Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #100×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1757 |
284 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 86 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=e,b^2=f,c^2=e,e^2=g,b^a=bd,f^a=fg,h^a=h^30,d^b=dg,h^b=h^23,h^c=h^30,h^e=h^52,h^f=h^52187 conjugacy classes — view the full character table.
| maximal subgroup of | #28310598, #28310601, #28310604, … |
| maximal normal subgroup of | #28310598, #28310601, #28310604, … |
| maximal quotient of | #28301554, #28301560, #28301567, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20267);