Finite Group DatabasebetaFinite Group Databasebeta| order | 34335 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×#11758281 |
| Fitting, socle, Hall | C5×C7×C109 ⋊ C9 |
| derived, Sylow | C109 ⋊ C5×C7×C9 |
| Hall | C7×C109 ⋊ C5×C9 |
| Hall | C5×C109 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | #11758281 |
| commutator, hypocenter | C109 | C5×C7×C9 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C109 | C9 |
| prime radical | C5×C7×C109⋊C3 | C3 |
| cosocle | C109⋊C3 | C3×C5×C7 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C5×C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3815 |
735 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34335, 7);