Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| isoclinism | isoclinic class of D27 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic27 |
| unambiguous semidirect product | C27⋊(C4×C5) |
| derived, Sylow | C27 ⋊ C4×C5 |
| Hall | C5×C27 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D27 |
| commutator, hypocenter | C27 | C4×C5 |
| Frattini | C2×C9 | C5×D3 |
| Fitting | C2×C5×C27 | C2 |
| socle, prime radical | C2×C3×C5 | D9 |
| cosocle | C2×C27 | C2×C5 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 540 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #11761661, #11761663, D5×Dic27, … |
| maximal normal subgroup of | #11761661, #11761663, D5×Dic27, … |
| maximal quotient of | C5×C27⋊C8, C2×C5×Dic27, C5×Dic81, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 1);