Finite Group DatabasebetaFinite Group Databasebeta| order | 19684 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D133⋊D37 |
| unambiguous semidirect product | D259⋊D19 |
| unambiguous semidirect product | D703⋊D7 |
| Fitting, socle, derived, Hall | C7×C19×C37 ⋊ C22 |
| Hall | C19×C37 ⋊ C2×D7 |
| Hall | C7×C37 ⋊ C2×D19 |
| Hall | C7×C19 ⋊ C2×D37 |
| Sylow | C37 ⋊ D7×D19 |
| Sylow | C19 ⋊ D7×D37 |
| Sylow | C7 ⋊ D19×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C19×C37 | C22 |
| LCS | G ▷ C7×C19×C37 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4921 |
Polycyclic presentation:
2^2,7,19,37|d^a=d^18,e^a=e^36,c^b=c^6,d^b=d^181279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19684, 20);