Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×C3⋊(C3⋊#157) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C32 |
| direct product | D3×C3⋊(C3⋊#157) |
| unambiguous semidirect product | (C3×D3)⋊(C3⋊#157) |
| Fitting, socle, derived, Sylow | C35 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C35 | C2×C4 |
| prime radical | C32×D3×C3⋊D3 | C2 |
| cosocle | C33×C3⋊D3 | C22 |
| LCS | G ▷ C35 | |
| UCS | C1 | |
872 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 872 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) = 72 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C3⋊D3×#157, D3×#10620203 |
| maximal normal subgroup of | D3×C3⋊D3×#157, D3×#10620203 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3898);