Finite Group DatabasebetaFinite Group Databasebeta| order | 5427 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | (C67⋊C9)⋊C9 |
| Sylow | C67 ⋊ C9⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C3×C67⋊C3 |
| commutator | C3×C67 | C3×C9 |
| Fitting | C3×C9×C67 | C3 |
| socle | C32×C67 | C32 |
| hypercenter | C3×C9 | C67⋊C3 |
| hypocenter | C67 | C9⋊C9 |
| LCS | G ▷ C3×C67 ▷ C67 | |
| UCS | C1 ◁ C32 ◁ C3×C9 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,67|a^3=d,b^3=c,b^a=bc,e^b=e^37627 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊C9×C67⋊C3, C3×(C67⋊C9)⋊C9, #30653885, … |
| maximal normal subgroup of | C9⋊C9×C67⋊C3, C3×(C67⋊C9)⋊C9, #30653885, … |
| maximal quotient of | C67⋊#6855, (C67⋊C9)⋊C27, #30653841, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5427, 20);