Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×Dic3×#272 |
| derived | C3×H(3,𝔽3) ⋊ C2×C3×C4 |
| Sylow | C32×H(3,𝔽3) ⋊ C2×C4 |
981 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 981 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic3×((C3⋊D3)⋊C3)⋊C2 |
| maximal normal subgroup of | C3×Dic3×((C3⋊D3)⋊C3)⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3081);