Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of C3⋊ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | D5⋊(C3⋊(C3⋊C8)) |
| derived, Hall | C32×C5 ⋊ C2×C8 |
| Sylow | C32 ⋊ D5⋊C8 |
| Sylow | C5 ⋊ C2×C3⋊(C3⋊C8) |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^4,3^2,5|a^2=c,b^2=d,c^2=d,e^a=e^2,f^a=f^2,g^a=g^3,g^c=g^484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 561);