Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×C33×D5 |
| unambiguous semidirect product | C5⋊(C22×C33) |
| unambiguous semidirect product | (C2×C5)⋊(C2×C33) |
| Fitting, socle | C2×C33×C5 ⋊ C2 |
| derived, Sylow | C5 ⋊ C22×C33 |
| Hall | C33×C5 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C33 | D5 |
| commutator, cosocle, hypocenter | C5 | C22×C33 |
| Frattini | C1 | G |
| Fitting, socle | C2×C33×C5 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C33 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 270 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C32×D5×Dic3, C32×#1201, C32×#1202, … |
| maximal normal subgroup of | C32×D5×Dic3, C32×#1201, C32×#1202, … |
| maximal quotient of | C33×Dic10, C33×C4×D5, C33×D20, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 112);