Finite Group DatabasebetaFinite Group Databasebeta| order | 5950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C5 |
| direct product | C7×C5⋊D85 |
| unambiguous semidirect product | C5⋊(C7×D85) |
| unambiguous semidirect product | C17⋊(C7×C5⋊D5) |
| Fitting, socle, Hall | C52×C7×C17 ⋊ C2 |
| derived, Hall | C52×C17 ⋊ C2×C7 |
| Hall | C52×C7 ⋊ D17 |
| Hall | C7×C17 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ C7×D17 |
| Sylow | C17 ⋊ C7×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C5⋊D85 |
| commutator, hypocenter | C52×C17 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C17 | C2 |
| LCS | G ▷ C52×C17 | |
| UCS | C1 ◁ C7 | |
64 conjugacy classes of subgroups.
1498 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#13133343, C7×#13133344, C7⋊#13133343, … |
| maximal normal subgroup of | C7×#13133343, C7×#13133344, C7⋊#13133343, … |
| maximal quotient of | C7×#13133334, C2×C7×C5⋊D85, C7×C3⋊(C5⋊D85), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5950, 18);