Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | C3×C3⋊(C5⋊D245) |
| unambiguous semidirect product | C3⋊(C3×C5⋊D245) |
| unambiguous semidirect product | C5⋊(C3×D735) |
| Fitting, Hall | C32×C52×C49 ⋊ C2 |
| derived | C3×C52×C49 ⋊ C2×C3 |
| Hall | C52×C49 ⋊ C3×D3 |
| Hall | C32×C49 ⋊ C5⋊D5 |
| Hall | C32×C52 ⋊ D49 |
| Sylow | C49 ⋊ C3×C3⋊(C5⋊D5) |
| Sylow | C52 ⋊ C3×D147 |
| Sylow | C32 ⋊ C5⋊D245 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(C5⋊D245) |
| commutator, cosocle, hypocenter | C3×C52×C49 | C2×C3 |
| Frattini | C7 | C3×C3⋊(C5⋊D35) |
| Fitting | C32×C52×C49 | C2 |
| socle | C32×C52×C7 | D7 |
| LCS | G ▷ C3×C52×C49 | |
| UCS | C1 ◁ C3 | |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7350 |
5517 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 144);