Finite Group DatabasebetaFinite Group Databasebeta| order | 33354 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C109 · Schur multiplier (H2) = C1 |
| direct product | C3×D51×C109 |
| unambiguous semidirect product | C3⋊(C3×D17×C109) |
| unambiguous semidirect product | C17⋊(C3×D3×C109) |
| Fitting, socle, Hall | C32×C17×C109 ⋊ C2 |
| derived | C3×C17 ⋊ C2×C3×C109 |
| Hall | C17×C109 ⋊ C3×D3 |
| Hall | C32×C109 ⋊ D17 |
| Hall | C32×C17 ⋊ C2×C109 |
| Sylow | C17 ⋊ C3×D3×C109 |
| Sylow | C32 ⋊ D17×C109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C109 | D51 |
| commutator, cosocle, hypocenter | C3×C17 | C2×C3×C109 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C109 | C2 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C3×C109 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11118 |
8829 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33354, 31);