Finite Group DatabasebetaFinite Group Databasebeta| order | 19684 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C19⋊#3866) |
| unambiguous semidirect product | C19⋊(C7⋊#3866) |
| Fitting, socle, derived, Hall | C7×C19×C37 ⋊ C4 |
| Hall | C19×C37 ⋊ Dic7 |
| Hall | C7×C37 ⋊ Dic19 |
| Hall | C7×C19 ⋊ #3866 |
| Sylow | C37 ⋊ Dic133 |
| Sylow | C19 ⋊ C7⋊#3866 |
| Sylow | C7 ⋊ C19⋊#3866 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C19×C37 | C4 |
| prime radical, cosocle | C7×C19×D37 | C2 |
| LCS | G ▷ C7×C19×C37 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4921 |
Polycyclic presentation:
2^2,7,19,37|a^2=b,c^a=c^6,d^a=d^18,e^a=e^31,e^b=e^361333 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19684, 15);