Finite Group DatabasebetaFinite Group Databasebeta| order | 22540 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C49 · Schur multiplier (H2) = C2 |
| direct product | D5×D23×C49 |
| unambiguous semidirect product | (D5×C23)⋊(C2×C49) |
| unambiguous semidirect product | (C5×D23)⋊(C2×C49) |
| unambiguous semidirect product | D115⋊(C2×C49) |
| Fitting, Hall | C5×C23×C49 ⋊ C22 |
| derived, Hall | C5×C23 ⋊ C22×C49 |
| Hall | C23×C49 ⋊ C2×D5 |
| Hall | C5×C49 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D5×C49 |
| Sylow | C5 ⋊ C2×D23×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | D5×D23 |
| commutator, hypocenter | C5×C23 | C22×C49 |
| Frattini | C7 | C7×D5×D23 |
| Fitting | C5×C23×C49 | C22 |
| socle, cosocle | C5×C7×C23 | C22×C7 |
| prime radical | C7×D5×D23 | C7 |
| LCS | G ▷ C5×C23 | |
| UCS | C1 ◁ C49 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5635 |
2548 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22540, 15);