Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of C3⋊#226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3×C3⋊#859 |
| unambiguous semidirect product | (C2×C3)⋊(C3×#859) |
| derived | C3×SL(2,𝔽3) ⋊ C2×C3×C4 |
715 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 715 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 39083);