Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#19152833 |
| Fitting, socle, derived | C3×C52×C19 ⋊ C3×C4 |
| Hall | C3×C19×C52⋊C3 ⋊ C4 |
| Hall | C52×C19 ⋊ C3×Dic3 |
| Hall | C3×C52⋊C3 ⋊ Dic19 |
| Sylow | C52 ⋊ C3×Dic57 |
| Sylow | C19 ⋊ C3⋊(#1043⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C19 | C3×C4 |
| prime radical | C3×C19×(C5⋊D5)⋊C3 | C2 |
| cosocle | C3×C19×C5⋊D5 | C2×C3 |
| LCS | G ▷ C3×C52×C19 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 855 |
Polycyclic presentation:
2,3,2,3,5^2,19|a^2=c,d^a=d^2,e^a=e^3,f^a=f^3,g^a=g^18,e^b=e^3f^3,f^b=e^4f,e^c=e^4,f^c=f^4294 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 437);