Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C11⋊(D19⋊C3))⋊D11 |
| unambiguous semidirect product | ((C11⋊D11)⋊D19)⋊C3 |
| Fitting, socle, derived, Hall | C112×C19 ⋊ C22×C3 |
| Hall | (C11⋊D11)⋊D19 ⋊ C3 |
| Hall | C112×C19⋊C3 ⋊ C22 |
| Sylow | C112 ⋊ C2×D19⋊C3 |
| Hall | C19⋊C3 ⋊ D112 |
| Sylow | C19 ⋊ C3×D112 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C19 | C22×C3 |
| LCS | G ▷ C112×C19 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 418 |
Polycyclic presentation:
2^2,3,11^2,19|d^a=d^10,f^a=f^18,d^b=d^10,e^b=e^10,f^c=f^7333 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 80);