Finite Group DatabasebetaFinite Group Databasebeta| order | 10449 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C81 · Schur multiplier (H2) = C3 |
| direct product | C3×C43⋊C81 |
| unambiguous semidirect product | (C3×C43)⋊C81 |
| derived, Sylow | C43 ⋊ C3×C81 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C27 | C43⋊C3 |
| commutator, hypocenter | C43 | C3×C81 |
| Frattini | C27 | C3×C43⋊C3 |
| Fitting | C3×C27×C43 | C3 |
| socle, prime radical | C32×C43 | C27 |
| cosocle | C27×C43 | C32 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C3×C27 | |
36 conjugacy classes of subgroups.
1377 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C81×C43⋊C9, C9×C43⋊C81, #44532086, … |
| maximal normal subgroup of | C81×C43⋊C9, C9×C43⋊C81, #44532086, … |
| maximal quotient of | C9×C43⋊C81, C32⋊(C43⋊C81), #44532198, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10449, 125);