Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | D171⋊(C5⋊D5) |
| Fitting, derived, Hall | C52×C9×C19 ⋊ C22 |
| Hall | C52×C19 ⋊ C2×D9 |
| Hall | C52×C9 ⋊ C2×D19 |
| Hall | C9×C19 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ D9×D19 |
| Sylow | C19 ⋊ D9×C5⋊D5 |
| Sylow | C9 ⋊ D19×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C52×C9×C19 | C22 |
| Frattini | C3 | D57⋊(C5⋊D5) |
| socle | C3×C52×C19 | C2×D3 |
| LCS | G ▷ C52×C9×C19 | |
| UCS | C1 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4275 |
Polycyclic presentation:
2^2,3,5^2,19,3|c^3=g^2,d^a=d^4,e^a=e^4,f^a=f^18,c^b=c^2g,d^b=d^4,e^b=e^4,g^b=g^21110 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 240);