Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C3⋊(C11⋊Dic209) |
| unambiguous semidirect product | C11⋊Dic627 |
| unambiguous semidirect product | C19⋊(C3⋊(C11⋊Dic11)) |
| derived, Hall | C3×C112×C19 ⋊ C4 |
| Hall | C112×C19 ⋊ Dic3 |
| Hall | C3×C112 ⋊ Dic19 |
| Sylow | C112 ⋊ Dic57 |
| Hall | C3×C19 ⋊ C11⋊Dic11 |
| Sylow | C19 ⋊ C3⋊(C11⋊Dic11) |
| Sylow | C3 ⋊ C11⋊Dic209 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C11⋊D209) |
| commutator, hypocenter | C3×C112×C19 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C112×C19 | C2 |
| LCS | G ▷ C3×C112×C19 | |
| UCS | C1 ◁ C2 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27588 |
Polycyclic presentation:
2,3,11^2,19,2|a^2=f,b^a=b^2,c^a=c^10,d^a=d^10,e^a=e^186900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 52);