Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | D4×PSU(3,𝔽2)⋊C3 |
| unambiguous semidirect product | C4⋊(C2×PSU(3,𝔽2)⋊C3) |
| unambiguous semidirect product | (D4×PSU(3,𝔽2))⋊C3 |
| Fitting | C32×D4 ⋊ SL(2,𝔽3) |
280 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
50 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 46233);