Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C32×C22⋊D5 |
| Fitting | C23×C32×C5 ⋊ C2 |
| Hall | C32×C5 ⋊ C2×D4 |
| Sylow | C5 ⋊ C2×C32×D4 |
324 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#90995, #13084763, C32×#3938, … |
| maximal normal subgroup of | C3×#90995, #13084763, C32×#3938, … |
| maximal quotient of | C2×C32×#683, C32×#4070, C2×C32×#685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 718);