Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C3×C5 |
| direct product | C52×C3⋊#64418 |
| unambiguous semidirect product | C3⋊(C52×#64418) |
| Fitting, socle | C3×C52×C72 ⋊ D3 |
| derived, Hall | C3×#3862 ⋊ C2×C52 |
| Hall | C3×C52×#3862 ⋊ C2 |
| Hall | C52×C72 ⋊ C3⋊D3 |
| Sylow | C72 ⋊ C52×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C3⋊#64418 |
| commutator, cosocle, hypocenter | C3×#3862 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C72 | D3 |
| LCS | G ▷ C3×#3862 | |
| UCS | C1 ◁ C52 | |
304 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1050 |
975 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 457);