Finite Group DatabasebetaFinite Group Databasebeta| order | 23826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C19 |
| direct product | C11×C3⋊(C19⋊D19) |
| unambiguous semidirect product | C3⋊(C11×C19⋊D19) |
| unambiguous semidirect product | C19⋊(C11×D57) |
| Fitting, socle, Hall | C3×C11×C192 ⋊ C2 |
| derived, Hall | C3×C192 ⋊ C2×C11 |
| Hall | C11×C192 ⋊ D3 |
| Sylow | C192 ⋊ D3×C11 |
| Hall | C3×C11 ⋊ C19⋊D19 |
| Sylow | C3 ⋊ C11×C19⋊D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C3⋊(C19⋊D19) |
| commutator, cosocle, hypocenter | C3×C192 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C192 | C2 |
| LCS | G ▷ C3×C192 | |
| UCS | C1 ◁ C11 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11913 |
5973 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23826, 43);