Finite Group DatabasebetaFinite Group Databasebeta| order | 33354 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊(#11758279⋊C2) |
| unambiguous semidirect product | #11758279⋊D17 |
| derived, Hall | C17×C109 ⋊ C2×C9 |
| Hall | C17×#11758279 ⋊ C2 |
| Hall | D1853 ⋊ C9 |
| Hall | #11758279 ⋊ D17 |
| Sylow | C109 ⋊ C9×D17 |
| Sylow | C17 ⋊ #11758279⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C17⋊(D109⋊C3) |
| commutator, hypocenter | C17×C109 | C2×C9 |
| Fitting, socle, cosocle | C3×C17×C109 | C2×C3 |
| prime radical | C3×D1853 | C3 |
| LCS | G ▷ C17×C109 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16677 |
Polycyclic presentation:
2,3,17,109,3|b^3=e,c^a=c^16,d^a=d^108,d^b=d^631008 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33354, 12);