Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1996 |
324 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 72 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=def,c^2=e,b^a=bd,c^a=ce,d^a=dg,h^a=h^23,d^b=dg,f^b=fg,h^b=h^30,h^c=h^52,h^f=h^52292 conjugacy classes — view the full character table.
| maximal subgroup of | #28302686, #28302687, #28302690, … |
| maximal normal subgroup of | #28302686, #28302687, #28302690, … |
| maximal quotient of | #28306246, #28306249, #28306250, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20701);