Finite Group DatabasebetaFinite Group Databasebeta| order | 33060 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C19⋊C3×#1181 |
| unambiguous semidirect product | (C19×#1181)⋊(C3×C5) |
| unambiguous semidirect product | (C5×C19×#1181)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C19⋊C3×#1181 |
| commutator, hypocenter | C19×C29 | C3×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C29 | C3×C4 |
| prime radical | C5×C19⋊C3×D29 | C2 |
| cosocle | C19×D29 | C2×C3×C5 |
| LCS | G ▷ C19×C29 | |
| UCS | C1 ◁ C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2755 |
495 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33060, 28);