Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#554 ⋊ C2 |
| Sylow | C53 ⋊ #3357 |
354 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 123 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=eg,b^2=g,c^2=eg,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^52,c^b=cg,d^b=de,f^c=fg679 conjugacy classes — view the full character table.
| maximal subgroup of | #27375030, #27375032, #27375075, … |
| maximal normal subgroup of | #27375030, #27375032, #27375075, … |
| maximal quotient of | #27400541, #27400546, #27401825, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17136);