Finite Group DatabasebetaFinite Group Databasebeta| order | 32300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊#13133352 |
| Fitting, socle, derived, Hall | C52×C17×C19 ⋊ C4 |
| Hall | C52×C19 ⋊ Dic17 |
| Hall | C52×C17 ⋊ Dic19 |
| Hall | C17×C19 ⋊ #1042 |
| Sylow | C52 ⋊ Dic323 |
| Sylow | C19 ⋊ #13133352 |
| Sylow | C17 ⋊ C19⋊#1042 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C17×C19 | C4 |
| prime radical, cosocle | C5×D5×C17×C19 | C2 |
| LCS | G ▷ C52×C17×C19 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6460 |
Polycyclic presentation:
2^2,5^2,17,19|a^2=b,c^a=c^2,d^a=d^4,e^a=e^16,f^a=f^18,c^b=c^43233 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32300, 75);