Finite Group DatabasebetaFinite Group Databasebeta| order | 15884 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C11⋊#13089659 |
| Fitting, socle, derived, Hall | C11×C192 ⋊ C4 |
| Sylow | C192 ⋊ Dic11 |
| Sylow | C11 ⋊ #13089659 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C192 | C4 |
| prime radical, cosocle | C11×C19⋊D19 | C2 |
| LCS | G ▷ C11×C192 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 418 |
Polycyclic presentation:
2^2,11,19^2|a^2=b,c^a=c^10,d^a=d^12e^14,e^a=d^10e^7,d^b=d^18,e^b=e^181004 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15884, 23);