Finite Group DatabasebetaFinite Group Databasebeta| order | 28677 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C121 · Schur multiplier (H2) = C1 |
| direct product | C121×C79⋊C3 |
| unambiguous semidirect product | C79⋊(C3×C121) |
| unambiguous semidirect product | (C79×C121)⋊C3 |
| Fitting, Hall | C79×C121 ⋊ C3 |
| derived, Sylow | C79 ⋊ C3×C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C121 | C79⋊C3 |
| commutator, hypocenter | C79 | C3×C121 |
| Frattini | C11 | C11×C79⋊C3 |
| Fitting | C79×C121 | C3 |
| socle, cosocle | C11×C79 | C3×C11 |
| prime radical | C11×C79⋊C3 | C11 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C121 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9559 |
3509 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28677, 2);