Finite Group DatabasebetaFinite Group Databasebeta| order | 30932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(C19⋊#3866) |
| unambiguous semidirect product | C19⋊(C11⋊#3866) |
| Fitting, socle, derived, Hall | C11×C19×C37 ⋊ C4 |
| Hall | C19×C37 ⋊ Dic11 |
| Hall | C11×C37 ⋊ Dic19 |
| Hall | C11×C19 ⋊ #3866 |
| Sylow | C37 ⋊ Dic209 |
| Sylow | C19 ⋊ C11⋊#3866 |
| Sylow | C11 ⋊ C19⋊#3866 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C19×C37 | C4 |
| prime radical, cosocle | C11×C19×D37 | C2 |
| LCS | G ▷ C11×C19×C37 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7733 |
Polycyclic presentation:
2^2,11,19,37|a^2=b,c^a=c^10,d^a=d^18,e^a=e^31,e^b=e^362093 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30932, 15);