Finite Group DatabasebetaFinite Group Databasebeta| order | 22450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D2245 |
| unambiguous semidirect product | C5⋊(C5×D449) |
| unambiguous semidirect product | C449⋊(C5×D5) |
| Fitting, socle, Hall | C52×C449 ⋊ C2 |
| derived | C5×C449 ⋊ C2×C5 |
| Sylow | C449 ⋊ C5×D5 |
| Sylow | C52 ⋊ D449 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D2245 |
| commutator, cosocle, hypocenter | C5×C449 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C449 | C2 |
| LCS | G ▷ C5×C449 | |
| UCS | C1 ◁ C5 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4490 |
5620 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22450, 8);