Finite Group DatabasebetaFinite Group Databasebeta| order | 15884 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C11⋊(C19⋊Dic19) |
| unambiguous semidirect product | C19⋊Dic209 |
| derived, Hall | C11×C192 ⋊ C4 |
| Sylow | C192 ⋊ Dic11 |
| Sylow | C11 ⋊ C19⋊Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊(C19⋊D19) |
| commutator, hypocenter | C11×C192 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C11×C192 | C2 |
| LCS | G ▷ C11×C192 | |
| UCS | C1 ◁ C2 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15884 |
Polycyclic presentation:
2,11,19^2,2|a^2=e,b^a=b^10,c^a=c^18,d^a=d^183974 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15884, 15);