Finite Group DatabasebetaFinite Group Databasebeta| order | 33660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3 |
| direct product | C11⋊C5×#10597479 |
| unambiguous semidirect product | (C11×#10597479)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C11×C17 | C4×C5 |
| prime radical | C11⋊C5×C3⋊D51 | C2 |
| cosocle | C11×C3⋊D51 | C2×C5 |
| LCS | G ▷ C32×C11×C17 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1122 |
294 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33660, 162);