Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| isoclinism | isoclinic class of D5×C3⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | D5×C3⋊D9 |
| unambiguous semidirect product | (C3×D5)⋊D9 |
| unambiguous semidirect product | (C9×D5)⋊D3 |
| Fitting, derived, Hall | C3×C5×C9 ⋊ C22 |
| Sylow | C3×C9 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×C3⋊D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C5×C9 | C22 |
| Frattini | C3 | D5×C3⋊D3 |
| socle | C32×C5 | C2×D3 |
| LCS | G ▷ C3×C5×C9 | |
| UCS | C1 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×C3⋊D9, (C3⋊D9)⋊AGL(1,𝔽5), D3×D5×D9, … |
| maximal normal subgroup of | AGL(1,𝔽5)×C3⋊D9, (C3⋊D9)⋊AGL(1,𝔽5), D3×D5×D9, … |
| maximal quotient of | #11761758, Dic5×C3⋊D9, #11761760, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 48);