Finite Group DatabasebetaFinite Group Databasebeta| order | 4950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
| direct product | C9×C5⋊D55 |
| unambiguous semidirect product | C5⋊(C9×D55) |
| unambiguous semidirect product | C11⋊(C9×C5⋊D5) |
| Fitting, Hall | C52×C9×C11 ⋊ C2 |
| derived, Hall | C52×C11 ⋊ C2×C9 |
| Hall | C52×C9 ⋊ D11 |
| Hall | C9×C11 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ C9×D11 |
| Sylow | C11 ⋊ C9×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C5⋊D55 |
| commutator, hypocenter | C52×C11 | C2×C9 |
| Frattini | C3 | C3×C5⋊D55 |
| Fitting | C52×C9×C11 | C2 |
| socle | C3×C52×C11 | C2×C3 |
| LCS | G ▷ C52×C11 | |
| UCS | C1 ◁ C9 | |
96 conjugacy classes of subgroups.
1251 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5⋊(C5⋊(C11⋊(D7⋊C9))), C7⋊C9×C5⋊D55, C9×C5⋊D385, … |
| maximal normal subgroup of | C7×C9×C5⋊D55 |
| maximal quotient of | C5⋊(C5⋊(C11⋊(D7⋊C9))), C7⋊C9×C5⋊D55, C9×C5⋊D385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4950, 50);