Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C92 · Schur multiplier (H2) = C2×C9 |
| direct product | C4×D3×C92 |
| Fitting | C3×C4×C92 ⋊ C2 |
| derived | C3 ⋊ C2×C4×C92 |
| Sylow | C3×C92 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C92 | D3 |
| commutator, hypocenter | C3 | C2×C4×C92 |
| Frattini | C2×C32 | C2×C32×D3 |
| Fitting | C3×C4×C92 | C2 |
| socle, cosocle | C2×C33 | C22×C32 |
| prime radical | C2×C32×D3 | C2×C32 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C4×C92 | |
488 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 253 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 648 |
972 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1672);