Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×#107×C53 ⋊ C2 |
| Sylow | C53 ⋊ #2076 |
256 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 81 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,c^2=dg,e^2=g,b^a=bd,c^a=ce,c^b=cf,h^b=h^52,e^c=eg760 conjugacy classes — view the full character table.
| maximal subgroup of | #27297308, #27297313, #27297318, … |
| maximal normal subgroup of | #27297308, #27297313, #27297318, … |
| maximal quotient of | #27288798, #27288808, #27288832, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5939);