Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of A4×PSU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×A4×PSU(3,𝔽2) |
| Fitting, socle | C23×C32 ⋊ C3×Q8 |
457 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 457 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | C2×A4×PSU(3,𝔽2)⋊C3, C2×A4×AΓL(1,𝔽9), C2×S4×PSU(3,𝔽2), … |
| maximal normal subgroup of | C2×A4×PSU(3,𝔽2)⋊C3, C2×A4×AΓL(1,𝔽9), C2×S4×PSU(3,𝔽2), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47873);