Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D27⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#6864⋊C4 |
| unambiguous semidirect product | (C2×#6864)⋊C4 |
| derived | C27 ⋊ C2×C4×C9 |
| Sylow | #6864 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D27⋊C3 |
| commutator, hypocenter | C27 | C2×C4×C9 |
| Frattini | C2×C3×C9 | C2×C3×D3 |
| Fitting | C22×#6864 | C2 |
| socle, prime radical | C22×C32 | C3×D9 |
| cosocle | C2×C3×C27 | C22×C3 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C22×C3 | |
141 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 141 conjugacy classes of subgroups — too many to draw. Only its 64 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, 432);