Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
| direct product | C3×C11⋊Dic209 |
| unambiguous semidirect product | C11⋊(C3×Dic209) |
| derived, Hall | C112×C19 ⋊ C3×C4 |
| Hall | C3×C112×C19 ⋊ C4 |
| Hall | C3×C112 ⋊ Dic19 |
| Sylow | C112 ⋊ C3×Dic19 |
| Hall | C3×C19 ⋊ C11⋊Dic11 |
| Sylow | C19 ⋊ C3×C11⋊Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C11⋊D209 |
| commutator, hypocenter | C112×C19 | C3×C4 |
| Frattini | C2 | C3×C11⋊D209 |
| Fitting, socle, prime radical | C2×C3×C112×C19 | C2 |
| cosocle | C2×C112×C19 | C2×C3 |
| LCS | G ▷ C112×C19 | |
| UCS | C1 ◁ C2×C3 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27588 |
6906 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 58);