Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C27 · Schur multiplier (H2) = C1 |
| direct product | Dic5×C27 |
| derived, Sylow | C5 ⋊ C4×C27 |
| Hall | C5×C27 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C27 | D5 |
| commutator, hypocenter | C5 | C4×C27 |
| Frattini | C2×C9 | C3×D5 |
| Fitting | C2×C5×C27 | C2 |
| socle, prime radical | C2×C3×C5 | C2×C9 |
| cosocle | C2×C5×C9 | C2×C3 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C27 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 540 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C27×#170, C27⋊#170, #11761661, … |
| maximal normal subgroup of | C27×#170, C27⋊#170, #11761661, … |
| maximal quotient of | C27×#168, C2×Dic5×C27, Dic5×C81, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 2);