Finite Group DatabasebetaFinite Group Databasebeta| order | 5950 |
| isoclinism | isoclinic class of C5⋊D35 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C5 |
| direct product | C17×C5⋊D35 |
| unambiguous semidirect product | C5⋊(C17×D35) |
| unambiguous semidirect product | C7⋊(C17×C5⋊D5) |
| Fitting, socle, Hall | C52×C7×C17 ⋊ C2 |
| derived, Hall | C52×C7 ⋊ C2×C17 |
| Hall | C52×C17 ⋊ D7 |
| Hall | C7×C17 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D7×C17 |
| Sylow | C7 ⋊ C17×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C5⋊D35 |
| commutator, hypocenter | C52×C7 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C17 | C2 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C17 | |
64 conjugacy classes of subgroups.
1513 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D17×C5⋊D35, D7×C17×C5⋊D5, D119⋊(C5⋊D5), … |
| maximal normal subgroup of | D17×C5⋊D35, D7×C17×C5⋊D5, D119⋊(C5⋊D5), … |
| maximal quotient of | C17×C7⋊#1039, C2×C17×C5⋊D35, C17×C3⋊(C5⋊D35), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5950, 19);