Finite Group DatabasebetaFinite Group Databasebeta| order | 16644 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C19⋊#64408) |
| unambiguous semidirect product | C19⋊(C3⋊#64408) |
| Fitting, socle, derived, Hall | C3×C19×C73 ⋊ C4 |
| Hall | C19×C73 ⋊ Dic3 |
| Hall | C3×C73 ⋊ Dic19 |
| Sylow | C73 ⋊ Dic57 |
| Hall | C3×C19 ⋊ #64408 |
| Sylow | C19 ⋊ C3⋊#64408 |
| Sylow | C3 ⋊ C19⋊#64408 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C19×C73 | C4 |
| prime radical, cosocle | C3×C19×D73 | C2 |
| LCS | G ▷ C3×C19×C73 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4161 |
Polycyclic presentation:
2^2,3,19,73|a^2=b,c^a=c^2,d^a=d^18,e^a=e^27,e^b=e^721086 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16644, 55);