Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
| direct product | Dic19×C112⋊C3 |
| derived, Hall | C112×C19 ⋊ C3×C4 |
| Hall | C112×Dic19 ⋊ C3 |
| Hall | C19×C112⋊C3 ⋊ C4 |
| Sylow | C112 ⋊ C3×Dic19 |
| Sylow | C19 ⋊ C4×C112⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D19×C112⋊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 |
946 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 48);