Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#6769 |
| Hall | C32×C5 ⋊ #41 |
| Sylow | C32 ⋊ #709 |
| Sylow | C5 ⋊ C3×#239 |
172 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | #13085726, #13085727, #13085730, … |
| maximal normal subgroup of | #13085726, #13085727, #13085730, … |
| maximal quotient of | C3×Dic3×Dic10, C3×#91334, C3×#91338, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 594);