Finite Group DatabasebetaFinite Group Databasebeta| order | 17340 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#19153591 |
| Fitting, Hall | C3×C5×C289 ⋊ C4 |
| derived, Hall | C5×C289 ⋊ C3×C4 |
| Hall | C3×C289 ⋊ AGL(1,𝔽5) |
| Sylow | C289 ⋊ C3×AGL(1,𝔽5) |
| Hall | C3×C5 ⋊ #11923876 |
| Sylow | C5 ⋊ C3×#11923876 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #19153591 |
| commutator, hypocenter | C5×C289 | C3×C4 |
| Frattini | C17 | C3×#66776 |
| Fitting | C3×C5×C289 | C4 |
| socle | C3×C5×C17 | #595 |
| prime radical | C3×D1445 | C2 |
| cosocle | D1445 | C2×C3 |
| LCS | G ▷ C5×C289 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4335 |
1095 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17340, 13);