Finite Group DatabasebetaFinite Group Databasebeta| order | 33354 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C109 · Schur multiplier (H2) = C3 |
| direct product | C109×C3⋊D51 |
| unambiguous semidirect product | C3⋊(D51×C109) |
| unambiguous semidirect product | C17⋊(C3⋊D3×C109) |
| Fitting, socle, Hall | C32×C17×C109 ⋊ C2 |
| derived, Hall | C32×C17 ⋊ C2×C109 |
| Hall | C17×C109 ⋊ C3⋊D3 |
| Hall | C32×C109 ⋊ D17 |
| Sylow | C17 ⋊ C3⋊D3×C109 |
| Sylow | C32 ⋊ D17×C109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C109 | C3⋊D51 |
| commutator, cosocle, hypocenter | C32×C17 | C2×C109 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C109 | C2 |
| LCS | G ▷ C32×C17 | |
| UCS | C1 ◁ C109 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16677 |
8502 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33354, 35);