Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×(C2×D3)⋊C4 |
| unambiguous semidirect product | (C2×D3)⋊(C3×C4×C5) |
| Fitting | C2×C32×C4×C5 ⋊ C2 |
| Hall | C32×C5 ⋊ C22⋊C4 |
| Sylow | C32 ⋊ C5×C22⋊C4 |
152 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 152 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×#91341, C3×#91342, C3×#91372, … |
| maximal normal subgroup of | C3×#91341, C3×#91342, C3×#91372, … |
| maximal quotient of | C3×C5×#805, C3×C5×#806, C3×C5×#809, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 329);