Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×C25⋊#64418 |
| unambiguous semidirect product | C25⋊(C3×#64418) |
| Fitting | C3×C72×C25 ⋊ D3 |
| derived | C25×#3862 ⋊ C2×C3 |
| Hall | C3×C25×#3862 ⋊ C2 |
| Hall | C72×C25 ⋊ C3×D3 |
| Hall | C3×#3862 ⋊ D25 |
| Sylow | C72 ⋊ C3×D75 |
| Sylow | C25 ⋊ C3×#64418 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C25⋊#64418 |
| commutator, cosocle, hypocenter | C25×#3862 | C2×C3 |
| Frattini | C5 | C3×C5⋊#64418 |
| Fitting | C3×C72×C25 | D3 |
| socle | C3×C5×C72 | D15 |
| LCS | G ▷ C25×#3862 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1050 |
744 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 178);