Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×D27⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | Dic3×D27⋊C3 |
| unambiguous semidirect product | D27⋊(C3×Dic3) |
| unambiguous semidirect product | (C3×D27⋊C3)⋊C4 |
| unambiguous semidirect product | (Dic3×D27)⋊C3 |
| derived | C3×C27 ⋊ C2×C3×C4 |
| Sylow | C3×C27⋊C3 ⋊ C2×C4 |
186 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1238);