Finite Group DatabasebetaFinite Group Databasebeta| order | 5427 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
| direct product | 3−1+2×C67⋊C3 |
| Fitting | 3−1+2×C67 ⋊ C3 |
| Sylow | C67 ⋊ C3×3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C32×C67⋊C3 |
| commutator, socle | C3×C67 | C33 |
| Fitting | 3−1+2×C67 | C3 |
| hypercenter | 3−1+2 | C67⋊C3 |
| hypocenter | C67 | C3×3−1+2 |
| LCS | G ▷ C3×C67 ▷ C67 | |
| UCS | C1 ◁ C3 ◁ 3−1+2 | |
76 conjugacy classes of subgroups.
275 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5427, 42);