, #27279948, … |
| maximal quotient of | #27383587, #27385069, #27386277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14325);