Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of D9×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| Fitting | C2×C5×C9 ⋊ C2×C4 |
| derived, Hall | C5×C9 ⋊ C22×C4 |
| Sylow | C9 ⋊ C22×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×C4×D9 |
162 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 90 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D9×AGL(1,𝔽5), AGL(1,𝔽5)×D36, D9×C4⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | C4×D9×AGL(1,𝔽5), AGL(1,𝔽5)×D36, D9×C4⋊AGL(1,𝔽5), … |
| maximal quotient of | D9×D5⋊C8, #13085162, D9×#700, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 395);