Finite Group DatabasebetaFinite Group Databasebeta| order | 33354 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊(#11758281⋊C2) |
| unambiguous semidirect product | #11758281⋊D17 |
| Fitting, socle, derived, Hall | C17×C109 ⋊ C2×C9 |
| Hall | C17×#11758281 ⋊ C2 |
| Hall | D1853 ⋊ C9 |
| Hall | #11758281 ⋊ D17 |
| Sylow | C109 ⋊ C9×D17 |
| Sylow | C17 ⋊ #11758281⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C109 | C2×C9 |
| prime radical | C17⋊(D109⋊C3) | C3 |
| cosocle | C17×C109⋊C3 | C2×C3 |
| LCS | G ▷ C17×C109 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1853 |
Polycyclic presentation:
2,3^2,17,109|b^3=c,d^a=d^16,e^a=e^108,e^b=e^16,e^c=e^63192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33354, 15);