Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of D5×AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | D5×AGL(1,𝔽9) |
| Fitting, socle, derived, Hall | C32×C5 ⋊ C2×C8 |
| Sylow | C32 ⋊ C8×D5 |
| Sylow | C5 ⋊ C2×AGL(1,𝔽9) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5 | C2×C8 |
| prime radical | D5×C3⋊D3 | C4 |
| cosocle | C5×#157 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 45 |
36 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 778);