Finite Group DatabasebetaFinite Group Databasebeta| order | 34119 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×C223⋊C9 |
| unambiguous semidirect product | C223⋊(C9×C17) |
| unambiguous semidirect product | (C17×C223)⋊C9 |
| derived, Sylow | C223 ⋊ C9×C17 |
| Hall | C17×C223 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C17 | C223⋊C3 |
| commutator, hypocenter | C223 | C9×C17 |
| Frattini | C3 | C17×C223⋊C3 |
| Fitting, socle, prime radical | C3×C17×C223 | C3 |
| cosocle | C3×C223 | C3×C17 |
| LCS | G ▷ C223 | |
| UCS | C1 ◁ C3×C17 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 34119 |
3927 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34119, 2);