Finite Group DatabasebetaFinite Group Databasebeta| order | 32300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C19⋊#13133347 |
| Fitting, socle, derived, Hall | C52×C17×C19 ⋊ C4 |
| Hall | C52×C19 ⋊ #595 |
| Hall | C52×C17 ⋊ Dic19 |
| Hall | C17×C19 ⋊ #1044 |
| Sylow | C52 ⋊ C19⋊#595 |
| Sylow | C19 ⋊ #13133347 |
| Sylow | C17 ⋊ C19⋊#1044 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C17×C19 | C4 |
| prime radical, cosocle | C19×C5⋊D85 | C2 |
| LCS | G ▷ C52×C17×C19 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3230 |
Polycyclic presentation:
2^2,5^2,17,19|a^2=b,c^a=c^2,d^a=d^3,e^a=e^13,f^a=f^18,c^b=c^4,d^b=d^4,e^b=e^162036 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32300, 105);