Finite Group DatabasebetaFinite Group Databasebeta| order | 25821 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C19 · Schur multiplier (H2) = C3 |
| direct product | C3×C19×C151⋊C3 |
| unambiguous semidirect product | C151⋊(C32×C19) |
| unambiguous semidirect product | (C3×C151)⋊(C3×C19) |
| Fitting, socle | C3×C19×C151 ⋊ C3 |
| derived, Sylow | C151 ⋊ C32×C19 |
| Hall | C19×C151 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C19 | C151⋊C3 |
| commutator, cosocle, hypocenter | C151 | C32×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C151 | C3 |
| LCS | G ▷ C151 | |
| UCS | C1 ◁ C3×C19 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8607 |
3021 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25821, 11);