Finite Group DatabasebetaFinite Group Databasebeta| order | 5427 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C3×C9×C67 ⋊ C3 |
| Sylow | C67 ⋊ #737 |
| subgroup | G/H | |
|---|---|---|
| center | C9 | C3×C67⋊C3 |
| commutator, socle | C3×C67 | C33 |
| Frattini | C3 | C32×C67⋊C3 |
| Fitting | C3×C9×C67 | C3 |
| hypercenter | C3×C9 | C67⋊C3 |
| hypocenter | C67 | #737 |
| LCS | G ▷ C3×C67 ▷ C67 | |
| UCS | C1 ◁ C9 ◁ C3×C9 | |
66 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,67|c^3=d,b^a=bd,e^b=e^37627 conjugacy classes — view the full character table.
| maximal subgroup of | #30653832, #30653834, #30653835, … |
| maximal normal subgroup of | #30653832, #30653834, #30653835, … |
| maximal quotient of | #30653886, #30653888, C9×C32⋊(C67⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5427, 47);