Finite Group DatabasebetaFinite Group Databasebeta| order | 17340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C3⋊#19153601 |
| derived, Hall | C3×C5×C172 ⋊ C4 |
| Hall | C5×C172 ⋊ Dic3 |
| Hall | C3×C172 ⋊ Dic5 |
| Sylow | C172 ⋊ Dic15 |
| Hall | C3×C5 ⋊ #11923880 |
| Sylow | C5 ⋊ C3⋊#11923880 |
| Sylow | C3 ⋊ #19153601 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C5⋊(C17⋊D17)) |
| commutator, hypocenter | C3×C5×C172 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C172 | C2 |
| LCS | G ▷ C3×C5×C172 | |
| UCS | C1 ◁ C2 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17340 |
Polycyclic presentation:
2,3,5,17^2,2|a^2=f,b^a=b^2,c^a=c^4,d^a=d^16,e^a=e^164338 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17340, 54);