Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×(C3⋊#859)⋊C3 |
| unambiguous semidirect product | (C2×C3⋊#859)⋊C3 |
| derived | C3×SL(2,𝔽3) ⋊ C2×C3×C4 |
414 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 12967);