Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D57⋊D121 |
| unambiguous semidirect product | D363⋊D19 |
| unambiguous semidirect product | D2299⋊D3 |
| Fitting, derived, Hall | C3×C19×C121 ⋊ C22 |
| Hall | C19×C121 ⋊ C2×D3 |
| Hall | C3×C121 ⋊ C2×D19 |
| Sylow | C121 ⋊ D3×D19 |
| Hall | C3×C19 ⋊ C2×D121 |
| Sylow | C19 ⋊ D3×D121 |
| Sylow | C3 ⋊ D19×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C19×C121 | C22 |
| Frattini | C11 | D33⋊D19 |
| socle | C3×C11×C19 | C2×D11 |
| LCS | G ▷ C3×C19×C121 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6897 |
Polycyclic presentation:
2^2,3,11,19,11|d^11=f^10,d^a=d^10f,e^a=e^18,f^a=f^10,c^b=c^2,d^b=d^10f,f^b=f^101833 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 24);