Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5×C7 |
| direct product | #3862×C3⋊(C5⋊D5) |
| unambiguous semidirect product | C3⋊(C5⋊D5×#3862) |
| unambiguous semidirect product | C5⋊(D15×#3862) |
| Fitting, socle, derived | C3×C52×C72 ⋊ C2×C3 |
| Hall | C3×C52×#3862 ⋊ C2 |
| Hall | C52×C72 ⋊ C3×D3 |
| Hall | C3×#3862 ⋊ C5⋊D5 |
| Sylow | C72 ⋊ C3×C3⋊(C5⋊D5) |
| Sylow | C52 ⋊ D3×#3862 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C72 | C2×C3 |
| LCS | G ▷ C3×C52×C72 | |
| UCS | C1 | |
352 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1575 |
741 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 488);