Finite Group DatabasebetaFinite Group Databasebeta| order | 5427 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C33 |
| direct product | C32×C67⋊C9 |
| derived, Sylow | C67 ⋊ C32×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33 | C67⋊C3 |
| commutator, hypocenter | C67 | C32×C9 |
| Frattini | C3 | C32×C67⋊C3 |
| Fitting, socle | C33×C67 | C3 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C33 | |
100 conjugacy classes of subgroups.
675 conjugacy classes — view the full character table.
| maximal subgroup of | C67⋊#6855, #30653819, #30653821, … |
| maximal normal subgroup of | C67⋊#6855, #30653819, #30653821, … |
| maximal quotient of | C3×C9×C67⋊C9, C3×C32⋊(C67⋊C9), C3×#19129460, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5427, 39);