Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of D3×PSU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3 |
| direct product | C4×D3×PSU(3,𝔽2) |
| Fitting | C33×C4 ⋊ C2×Q8 |
| Sylow | C33 ⋊ C2×C4×Q8 |
666 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 666 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #624×PSU(3,𝔽2), C4×D3×PSU(3,𝔽2)⋊C3 |
| maximal normal subgroup of | C4×D3×PSU(3,𝔽2)⋊C3 |
| maximal quotient of | #624×PSU(3,𝔽2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 46689);