Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C112 · Schur multiplier (H2) = C11 |
| direct product | C112×Dic57 |
| unambiguous semidirect product | C3⋊(C112×Dic19) |
| unambiguous semidirect product | C19⋊(C112×Dic3) |
| derived, Hall | C3×C19 ⋊ C4×C112 |
| Hall | C3×C112×C19 ⋊ C4 |
| Hall | C112×C19 ⋊ Dic3 |
| Hall | C3×C112 ⋊ Dic19 |
| Sylow | C19 ⋊ C112×Dic3 |
| Sylow | C3 ⋊ C112×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C112 | D57 |
| commutator, hypocenter | C3×C19 | C4×C112 |
| Frattini | C2 | C112×D57 |
| Fitting, socle, prime radical | C2×C3×C112×C19 | C2 |
| cosocle | C2×C3×C19 | C2×C112 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C2×C112 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27588 |
7260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 56);