Finite Group DatabasebetaFinite Group Databasebeta| order | 22385 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C11×C37 · Schur multiplier (H2) = C1 |
| direct product | C11×C37×C11⋊C5 |
| unambiguous semidirect product | C11⋊(C5×C11×C37) |
| unambiguous semidirect product | (C11×C37)⋊(C5×C11) |
| Fitting, socle, Hall | C112×C37 ⋊ C5 |
| derived | C11 ⋊ C5×C11×C37 |
| Sylow | C112 ⋊ C5×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C37 | C11⋊C5 |
| commutator, cosocle, hypocenter | C11 | C5×C11×C37 |
| Frattini | C1 | G |
| Fitting, socle | C112×C37 | C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C11×C37 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2035 |
2849 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22385, 4);