Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×C9×Dic5 |
| derived, Sylow | C5 ⋊ C3×C4×C9 |
| Hall | C3×C5×C9 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C9 | D5 |
| commutator, hypocenter | C5 | C3×C4×C9 |
| Frattini | C2×C3 | C32×D5 |
| Fitting | C2×C3×C5×C9 | C2 |
| socle, prime radical | C2×C32×C5 | C2×C3 |
| cosocle | C2×C3×C5 | C2×C32 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C3×C9 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 540 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C9×#170, C3×C9⋊#170, C9×C3⋊#170, … |
| maximal normal subgroup of | C3×C9×#170, C3×C9⋊#170, C9×C3⋊#170, … |
| maximal quotient of | C3×C9×#168, C2×C3×C9×Dic5, C92×Dic5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 13);