Finite Group DatabasebetaFinite Group Databasebeta| order | 22570 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×D185 |
| unambiguous semidirect product | C5⋊(C61×D37) |
| unambiguous semidirect product | C37⋊(D5×C61) |
| Fitting, socle, Hall | C5×C37×C61 ⋊ C2 |
| derived, Hall | C5×C37 ⋊ C2×C61 |
| Hall | C37×C61 ⋊ D5 |
| Hall | C5×C61 ⋊ D37 |
| Sylow | C37 ⋊ D5×C61 |
| Sylow | C5 ⋊ C61×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | D185 |
| commutator, cosocle, hypocenter | C5×C37 | C2×C61 |
| Frattini | C1 | G |
| Fitting, socle | C5×C37×C61 | C2 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 ◁ C61 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11285 |
5734 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22570, 8);