Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of D9×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | D9×#170 |
| derived, Hall | C5×C9 ⋊ C2×C8 |
| Sylow | C9 ⋊ C2×#170 |
| Sylow | C5 ⋊ C8×D9 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D5⋊C8, #13085162, D9×#700, … |
| maximal normal subgroup of | D9×D5⋊C8, #13085162, D9×#700, … |
| maximal quotient of | D9×#674, #13083908, Dic9×#170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 95);