Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D27⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×C3×D27⋊C3 |
| unambiguous semidirect product | D27⋊(C22×C32) |
| Fitting | C22×C3×C27⋊C3 ⋊ C2 |
| derived | C27 ⋊ C23×C32 |
| Sylow | C3×C27⋊C3 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D27⋊C3 |
| commutator, cosocle, hypocenter | C27 | C23×C32 |
| Frattini | C9 | C22×C32×D3 |
| Fitting | C22×C3×C27⋊C3 | C2 |
| socle | C22×C32 | C3×D9 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C22×C3 | |
474 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 166 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, 2869);