Finite Group DatabasebetaFinite Group Databasebeta| order | 32300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊#13133323 |
| Fitting, derived, Hall | C17×C19×C25 ⋊ C4 |
| Hall | C19×C25 ⋊ #595 |
| Hall | C17×C25 ⋊ Dic19 |
| Hall | C17×C19 ⋊ #1035 |
| Sylow | C25 ⋊ C19⋊#595 |
| Sylow | C19 ⋊ #13133323 |
| Sylow | C17 ⋊ C19⋊#1035 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C17×C19×C25 | C4 |
| Frattini | C5 | C19⋊#66775 |
| socle | C5×C17×C19 | AGL(1,𝔽5) |
| prime radical, cosocle | C19×D425 | C2 |
| LCS | G ▷ C17×C19×C25 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8075 |
Polycyclic presentation:
2^2,5,17,19,5|a^2=b,c^5=f,c^a=c^2f,d^a=d^13,e^a=e^18,f^a=f^2,c^b=c^4f^4,d^b=d^16,f^b=f^42036 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32300, 16);