Finite Group DatabasebetaFinite Group Databasebeta| order | 5427 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C32⋊(C67⋊C9) |
| Sylow | C67 ⋊ C32⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C3×C67⋊C3 |
| commutator | C3×C67 | C3×C9 |
| Fitting | C33×C67 | C3 |
| socle | C32×C67 | C32 |
| hypercenter | C33 | C67⋊C3 |
| hypocenter | C67 | C32⋊C9 |
| LCS | G ▷ C3×C67 ▷ C67 | |
| UCS | C1 ◁ C32 ◁ C33 | |
46 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,67|a^3=d,b^a=bc,e^a=e^37627 conjugacy classes — view the full character table.
| maximal subgroup of | #30653792, #30653793, #30653794, … |
| maximal normal subgroup of | #30653792, #30653793, #30653794, … |
| maximal quotient of | C67⋊#6855, C32⋊(C67⋊C27), #30653818, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5427, 19);