Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| isoclinism | isoclinic class of #1113 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#1113 |
| Fitting, socle, Hall | C33×C5 ⋊ C22 |
| derived, Sylow | C33 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #1113 |
| commutator, cosocle, hypocenter | C33 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C33×C5 | C22 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C5 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
75 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D32⋊D3, #11762179, C5×#157⋊D3, … |
| maximal normal subgroup of | C5×D32⋊D3, #11762179, C5×#157⋊D3, … |
| maximal quotient of | C5×#6294, C5×#6295, C5×#6296, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 109);