Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1833 |
172 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 62 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=e,c^2=d,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^30,f^b=fg,f^c=fg,h^f=h^52448 conjugacy classes — view the full character table.
| maximal subgroup of | #28311408, #28311409, #28311447, … |
| maximal normal subgroup of | #28311408, #28311409, #28311447, … |
| maximal quotient of | #28303518, #28303521, #28303522, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20429);