Finite Group DatabasebetaFinite Group Databasebeta| order | 22385 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×C121⋊C5 |
| unambiguous semidirect product | C121⋊(C5×C37) |
| unambiguous semidirect product | (C37×C121)⋊C5 |
| Fitting, Hall | C37×C121 ⋊ C5 |
| derived, Sylow | C121 ⋊ C5×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C121⋊C5 |
| commutator, cosocle, hypocenter | C121 | C5×C37 |
| Frattini | C11 | C37×C11⋊C5 |
| Fitting | C37×C121 | C5 |
| socle | C11×C37 | C11⋊C5 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C37 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4477 |
1073 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22385, 2);