Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×Dic3⋊C4 |
| unambiguous semidirect product | Dic3⋊(C3×C4×C5) |
| Hall | C32×C5 ⋊ C4⋊C4 |
| Sylow | C32 ⋊ C5×C4⋊C4 |
120 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#91334, C3×#91339, C3×#91343, … |
| maximal normal subgroup of | C3×#91334, C3×#91339, C3×#91343, … |
| maximal quotient of | C3×C5×#807, C3×C5×#808, C3×C5×Dic3⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 327);