Finite Group DatabasebetaFinite Group Databasebeta| order | 19521 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C3 |
| direct product | C27×C241⋊C3 |
| Fitting | C27×C241 ⋊ C3 |
| derived, Sylow | C241 ⋊ C3×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C27 | C241⋊C3 |
| commutator, hypocenter | C241 | C3×C27 |
| Frattini | C9 | C3×C241⋊C3 |
| Fitting | C27×C241 | C3 |
| socle | C3×C241 | C3×C9 |
| prime radical | C3×C241⋊C3 | C9 |
| cosocle | C9×C241 | C32 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C27 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6507 |
2241 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19521, 23);