Finite Group DatabasebetaFinite Group Databasebeta| order | 32307 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C121 · Schur multiplier (H2) = C1 |
| direct product | C3×C89⋊C121 |
| unambiguous semidirect product | C89⋊(C3×C121) |
| unambiguous semidirect product | (C3×C89)⋊C121 |
| derived, Sylow | C89 ⋊ C3×C121 |
| Hall | C3×C89 ⋊ C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | C89⋊C11 |
| commutator, hypocenter | C89 | C3×C121 |
| Frattini | C11 | C3×C89⋊C11 |
| Fitting, socle, prime radical | C3×C11×C89 | C11 |
| cosocle | C11×C89 | C3×C11 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C3×C11 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32307 |
627 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32307, 2);