Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| isoclinism | isoclinic class of D5×(C3⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | D5×(C3⋊D3)⋊C3 |
| unambiguous semidirect product | (D5×C3⋊D3)⋊C3 |
| Fitting, Hall | C5×H(3,𝔽3) ⋊ C22 |
| derived | C32×C5 ⋊ C22×C3 |
| Sylow | H(3,𝔽3) ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×(C3⋊D3)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C5 | C22×C3 |
| Frattini | C3 | C3×D3×D5 |
| Fitting | C5×H(3,𝔽3) | C22 |
| socle | C3×C5 | C2×C3×D3 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 45 |
40 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 46);