Finite Group DatabasebetaFinite Group Databasebeta| order | 8580 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D55⋊(D13⋊C3) |
| unambiguous semidirect product | (C5⋊(D13⋊C3))⋊D11 |
| unambiguous semidirect product | (C11⋊(D13⋊C3))⋊D5 |
| unambiguous semidirect product | (D55⋊D13)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C11×C13 | C22×C3 |
| LCS | G ▷ C5×C11×C13 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,11,13|e^a=e^10,f^a=f^12,d^b=d^4,e^b=e^10,f^c=f^3142 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D55⋊(D13⋊C3), (C11⋊(D13⋊C3))⋊D15, (C5⋊(D13⋊C3))⋊D33, … |
| maximal normal subgroup of | C3×D55⋊(D13⋊C3) |
| maximal quotient of | D55⋊(D13⋊C9), C3×D55⋊(D13⋊C3), (C11⋊(D13⋊C3))⋊D15, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8580, 75);