Finite Group DatabasebetaFinite Group Databasebeta| order | 5427 |
| isoclinism | isoclinic class of C67⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C3 |
| direct product | C27×C67⋊C3 |
| Fitting | C27×C67 ⋊ C3 |
| derived, Sylow | C67 ⋊ C3×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C27 | C67⋊C3 |
| commutator, hypocenter | C67 | C3×C27 |
| Frattini | C9 | C3×C67⋊C3 |
| Fitting | C27×C67 | C3 |
| socle | C3×C67 | C3×C9 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C27 | |
28 conjugacy classes of subgroups.
675 conjugacy classes — view the full character table.
| maximal subgroup of | C81×C67⋊C3, #30653848, #30653849, … |
| maximal normal subgroup of | C81×C67⋊C3, #30653848, #30653849, … |
| maximal quotient of | C27×C67⋊C9, (C3×C67⋊C3)⋊C27, (C67⋊C9)⋊C27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5427, 23);