Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×D5×H(3,𝔽3) |
| unambiguous semidirect product | C5⋊(C22×H(3,𝔽3)) |
| unambiguous semidirect product | (C2×C5)⋊(C2×H(3,𝔽3)) |
| unambiguous semidirect product | (C2×C32×D5)⋊C3 |
| Fitting | C2×C5×H(3,𝔽3) ⋊ C2 |
| Hall | C5×H(3,𝔽3) ⋊ C22 |
| Sylow | C5 ⋊ C22×H(3,𝔽3) |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | D5×(C3⋊Dic3)⋊C3, #67138⋊C3, #67139⋊C3, … |
| maximal normal subgroup of | D5×(C3⋊Dic3)⋊C3, #67138⋊C3, #67139⋊C3, … |
| maximal quotient of | H(3,𝔽3)×Dic10, C4×D5×H(3,𝔽3), H(3,𝔽3)×D20, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 63);