Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | (C19⋊C3)⋊#92150 |
| Fitting, socle, derived, Hall | C112×C19 ⋊ C3×C4 |
| Hall | C19⋊#92150 ⋊ C3 |
| Hall | C112×C19⋊C3 ⋊ C4 |
| Sylow | C112 ⋊ (C19⋊C3)⋊C4 |
| Hall | C19⋊C3 ⋊ #92150 |
| Sylow | C19 ⋊ C3×#92150 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C112×C19 | C3×C4 |
| prime radical | C19⋊C3×C11⋊D11 | C2 |
| cosocle | C19×C11⋊D11 | C2×C3 |
| LCS | G ▷ C112×C19 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 418 |
Polycyclic presentation:
2,3,2,11^2,19|a^2=c,d^a=d^8e^8,e^a=d^7e^3,f^a=f^18,f^b=f^7,d^c=d^10,e^c=e^10288 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 64);