Finite Group DatabasebetaFinite Group Databasebeta| order | 23829 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13×C47 · Schur multiplier (H2) = C1 |
| direct product | C13×C13⋊C3×C47 |
| unambiguous semidirect product | C13⋊(C3×C13×C47) |
| unambiguous semidirect product | (C13×C47)⋊(C3×C13) |
| Fitting, socle, Hall | C132×C47 ⋊ C3 |
| derived | C13 ⋊ C3×C13×C47 |
| Sylow | C132 ⋊ C3×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C47 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C3×C13×C47 |
| Frattini | C1 | G |
| Fitting, socle | C132×C47 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C13×C47 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1833 |
4277 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23829, 4);