Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| direct product | C2×D3×C9×D9 |
| Fitting | C2×C3×C92 ⋊ C22 |
| derived | C3×C9 ⋊ C23×C9 |
| Sylow | C3×C92 ⋊ C23 |
446 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3×#92265, D3×C9×#611, C2×D3×D92, … |
| maximal normal subgroup of | C2×D3×#92265, D3×C9×#611, C2×D3×D92, … |
| maximal quotient of | D3×C9×#611, D32×C9×D9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2674);