Finite Group DatabasebetaFinite Group Databasebeta| order | 33354 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D17×#11758279 |
| unambiguous semidirect product | C17⋊(C2×#11758279) |
| derived, Hall | C17×C109 ⋊ C2×C9 |
| Hall | C17×#11758279 ⋊ C2 |
| Hall | D17×C109 ⋊ C9 |
| Sylow | C109 ⋊ C9×D17 |
| Sylow | C17 ⋊ C2×#11758279 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D17×C109⋊C3 |
| commutator, hypocenter | C17×C109 | C2×C9 |
| Fitting, socle, cosocle | C3×C17×C109 | C2×C3 |
| prime radical | C3×D17×C109 | C3 |
| LCS | G ▷ C17×C109 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16677 |
1170 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33354, 11);