Finite Group DatabasebetaFinite Group Databasebeta| order | 23199 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11×C37 · Schur multiplier (H2) = C1 |
| direct product | C11×C37×C19⋊C3 |
| unambiguous semidirect product | C19⋊(C3×C11×C37) |
| unambiguous semidirect product | (C11×C19)⋊(C3×C37) |
| Fitting, socle, Hall | C11×C19×C37 ⋊ C3 |
| derived, Sylow | C19 ⋊ C3×C11×C37 |
| Hall | C19×C37 ⋊ C3×C11 |
| Hall | C11×C19 ⋊ C3×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C37 | C19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C3×C11×C37 |
| Frattini | C1 | G |
| Fitting, socle | C11×C19×C37 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C11×C37 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7733 |
3663 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23199, 3);