Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | C22⋊(C52⋊#4296) |
| unambiguous semidirect product | C52⋊(C22⋊#4296) |
| Fitting, socle, derived, Hall | C22×C52×C19 ⋊ C9 |
| Hall | C52×C19 ⋊ C22⋊C9 |
| Hall | C22×C52 ⋊ #4296 |
| Hall | C22×C19 ⋊ C52⋊C9 |
| Sylow | C52 ⋊ C22⋊#4296 |
| Sylow | C19 ⋊ C22⋊(C52⋊C9) |
| Sylow | C22 ⋊ C52⋊#4296 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C22×C52×C19 | C9 |
| prime radical, cosocle | C22×C52×C19⋊C3 | C3 |
| LCS | G ▷ C22×C52×C19 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 570 |
Polycyclic presentation:
3^2,2^2,5^2,19|a^3=b,c^a=d,d^a=cd,e^a=ef^2,f^a=ef^3,g^a=g^4,g^b=g^7308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 457);