Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C9×#170 |
| derived, Sylow | C5 ⋊ C2×C8×C9 |
| Hall | C5×C9 ⋊ C2×C8 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 720 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | Dic9×#170, Dic9⋊#170, #13083930, … |
| maximal normal subgroup of | Dic9×#170, Dic9⋊#170, #13083930, … |
| maximal quotient of | C2×C9×#674, C9×#3998, C4×C9×#170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 115);