Finite Group DatabasebetaFinite Group Databasebeta| order | 30932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D209⋊D37 |
| unambiguous semidirect product | D407⋊D19 |
| unambiguous semidirect product | D703⋊D11 |
| Fitting, socle, derived, Hall | C11×C19×C37 ⋊ C22 |
| Hall | C19×C37 ⋊ C2×D11 |
| Hall | C11×C37 ⋊ C2×D19 |
| Hall | C11×C19 ⋊ C2×D37 |
| Sylow | C37 ⋊ D11×D19 |
| Sylow | C19 ⋊ D11×D37 |
| Sylow | C11 ⋊ D19×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C19×C37 | C22 |
| LCS | G ▷ C11×C19×C37 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7733 |
Polycyclic presentation:
2^2,11,19,37|d^a=d^18,e^a=e^36,c^b=c^10,d^b=d^181985 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30932, 20);