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 |
No aliases for this group.
| derived, Hall | C5×C9 ⋊ C2×C8 |
| Sylow | C9 ⋊ D5⋊C8 |
| Sylow | C5 ⋊ C8×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×AGL(1,𝔽5) |
| commutator, hypocenter | C5×C9 | C2×C8 |
| Frattini | C2×C3 | D3×AGL(1,𝔽5) |
| Fitting | C2×C5×C9 | C2×C4 |
| socle | C2×C3×C5 | C4×D3 |
| prime radical | C2×D45 | C4 |
| cosocle | C9×Dic5 | C22 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C2 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^4,3,5,3|a^2=c,b^2=d,c^2=d,e^3=g,f^a=f^2,e^b=e^2g^2,g^b=g^2,f^c=f^460 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D5⋊C8, #13085165, #13085166, … |
| maximal normal subgroup of | D9×D5⋊C8, #13085165, #13085166, … |
| maximal quotient of | #13083907, #13083909, Dic9×#170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 96);