Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #1822 |
272 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,b^2=g,c^2=d,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^52,f^c=fg1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271126, #27271127, #27276593, … |
| maximal normal subgroup of | #27271126, #27271127, #27276593, … |
| maximal quotient of | #27277418, #27277421, #27277427, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4593);