Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊C8×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1852 |
360 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 88 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,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^23,d^b=dg,h^b=h^30,h^f=h^52298 conjugacy classes — view the full character table.
| maximal subgroup of | #28303708, #28303710, #28303711, … |
| maximal normal subgroup of | #28303708, #28303710, #28303711, … |
| maximal quotient of | #28303622, #28303623, #28303624, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20459);