Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×#272 |
| Fitting, derived, Hall | C5×H(3,𝔽3) ⋊ C22 |
| Sylow | H(3,𝔽3) ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×#272 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D5×C3⋊D3 |
| commutator, Fitting, cosocle, hypocenter | C5×H(3,𝔽3) | C22 |
| socle | C3×C5 | C2×C3⋊D3 |
| LCS | G ▷ C5×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 45 |
40 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#272, #11761932, D5×#1088, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#272, #11761932, D5×#1088, … |
| maximal quotient of | D5×#1084, Dic5×#272, #11761767, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 49);