Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C27 · Schur multiplier (H2) = C2 |
| direct product | D3×Dic3×C27 |
| unambiguous semidirect product | (C3×D3)⋊(C4×C27) |
| derived | C32 ⋊ C2×C4×C27 |
| Sylow | C32×C27 ⋊ C2×C4 |
200 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
486 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1232);