Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32×C4 |
| direct product | C2×#127⋊H(3,𝔽3) |
| unambiguous semidirect product | (C2×#127)⋊H(3,𝔽3) |
| unambiguous semidirect product | (C2×C3×#127⋊C3)⋊C3 |
| Fitting | C2×C32×#127 ⋊ C3 |
| Sylow | C2×#127 ⋊ H(3,𝔽3) |
633 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 633 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18252);