Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of #67077 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#67082 |
| Hall | C3×C5×C9 ⋊ D4 |
| Sylow | C3×C9 ⋊ C22⋊D5 |
| Sylow | C5 ⋊ C3×#611 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D5×D9 |
| commutator, cosocle | C2×C5×C9 | C22×C3 |
| Frattini | C2×C3 | C3×D3×D5 |
| Fitting | C2×C3×C5×C9 | C22 |
| socle | C2×C32×C5 | C2×D3 |
| hypocenter | C5×C9 | C3×D4 |
| LCS | G ▷ C2×C5×C9 ▷ C5×C9 | |
| UCS | C1 ◁ C2×C3 | |
116 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 81);