Finite Group DatabasebetaFinite Group Databasebeta| order | 8580 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D33⋊D65 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C11×C13 | C22 |
| LCS | G ▷ C3×C5×C11×C13 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,11,13|d^a=d^4,e^a=e^10,f^a=f^12,c^b=c^2,e^b=e^10597 conjugacy classes — view the full character table.
| maximal subgroup of | D99⋊D65, D33⋊(C5⋊(D13⋊C3)), C3×D33⋊D65, … |
| maximal normal subgroup of | D33⋊(C5⋊(D13⋊C3)), C3×D33⋊D65 |
| maximal quotient of | D99⋊D65, C3×D33⋊D65, D33⋊D195, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8580, 149);