Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #1944 |
240 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|a^2=f,b^2=f,c^2=eg,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^52,c^b=cg1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27270897, #27270899, #27270900, … |
| maximal normal subgroup of | #27270897, #27270899, #27270900, … |
| maximal quotient of | #27282644, #27282664, #27282774, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5253);