Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×SL(2,ℤ/9) |
| unambiguous semidirect product | #6296⋊C32 |
| unambiguous semidirect product | (C3×#6296)⋊C3 |
| derived | #6296 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #1113⋊C3 |
| commutator, cosocle, hypocenter | #6296 | C32 |
| Frattini | C2 | C3×#1113⋊C3 |
| Fitting, socle | C2×C34 | A4 |
| LCS | G ▷ #6296 | |
| UCS | C1 ◁ C2×C3 | |
206 conjugacy classes of subgroups; only the 14 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 14 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
75 conjugacy classes — view the full character table.
| derived subgroup of | #72228152 |
| maximal subgroup of | #72209635, #72209947, C3×#13049364, … |
| maximal normal subgroup of | #72209947, C3×#13049364, #72228152 |
| maximal quotient of | #72209947, C3×#72277444 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3782);