Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of D27 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C5×D27 |
| Fitting | C2×C3×C5×C27 ⋊ C2 |
| derived | C27 ⋊ C22×C3×C5 |
| Hall | C3×C5×C27 ⋊ C22 |
| Sylow | C3×C27 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | D27 |
| commutator, cosocle, hypocenter | C27 | C22×C3×C5 |
| Frattini | C9 | C2×C3×C5×D3 |
| Fitting | C2×C3×C5×C27 | C2 |
| socle | C2×C32×C5 | D9 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C2×C3×C5 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 540 |
450 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 179);