Finite Group DatabasebetaFinite Group Databasebeta| order | 5427 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
| direct product | C3×#14268673 |
| Sylow | C67 ⋊ C3×3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center | C32 | C3×C67⋊C3 |
| commutator | C3×C67 | C33 |
| Frattini | C3 | C32×C67⋊C3 |
| Fitting | C33×C67 | C3 |
| socle | C32×C67 | C32 |
| hypercenter | C33 | C67⋊C3 |
| hypocenter | C67 | C3×3−1+2 |
| LCS | G ▷ C3×C67 ▷ C67 | |
| UCS | C1 ◁ C32 ◁ C33 | |
76 conjugacy classes of subgroups.
627 conjugacy classes — view the full character table.
| maximal subgroup of | #30653794, #30653795, #30653796, … |
| maximal normal subgroup of | #30653794, #30653795, #30653796, … |
| maximal quotient of | C3×C32⋊(C67⋊C9), C3×(C67⋊C9)⋊C9, C9×#14268673, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5427, 45);