Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×D27 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×D3×D27 |
| Fitting | C2×C32×C27 ⋊ C22 |
| derived | C3×C27 ⋊ C23×C3 |
| Sylow | C32×C27 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D3×D27 |
| commutator, cosocle, hypocenter | C3×C27 | C23×C3 |
| Frattini | C9 | C2×C3×D32 |
| Fitting | C2×C32×C27 | C22 |
| socle | C2×C33 | C2×D9 |
| LCS | G ▷ C3×C27 | |
| UCS | C1 ◁ C2×C3 | |
348 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2688);