Finite Group DatabasebetaFinite Group Databasebeta| order | 5427 |
| isoclinism | isoclinic class of C67⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C33 |
| direct product | C3×C9×C67⋊C3 |
| Fitting | C3×C9×C67 ⋊ C3 |
| derived, Sylow | C67 ⋊ C32×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C9 | C67⋊C3 |
| commutator, hypocenter | C67 | C32×C9 |
| Frattini | C3 | C32×C67⋊C3 |
| Fitting | C3×C9×C67 | C3 |
| socle | C32×C67 | C32 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C3×C9 | |
100 conjugacy classes of subgroups.
675 conjugacy classes — view the full character table.
| maximal subgroup of | (C3×C67⋊C3)⋊C27, #30653823, C92×C67⋊C3, … |
| maximal normal subgroup of | (C3×C67⋊C3)⋊C27, #30653823, C92×C67⋊C3, … |
| maximal quotient of | C92×C67⋊C3, C3×C9×C67⋊C9, C32⋊C9×C67⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5427, 38);