Finite Group DatabasebetaFinite Group Databasebeta| order | 34542 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C3×C19×D303 |
| unambiguous semidirect product | C3⋊(C3×C19×D101) |
| unambiguous semidirect product | C101⋊(C3×D3×C19) |
| Fitting, socle, Hall | C32×C19×C101 ⋊ C2 |
| derived | C3×C101 ⋊ C2×C3×C19 |
| Hall | C19×C101 ⋊ C3×D3 |
| Hall | C32×C101 ⋊ C2×C19 |
| Hall | C32×C19 ⋊ D101 |
| Sylow | C101 ⋊ C3×D3×C19 |
| Sylow | C32 ⋊ C19×D101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C19 | D303 |
| commutator, cosocle, hypocenter | C3×C101 | C2×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C32×C19×C101 | C2 |
| LCS | G ▷ C3×C101 | |
| UCS | C1 ◁ C3×C19 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11514 |
8721 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34542, 30);