Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | (C11⋊Dic11)⋊(C19⋊C3) |
| derived, Hall | C112×C19 ⋊ C3×C4 |
| Hall | C19×C11⋊Dic11 ⋊ C3 |
| Hall | C19⋊(C112⋊C3) ⋊ C4 |
| Hall | C11⋊Dic11 ⋊ C19⋊C3 |
| Sylow | C112 ⋊ C4×C19⋊C3 |
| Sylow | C19 ⋊ (C11⋊Dic11)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C11⋊D11)⋊(C19⋊C3) |
| commutator, hypocenter | C112×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C112×C19 | C2×C3 |
| prime radical | C2×C19⋊(C112⋊C3) | C2 |
| LCS | G ▷ C112×C19 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2508 |
Polycyclic presentation:
2,3,11^2,19,2|a^2=f,c^a=c^10,d^a=d^10,c^b=c^3d^9,d^b=cd^7,e^b=e^7796 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 45);