Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D27⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C4×D27⋊C3 |
| unambiguous semidirect product | D27⋊(C32×C4) |
| unambiguous semidirect product | (C4×D27)⋊C32 |
| unambiguous semidirect product | (C3×C4×D27)⋊C3 |
| Fitting | C3×C4×C27⋊C3 ⋊ C2 |
| derived | C27 ⋊ C2×C32×C4 |
| Sylow | C3×C27⋊C3 ⋊ C2×C4 |
246 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1736);