Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×H(3,𝔽3)⋊(C22⋊C9) |
| unambiguous semidirect product | (C2×H(3,𝔽3))⋊(C22⋊C9) |
| Sylow | C23 ⋊ H(3,𝔽3)⋊C9 |
412 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1018);