Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C5×C3⋊C8 |
| unambiguous semidirect product | (C2×C3)⋊(C3×C5×C8) |
| derived | C3 ⋊ C2×C3×C5×C8 |
| Hall | C32×C5 ⋊ C2×C8 |
| Sylow | C32 ⋊ C2×C5×C8 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic5×C3⋊C8, C3×#90951, C3×#90952, … |
| maximal normal subgroup of | C3×Dic5×C3⋊C8, C3×#90951, C3×#90952, … |
| maximal quotient of | C3×C4×C5×C3⋊C8, C3×C5×C4⋊(C3⋊C8), C2×C3×C5×C3⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 324);