Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | SL(2,𝔽3)×C4⋊(C3⋊D3) |
| unambiguous semidirect product | C4⋊(C3⋊D3×SL(2,𝔽3)) |
| Fitting | C32×C4×Q8 ⋊ C2×C3 |
718 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
147 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 39211);