Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#64267⋊C3 |
| unambiguous semidirect product | (C2×#64267)⋊C3 |
| Fitting | C2×C32×#41 ⋊ D3 |
| derived | C3×SL(2,𝔽3) ⋊ C23×C3 |
682 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10593663⋊C3 |
| maximal normal subgroup of | C2×#10593663⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30492);