Finite Group DatabasebetaFinite Group Databasebeta| order | 17340 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×#11923883 |
| Fitting, socle, Hall | C3×C5×C172 ⋊ C4 |
| derived, Sylow | C172 ⋊ C3×C4×C5 |
| Hall | C5×C172 ⋊ C3×C4 |
| Hall | C3×C172 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | #11923883 |
| commutator, hypocenter | C172 | C3×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C172 | C4 |
| prime radical | C3×C5×C17⋊D17 | C2 |
| cosocle | C17⋊D17 | C2×C3×C5 |
| LCS | G ▷ C172 | |
| UCS | C1 ◁ C3×C5 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4335 |
1140 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17340, 77);