Finite Group DatabasebetaFinite Group Databasebeta| order | 17340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C17 |
| direct product | C5×#16812402 |
| Fitting, socle, Hall | C5×C172 ⋊ Dic3 |
| derived, Hall | C172⋊C3 ⋊ C4×C5 |
| Hall | C5×C172⋊C3 ⋊ C4 |
| Sylow | C172 ⋊ C5×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #16812402 |
| commutator, hypocenter | C172⋊C3 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C172 | Dic3 |
| prime radical | C5×(C17⋊D17)⋊C3 | C2 |
| cosocle | (C17⋊D17)⋊C3 | C2×C5 |
| LCS | G ▷ C172⋊C3 | |
| UCS | C1 ◁ C5 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 255 |
150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17340, 57);