Finite Group DatabasebetaFinite Group Databasebeta| order | 19532 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊#11759967 |
| Fitting, socle, derived, Hall | C19×C257 ⋊ C4 |
| Sylow | C257 ⋊ Dic19 |
| Sylow | C19 ⋊ #11759967 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C257 | C4 |
| prime radical, cosocle | C19×D257 | C2 |
| LCS | G ▷ C19×C257 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4883 |
Polycyclic presentation:
2^2,19,257|a^2=b,c^a=c^18,d^a=d^241,d^b=d^2561238 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19532, 7);