Finite Group DatabasebetaFinite Group Databasebeta| order | 23845 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×C251⋊C5 |
| unambiguous semidirect product | C251⋊(C5×C19) |
| unambiguous semidirect product | (C19×C251)⋊C5 |
| Fitting, socle, Hall | C19×C251 ⋊ C5 |
| derived, Sylow | C251 ⋊ C5×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | C251⋊C5 |
| commutator, cosocle, hypocenter | C251 | C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C251 | C5 |
| LCS | G ▷ C251 | |
| UCS | C1 ◁ C19 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4769 |
1045 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23845, 1);