Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| direct product | D4×C9×D5 |
| Fitting | C5×D4×C9 ⋊ C2 |
| Hall | C5×C9 ⋊ C2×D4 |
| Sylow | C5 ⋊ C2×D4×C9 |
162 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#4007, #13083996, D5×#3672, … |
| maximal normal subgroup of | C9×#4007, #13083996, D5×#3672, … |
| maximal quotient of | C9×#4024, C9×#4031, C9×D5×C22⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 159);