Finite Group DatabasebetaFinite Group Databasebeta| order | 8580 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C11⋊#63120) |
| unambiguous semidirect product | C11⋊(C3⋊#63120) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C11×C13 | C4 |
| LCS | G ▷ C3×C5×C11×C13 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,11,13|a^2=b,c^a=c^2,d^a=d^2,e^a=e^10,f^a=f^12,d^b=d^4861 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8580, 126);