Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | #67×PSU(3,𝔽2) |
| Fitting | C22×C33 ⋊ C2×Q8 |
| Sylow | C33 ⋊ D4×Q8 |
630 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | #67×PSU(3,𝔽2)⋊C3, C3×#67×PSU(3,𝔽2), #626×PSU(3,𝔽2) |
| maximal normal subgroup of | #67×PSU(3,𝔽2)⋊C3, C3×#67×PSU(3,𝔽2) |
| maximal quotient of | C3×#67×PSU(3,𝔽2), #626×PSU(3,𝔽2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 46708);