Finite Group DatabasebetaFinite Group Databasebeta| order | 5427 |
| automorphism | ? |
| homology | Abelianization (H1) = C81 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C67⋊C81 |
| derived, Sylow | C67 ⋊ C81 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C27 | C67⋊C3 |
| commutator, hypocenter | C67 | C81 |
| Fitting | C27×C67 | C3 |
| socle | C3×C67 | C27 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C27 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,67|a^3=b,b^3=c,c^3=d,e^a=e^37675 conjugacy classes — view the full character table.
| maximal subgroup of | C81×C67⋊C3, C3×C67⋊C81, #30653848, … |
| maximal normal subgroup of | C81×C67⋊C3, C3×C67⋊C81, #30653848, … |
| maximal quotient of | C67⋊C243, C3×C67⋊C81 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5427, 16);