Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| isoclinism | isoclinic class of D3×C3⋊D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | D3×C3⋊D15 |
| unambiguous semidirect product | (C3×D3)⋊D15 |
| unambiguous semidirect product | (C5×D3)⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C33×C5 ⋊ C22 |
| Sylow | C33 ⋊ C2×D5 |
| Sylow | C5 ⋊ D3×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C33×C5 | C22 |
| LCS | G ▷ C33×C5 | |
| UCS | C1 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4380, D3×D5×C3⋊D3, D32×D15, … |
| maximal normal subgroup of | D3×#4380, D3×D5×C3⋊D3, D32×D15, … |
| maximal quotient of | Dic3×C3⋊D15, D3×C3⋊Dic15, #11762082, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 107);