Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊#6188 |
| unambiguous semidirect product | C3⋊(C3×#6188) |
| derived | C3×H(3,𝔽3) ⋊ C3×C8 |
| Sylow | C32×H(3,𝔽3) ⋊ C8 |
411 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 411 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2987);