Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#10619761 |
| derived | C32⋊(C22⋊C9) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C3⋊((C22⋊C9)⋊C2) |
| commutator, cosocle, hypocenter | C32⋊(C22⋊C9) | C2×C3 |
| Frattini | C32 | C3×C3⋊S4 |
| Fitting | C22×C34 | D3 |
| socle | C22×C33 | C3⋊D3 |
| LCS | G ▷ C32⋊(C22⋊C9) | |
| UCS | C1 ◁ C32 | |
508 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2483);