Finite Group DatabasebetaFinite Group Databasebeta| order | 33060 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×Dic285 |
| unambiguous semidirect product | C3⋊(C29×Dic95) |
| unambiguous semidirect product | C19⋊(C29×Dic15) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C29 | D285 |
| commutator, hypocenter | C3×C5×C19 | C4×C29 |
| Frattini | C2 | C29×D285 |
| Fitting, socle, prime radical | C2×C3×C5×C19×C29 | C2 |
| cosocle | C2×C3×C5×C19 | C2×C29 |
| LCS | G ▷ C3×C5×C19 | |
| UCS | C1 ◁ C2×C29 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33060 |
8352 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33060, 16);