Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C5×#638 |
| Fitting | C22×C33×C5 ⋊ C2 |
| Hall | C33×C5 ⋊ D4 |
| Sylow | C33 ⋊ C5×D4 |
272 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
315 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 468);